The open source repository for the action RPG game in development by Sig Productions titled 'Adventures in Lestoria'!
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2485 lines
73 KiB
2485 lines
73 KiB
/*
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OneLoneCoder - Geometry 2D v2.0
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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A collection of 2D Geometric primitives and functions to work with
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and between them.
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License (OLC-3)
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~~~~~~~~~~~~~~~
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Copyright 2018 - 2024 OneLoneCoder.com
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions
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are met:
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1. Redistributions or derivations of source code must retain the above
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copyright notice, this list of conditions and the following disclaimer.
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2. Redistributions or derivative works in binary form must reproduce
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the above copyright notice. This list of conditions and the following
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disclaimer must be reproduced in the documentation and/or other
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materials provided with the distribution.
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3. Neither the name of the copyright holder nor the names of its
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contributors may be used to endorse or promote products derived
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from this software without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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Links
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~~~~~
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YouTube: https://www.youtube.com/javidx9
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Discord: https://discord.gg/WhwHUMV
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Twitter: https://www.twitter.com/javidx9
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Twitch: https://www.twitch.tv/javidx9
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GitHub: https://www.github.com/onelonecoder
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Homepage: https://www.onelonecoder.com
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Authors
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~~~~~~~
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David Barr, aka javidx9, (c) OneLoneCoder 2019, 2020, 2021, 2022,© 2024, 2024
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With significant contributions from:
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Piratux, Gusgo99, Gorbit99, MaGetzUb, Dandistine, Moros1138
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cstdint, sigonasr, bixxy, Qwerasd, starfreakclone, fux
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Changes:
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v1.01: +Made constants inline
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+Header guards (lol... sigh...)
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v2.0: +Major file contribution and restructuring
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*/
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/*
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What Is This?
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~~~~~~~~~~~~~
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I've worked with 2D stuff for decades and I'm tired of reapeatedly researching, deriving
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and implementing geometric analysis routines, so wanted a "one-stop-shop" to collate all
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these mathematics. You don't even need olc::PixelGameEngine, this file will run as a
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standalone 2D vector/geometry utility.
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As well as a robust 2D Vector implementation, this file offers definitions of the following
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shapes:
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point - A 2D (x,y) vector from (0,0)
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line - A line segment defined by a start and end point
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circle - A circle defined by a middle point and a radius
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rectangle - An axis aligned quad defined by a top left point, and a size
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triangle - A triangle defined by 3 points
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ray - A special case "line" with an origin and a direction
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Functions have been provided that yield useful analyses for almost every combination
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of shapes. The function groups all have the same names, and are differentiated via
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argument type:
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point closest(a, b)
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Returns closest point on Shape A to Shape B
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bool overlaps(a, b)
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Returns true if any part of Shape A overlaps any part of Shape B, including boundaries
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bool contains(a, b)
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Returns true if Shape A wholly contains Shape B within and including it's boundary
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vector<point> intersects(a, b)
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Returns a vector of points where Shape A boundary intersects with Shape B boundary
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optional<point> project(a, b, ray)
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Projects Shape A along a ray, until and if it contacts shape B. If it never contacts
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then nothing is returned. If it does contact the closest position Shape A can be to
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Shape B is returned without the shapes overlapping
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rect envelope_r(a) / bounding_box(a)
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Returns the minimum area rectangle that fully encompasses Shape A
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rect envelope_c(a) / bounding_circle(a)
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Returns the minimum area circle that fully encompasses Shape A
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ray reflect(ray, a)
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Returns a ray that is a reflection of supplied incident ray against Shape A
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optional<point, normal> collision(ray, a)
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Returns the point and normal where a ray collides with Shape A
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*/
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/*
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Quick Navigation
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~~~~~~~~~~~~~~~~
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To jump to an implementation quickly, use your editor to search in the following way:
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f(a, b)
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where:
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f = overlaps, intersects, contains, closest, envelope_r, envelope_b, reflects, collision
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a = p, l, r, c, t, q, pol (point, line, rect, circ, triangle, ray, polygon)
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example:
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"contains(r,c)" - takes you to implementation for contains(rect, circ)
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- Does the rectangle contain the circle?
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*/
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/*
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Function Matrix - Function(A, B)
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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A B>| POINT | LINE | RECT | CIRCLE | TRIANGLE | RAY |
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---------+--------------+--------------+--------------+--------------+--------------+--------------+
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POINT | contains | contains | contains | contains | contains | |
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| closest | closest | closest | closest | closest | closest |
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| overlaps | overlaps | overlaps | overlaps | overlaps | |
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| intersects | intersects | intersects | intersects | intersects | |
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| | | | | | |
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---------+--------------+--------------+--------------+--------------+--------------+--------------+
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LINE | contains | contains | contains | contains | contains | |
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| closest | | | closest | | |
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| overlaps | overlaps | overlaps | overlaps | overlaps | |
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| intersects | intersects | intersects | intersects | intersects | |
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| | | | | | |
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---------+--------------+--------------+--------------+--------------+--------------+--------------+
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RECT | contains | contains | contains | contains | contains | |
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| closest | | | | | |
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| overlaps | overlaps | overlaps | overlaps | overlaps | |
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| intersects | intersects | intersects | intersects | intersects | |
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| | | | | | |
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---------+--------------+--------------+--------------+--------------+--------------+--------------+
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CIRCLE | contains | contains | contains | contains | contains | |
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| closest | closest | | | | |
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| overlaps | overlaps | overlaps | overlaps | overlaps | |
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| intersects | intersects | intersects | intersects | intersects | |
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| project | project | | project | | |
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---------+--------------+--------------+--------------+--------------+--------------+--------------+
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TRIANGLE | contains | contains | contains | contains | contains | |
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| closest | | | | | |
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| overlaps | overlaps | overlaps | overlaps | overlaps | |
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| intersects | intersects | intersects | intersects | intersects | |
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| | | | | | |
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---------+--------------+--------------+--------------+--------------+--------------+--------------+
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RAY | | | | | | |
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| | | | | | |
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| | collision | collision | collision | collision | collision* |
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| | intersects | intersects | intersects | intersects | intersects |
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| | reflect | reflect | reflect | reflect | reflect* |
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---------+--------------+--------------+--------------+--------------+--------------+--------------+
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* Exists but always fails
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*/
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#pragma once
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#include <string>
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#include <cmath>
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#include <vector>
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#include <algorithm>
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#include <cstdint>
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#include <optional>
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#include <cassert>
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#include <numeric>
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#ifndef OLC_V2D_TYPE
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#define OLC_V2D_TYPE
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namespace olc
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{
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/*
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A complete 2D geometric vector structure, with a variety
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of useful utility functions and operator overloads
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*/
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template<class T>
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struct v_2d
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{
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static_assert(std::is_arithmetic<T>::value, "olc::v_2d<type> must be numeric");
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// x-axis component
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T x = 0;
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// y-axis component
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T y = 0;
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// Default constructor
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inline constexpr v_2d() = default;
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// Specific constructor
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inline constexpr v_2d(T _x, T _y) : x(_x), y(_y)
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{}
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// Copy constructor
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inline constexpr v_2d(const v_2d& v) = default;
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// Assignment operator
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inline constexpr v_2d& operator=(const v_2d& v) = default;
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// Returns rectangular area of vector
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inline constexpr auto area() const
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{
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return x * y;
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}
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// Returns magnitude of vector
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inline auto mag() const
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{
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return std::sqrt(x * x + y * y);
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}
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// Returns magnitude squared of vector (useful for fast comparisons)
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inline constexpr T mag2() const
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{
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return x * x + y * y;
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}
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// Returns normalised version of vector
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inline v_2d norm() const
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{
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auto r = 1 / mag();
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return v_2d(x * r, y * r);
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}
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// Returns vector at 90 degrees to this one
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inline constexpr v_2d perp() const
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{
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return v_2d(-y, x);
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}
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// Rounds both components down
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inline constexpr v_2d floor() const
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{
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return v_2d(std::floor(x), std::floor(y));
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}
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// Rounds both components up
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inline constexpr v_2d ceil() const
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{
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return v_2d(std::ceil(x), std::ceil(y));
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}
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// Returns 'element-wise' max of this and another vector
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inline constexpr v_2d max(const v_2d& v) const
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{
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return v_2d(std::max(x, v.x), std::max(y, v.y));
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}
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// Returns 'element-wise' min of this and another vector
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inline constexpr v_2d min(const v_2d& v) const
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{
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return v_2d(std::min(x, v.x), std::min(y, v.y));
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}
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// Calculates scalar dot product between this and another vector
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inline constexpr auto dot(const v_2d& rhs) const
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{
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return this->x * rhs.x + this->y * rhs.y;
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}
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// Calculates 'scalar' cross product between this and another vector (useful for winding orders)
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inline constexpr auto cross(const v_2d& rhs) const
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{
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return this->x * rhs.y - this->y * rhs.x;
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}
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// Treat this as polar coordinate (R, Theta), return cartesian equivalent (X, Y)
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inline constexpr v_2d cart() const
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{
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return v_2d(std::cos(y) * x, std::sin(y) * x);
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}
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// Treat this as cartesian coordinate (X, Y), return polar equivalent (R, Theta)
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inline constexpr v_2d polar() const
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{
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return v_2d(mag(), std::atan2(y, x));
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}
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// Clamp the components of this vector in between the 'element-wise' minimum and maximum of 2 other vectors
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inline constexpr v_2d clamp(const v_2d& v1, const v_2d& v2) const
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{
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return this->max(v1).min(v2);
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}
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// Linearly interpolate between this vector, and another vector, given normalised parameter 't'
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inline constexpr v_2d lerp(const v_2d& v1, const double t) const
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{
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return (*this) * (T(1.0 - t)) + (v1 * T(t));
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}
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// Compare if this vector is numerically equal to another
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inline constexpr bool operator == (const v_2d& rhs) const
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{
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return (this->x == rhs.x && this->y == rhs.y);
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}
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// Compare if this vector is not numerically equal to another
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inline constexpr bool operator != (const v_2d& rhs) const
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{
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return (this->x != rhs.x || this->y != rhs.y);
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}
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// Return this vector as a std::string, of the form "(x,y)"
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inline constexpr std::string str() const
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{
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return std::string("(") + std::to_string(this->x) + "," + std::to_string(this->y) + ")";
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}
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// Assuming this vector is incident, given a normal, return the reflection
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inline constexpr v_2d reflect(const v_2d& n) const
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{
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return (*this) - 2.0 * (this->dot(n) * n);
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}
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// Allow 'casting' from other v_2d types
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template<class F>
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inline constexpr operator v_2d<F>() const
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{
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return { static_cast<F>(this->x), static_cast<F>(this->y) };
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}
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};
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// Multiplication operator overloads between vectors and scalars, and vectors and vectors
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template<class TL, class TR>
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inline constexpr auto operator * (const TL& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs * rhs.x, lhs * rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator * (const v_2d<TL>& lhs, const TR& rhs)
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{
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return v_2d(lhs.x * rhs, lhs.y * rhs);
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}
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template<class TL, class TR>
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inline constexpr auto operator * (const v_2d<TL>& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs.x * rhs.x, lhs.y * rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator *= (v_2d<TL>& lhs, const TR& rhs)
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{
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lhs = lhs * rhs;
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return lhs;
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}
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// Division operator overloads between vectors and scalars, and vectors and vectors
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template<class TL, class TR>
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inline constexpr auto operator / (const TL& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs / rhs.x, lhs / rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator / (const v_2d<TL>& lhs, const TR& rhs)
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{
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return v_2d(lhs.x / rhs, lhs.y / rhs);
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}
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template<class TL, class TR>
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inline constexpr auto operator / (const v_2d<TL>& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs.x / rhs.x, lhs.y / rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator /= (v_2d<TL>& lhs, const TR& rhs)
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{
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lhs = lhs / rhs;
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return lhs;
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}
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// Unary Addition operator (pointless but i like the platinum trophies)
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template<class T>
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inline constexpr auto operator + (const v_2d<T>& lhs)
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{
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return v_2d(+lhs.x, +lhs.y);
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}
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// Addition operator overloads between vectors and scalars, and vectors and vectors
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template<class TL, class TR>
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inline constexpr auto operator + (const TL& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs + rhs.x, lhs + rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator + (const v_2d<TL>& lhs, const TR& rhs)
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{
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return v_2d(lhs.x + rhs, lhs.y + rhs);
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}
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template<class TL, class TR>
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inline constexpr auto operator + (const v_2d<TL>& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs.x + rhs.x, lhs.y + rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator += (v_2d<TL>& lhs, const TR& rhs)
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{
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lhs = lhs + rhs;
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return lhs;
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}
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template<class TL, class TR>
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inline constexpr auto operator += (v_2d<TL>& lhs, const v_2d<TR>& rhs)
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{
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lhs = lhs + rhs;
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return lhs;
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}
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// Unary negation operator overoad for inverting a vector
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template<class T>
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inline constexpr auto operator - (const v_2d<T>& lhs)
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{
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return v_2d(-lhs.x, -lhs.y);
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}
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// Subtraction operator overloads between vectors and scalars, and vectors and vectors
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template<class TL, class TR>
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inline constexpr auto operator - (const TL& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs - rhs.x, lhs - rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator - (const v_2d<TL>& lhs, const TR& rhs)
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{
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return v_2d(lhs.x - rhs, lhs.y - rhs);
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}
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template<class TL, class TR>
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inline constexpr auto operator - (const v_2d<TL>& lhs, const v_2d<TR>& rhs)
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{
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return v_2d(lhs.x - rhs.x, lhs.y - rhs.y);
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}
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template<class TL, class TR>
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inline constexpr auto operator -= (v_2d<TL>& lhs, const TR& rhs)
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{
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lhs = lhs - rhs;
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return lhs;
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}
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// Greater/Less-Than Operator overloads - mathematically useless, but handy for "sorted" container storage
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template<class TL, class TR>
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inline constexpr bool operator < (const v_2d<TL>& lhs, const v_2d<TR>& rhs)
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{
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return (lhs.y < rhs.y) || (lhs.y == rhs.y && lhs.x < rhs.x);
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}
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template<class TL, class TR>
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inline constexpr bool operator > (const v_2d<TL>& lhs, const v_2d<TR>& rhs)
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{
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return (lhs.y > rhs.y) || (lhs.y == rhs.y && lhs.x > rhs.x);
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}
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// Allow olc::v_2d to play nicely with std::cout
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template<class T>
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inline constexpr std::ostream& operator << (std::ostream& os, const v_2d<T>& rhs)
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{
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os << rhs.str();
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return os;
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}
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// Convenient types ready-to-go
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typedef v_2d<int32_t> vi2d;
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typedef v_2d<uint32_t> vu2d;
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typedef v_2d<float> vf2d;
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typedef v_2d<double> vd2d;
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}
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#else
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#include "olcPixelGameEngine.h"
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#endif
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#ifndef OLC_DECALSTRUCT
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#define OLC_DECALSTRUCT
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namespace olc{
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enum class DecalStructure
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{
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LINE,
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FAN,
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STRIP,
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LIST
|
|
};
|
|
}
|
|
#endif
|
|
|
|
namespace olc::utils::geom2d
|
|
{
|
|
// Lemon Meringue
|
|
inline const double pi = 3.141592653589793238462643383279502884;
|
|
|
|
// Floating point error margin
|
|
inline const double epsilon = 0.001;
|
|
|
|
namespace internal
|
|
{
|
|
template<typename T>
|
|
inline std::vector<olc::v_2d<T>> filter_duplicate_points(const std::vector<olc::v_2d<T>>& points) {
|
|
std::vector<olc::v_2d<T>> filtered_points;
|
|
|
|
for (const auto& point : points)
|
|
{
|
|
bool is_duplicate = false;
|
|
|
|
for (const auto& filtered_point : filtered_points)
|
|
{
|
|
if (std::abs(point.x - filtered_point.x) < epsilon && std::abs(point.y - filtered_point.y) < epsilon)
|
|
{
|
|
is_duplicate = true;
|
|
break;
|
|
}
|
|
}
|
|
|
|
if (!is_duplicate)
|
|
{
|
|
filtered_points.push_back(point);
|
|
}
|
|
}
|
|
|
|
return filtered_points;
|
|
}
|
|
};
|
|
|
|
//https://stackoverflow.com/questions/1903954/is-there-a-standard-sign-function-signum-sgn-in-c-c
|
|
template <typename T>
|
|
constexpr int sgn(T val) { return (T(0) < val) - (val < T(0)); }
|
|
|
|
// Defines a line segment
|
|
template<typename T>
|
|
struct line
|
|
{
|
|
olc::v_2d<T> start;
|
|
olc::v_2d<T> end;
|
|
|
|
inline line(const olc::v_2d<T>& s = { T(0), T(0) },
|
|
const olc::v_2d<T>& e = { T(0), T(0) })
|
|
: start(s), end(e)
|
|
{ }
|
|
|
|
// Get vector pointing from start to end
|
|
inline constexpr olc::v_2d<T> vector()const
|
|
{
|
|
return (end - start);
|
|
}
|
|
|
|
// Get length of line
|
|
inline constexpr T length()const
|
|
{
|
|
return vector().mag();
|
|
}
|
|
|
|
// Get length of line^2
|
|
inline constexpr T length2()const
|
|
{
|
|
return vector().mag2();
|
|
}
|
|
|
|
|
|
|
|
// Given a real distance, get point along line
|
|
inline constexpr olc::v_2d<T> rpoint(const T& distance) const
|
|
{
|
|
if(abs(distance)<0.01f){
|
|
return start;
|
|
}else{
|
|
return start + vector().norm() * distance;
|
|
}
|
|
}
|
|
|
|
// Given a unit distance, get point along line
|
|
inline constexpr olc::v_2d<T> upoint(const T& distance) const
|
|
{
|
|
return start + vector() * distance;
|
|
}
|
|
|
|
// Return which side of the line does a point lie
|
|
inline constexpr int32_t side(const olc::v_2d<T>& point) const
|
|
{
|
|
double d = vector().cross(point - start);
|
|
if (d < 0)
|
|
return -1;
|
|
else
|
|
if (d > 0)
|
|
return 1;
|
|
else
|
|
return 0;
|
|
}
|
|
|
|
// Returns line equation "mx + a" coefficients where:
|
|
// x: m
|
|
// y: a
|
|
// NOTE: Returns {inf, inf} if std::abs(end.x - start.x) < epsilon:
|
|
inline constexpr olc::vd2d coefficients() const
|
|
{
|
|
double x1 = start.x;
|
|
double x2 = end.x;
|
|
double y1 = start.y;
|
|
double y2 = end.y;
|
|
|
|
// check if line is vertical or close to vertical
|
|
if (std::abs(x2 - x1) < epsilon) {
|
|
return olc::vd2d{ std::numeric_limits<double>::infinity(), std::numeric_limits<double>::infinity() };
|
|
}
|
|
|
|
double m = (y2 - y1) / (x2 - x1);
|
|
return olc::vd2d {m, -m * x1 + y1};
|
|
}
|
|
};
|
|
|
|
template<typename T>
|
|
struct ray
|
|
{
|
|
olc::v_2d<T> origin;
|
|
olc::v_2d<T> direction;
|
|
|
|
inline ray(const olc::v_2d<T>& o = { T(0), T(0) },
|
|
const olc::v_2d<T>& d = { T(0), T(0) })
|
|
: origin(o), direction(d)
|
|
{ }
|
|
};
|
|
|
|
template<typename T>
|
|
struct rect
|
|
{
|
|
olc::v_2d<T> pos;
|
|
olc::v_2d<T> size;
|
|
|
|
inline rect(const olc::v_2d<T>& p = { T(0), T(0) },
|
|
const olc::v_2d<T>& s = { T(1), T(1) })
|
|
: pos(p), size(s)
|
|
{ }
|
|
|
|
inline olc::v_2d<T> middle() const
|
|
{
|
|
return pos + (size * double(0.5));
|
|
}
|
|
|
|
// Get line segment from top side of rectangle
|
|
inline line<T> top() const
|
|
{
|
|
return { pos, {pos.x + size.x, pos.y } };
|
|
}
|
|
|
|
// Get line segment from bottom side of rectangle
|
|
inline line<T> bottom() const
|
|
{
|
|
return { {pos.x, pos.y + size.y}, pos + size };
|
|
}
|
|
|
|
// Get line segment from left side of rectangle
|
|
inline line<T> left() const
|
|
{
|
|
return { pos, {pos.x, pos.y + size.y} };
|
|
}
|
|
|
|
// Get line segment from right side of rectangle
|
|
inline line<T> right() const
|
|
{
|
|
return { {pos.x + size.x, pos.y }, pos + size };
|
|
}
|
|
|
|
// Get a line from an indexed side, starting top, going clockwise
|
|
inline line<T> side(const size_t i) const
|
|
{
|
|
if ((i & 0b11) == 0) return top();
|
|
if ((i & 0b11) == 1) return right();
|
|
if ((i & 0b11) == 2) return bottom();
|
|
//if ((i & 0b11) == 3) return left(); // Dumb compilers cant fathom this
|
|
return left();
|
|
}
|
|
|
|
// Get area of rectangle
|
|
inline constexpr T area() const
|
|
{
|
|
return size.x * size.y;
|
|
}
|
|
|
|
// Get perimeter of rectangle
|
|
inline constexpr T perimeter() const
|
|
{
|
|
return T(2) * (size.x + size.y);
|
|
}
|
|
|
|
// Returns side count: 4
|
|
inline constexpr size_t side_count() const {
|
|
return 4;
|
|
}
|
|
};
|
|
|
|
|
|
template<typename T>
|
|
struct circle
|
|
{
|
|
olc::v_2d<T> pos;
|
|
T radius = T(0);
|
|
|
|
inline circle(const olc::v_2d<T>& p = { T(0), T(0) }, const T r = T(0))
|
|
: pos(p), radius(r)
|
|
{ }
|
|
|
|
// Get area of circle
|
|
inline constexpr T area() const
|
|
{
|
|
return T(pi) * radius * radius;
|
|
}
|
|
|
|
// Get circumference of circle
|
|
inline constexpr T perimeter() const
|
|
{
|
|
return T(2.0 * pi) * radius;
|
|
}
|
|
|
|
// Get circumference of circle
|
|
inline constexpr T circumference() const
|
|
{
|
|
return perimeter();
|
|
}
|
|
};
|
|
|
|
|
|
template<typename T>
|
|
struct triangle
|
|
{
|
|
std::array<olc::v_2d<T>, 3> pos;
|
|
|
|
inline triangle(
|
|
const olc::v_2d<T>& p0 = { T(0), T(0) },
|
|
const olc::v_2d<T>& p1 = { T(0), T(0) },
|
|
const olc::v_2d<T>& p2 = { T(0), T(0) })
|
|
: pos{ p0,p1,p2 }
|
|
{ }
|
|
|
|
// Get a line from an indexed side, starting top, going clockwise
|
|
inline line<T> side(const size_t i) const
|
|
{
|
|
return line(pos[i % 3], pos[(i + 1) % 3]);
|
|
}
|
|
|
|
// Get area of triangle
|
|
inline constexpr T area() const
|
|
{
|
|
return double(0.5) * std::abs(
|
|
(pos[0].x * (pos[1].y - pos[2].y)) +
|
|
(pos[1].x * (pos[2].y - pos[0].y)) +
|
|
(pos[2].x * (pos[0].y - pos[1].y)));
|
|
}
|
|
|
|
// Get perimeter of triangle
|
|
inline constexpr T perimeter() const
|
|
{
|
|
return line(pos[0], pos[1]).length()
|
|
+ line(pos[1], pos[2]).length()
|
|
+ line(pos[2], pos[0]).length();
|
|
}
|
|
|
|
// Returns side count: 3
|
|
inline constexpr size_t side_count() const {
|
|
return 3;
|
|
}
|
|
};
|
|
|
|
|
|
template<typename T>
|
|
struct polygon
|
|
{
|
|
std::vector<olc::v_2d<T>> pos;
|
|
|
|
inline constexpr olc::v_2d<T>middle()const{
|
|
vf2d total=std::accumulate(pos.begin(),pos.end(),olc::v_2d<T>{},[](const olc::v_2d<T>&middle,const olc::v_2d<T>&point){return std::move(middle)+point;});
|
|
return total/pos.size();
|
|
}
|
|
|
|
inline constexpr T area()const{
|
|
return abs(signed_area());
|
|
}
|
|
|
|
//Maths. https://www.omnicalculator.com/math/irregular-polygon-area
|
|
inline constexpr T signed_area()const{
|
|
T sum{};
|
|
for(int i=0;i<pos.size();i++){
|
|
sum+=(pos[i].x*pos[(i+1)%pos.size()].y)-(pos[(i+1)%pos.size()].x*pos[i].y);
|
|
}
|
|
sum*=0.5f;
|
|
return sum;
|
|
}
|
|
|
|
//Because Maths. https://www.omnicalculator.com/math/centroid
|
|
inline constexpr v_2d<T>centroid()const{
|
|
v_2d<T>centroid{};
|
|
for(int i=0;i<pos.size();i++){
|
|
centroid.x+=(pos[i].x+pos[(i+1)%pos.size()].x)*((pos[i].x*pos[(i+1)%pos.size()].y)-(pos[(i+1)%pos.size()].x*pos[i].y));
|
|
centroid.y+=(pos[i].y+pos[(i+1)%pos.size()].y)*((pos[i].x*pos[(i+1)%pos.size()].y)-(pos[(i+1)%pos.size()].x*pos[i].y));
|
|
}
|
|
centroid*=1.f/(6.f*signed_area());
|
|
return centroid;
|
|
}
|
|
};
|
|
|
|
|
|
// =========================================================================================================================
|
|
// Closest(shape, point) ===================================================================================================
|
|
|
|
// Closest location on [SHAPE] to Point
|
|
|
|
// closest(p,p)
|
|
// Returns closest point on point to any shape (aka the original point) :P
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const olc::v_2d<T1>& p, [[maybe_unused]] const T2& anything_who_cares)
|
|
{
|
|
return p;
|
|
}
|
|
|
|
// closest(l,p)
|
|
// Returns closest point on line to point
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const line<T1>& l, const olc::v_2d<T2>& p)
|
|
{
|
|
auto d = l.vector();
|
|
double u = std::clamp(double(d.dot(p - l.start)) / d.mag2(), 0.0, 1.0);
|
|
return l.start + u * d;
|
|
}
|
|
|
|
// closest(c,p)
|
|
// Returns closest point on circle to point
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const circle<T1>& c, const olc::v_2d<T2>& p)
|
|
{
|
|
return c.pos + olc::vd2d(p - c.pos).norm() * c.radius;
|
|
}
|
|
|
|
// closest(r,p)
|
|
// Returns closest point on rectangle to point
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const rect<T1>& r, const olc::v_2d<T2>& p)
|
|
{
|
|
// Note: this algorithm can be reused for polygon
|
|
auto c1 = closest(r.top(), p);
|
|
auto c2 = closest(r.bottom(), p);
|
|
auto c3 = closest(r.left(), p);
|
|
auto c4 = closest(r.right(), p);
|
|
|
|
auto d1 = (c1 - p).mag2();
|
|
auto d2 = (c2 - p).mag2();
|
|
auto d3 = (c3 - p).mag2();
|
|
auto d4 = (c4 - p).mag2();
|
|
|
|
auto dmin = d1;
|
|
auto cmin = c1;
|
|
|
|
if (d2 < dmin) {
|
|
dmin = d2;
|
|
cmin = c2;
|
|
}
|
|
if (d3 < dmin) {
|
|
dmin = d3;
|
|
cmin = c3;
|
|
}
|
|
if (d4 < dmin) {
|
|
dmin = d4;
|
|
cmin = c4;
|
|
}
|
|
|
|
return cmin;
|
|
}
|
|
|
|
// closest(t,p)
|
|
// Returns closest point on triangle to point
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const triangle<T1>& t, const olc::v_2d<T2>& p)
|
|
{
|
|
olc::utils::geom2d::line<T1> l{ t.pos[0], t.pos[1] };
|
|
auto p0 = closest(l, p);
|
|
auto d0 = (p0 - p).mag2();
|
|
|
|
l.end = t.pos[2];
|
|
auto p1 = closest(l, p);
|
|
auto d1 = (p1 - p).mag2();
|
|
|
|
l.start = t.pos[1];
|
|
auto p2 = closest(l, p);
|
|
auto d2 = (p2 - p).mag2();
|
|
|
|
if ((d0 <= d1) && (d0 <= d2)) {
|
|
return p0;
|
|
}
|
|
else if ((d1 <= d0) && (d1 <= d2)) {
|
|
return p1;
|
|
}
|
|
else {
|
|
return p2;
|
|
}
|
|
}
|
|
|
|
|
|
// Closest location on [SHAPE] to Line
|
|
|
|
// closest(l,l)
|
|
// Returns closest point on line to line
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const line<T1>& l1, const line<T2>& l2)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
// closest(r,l)
|
|
// Returns closest point on rectangle to line
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const rect<T1>& r, const line<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
// closest(c,l)
|
|
// Returns closest point on circle to line
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const circle<T1>& c, const line<T2>& l)
|
|
{
|
|
const auto p1 = closest(l, c.pos);
|
|
return c.pos + olc::vd2d(p1 - c.pos).norm() * c.radius;
|
|
}
|
|
|
|
// closest(t,l)
|
|
// Returns closest point on triangle to line
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const triangle<T1>& t, const line<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
|
|
// Closest location on [SHAPE] to Circle
|
|
|
|
// closest(l,c)
|
|
// Returns closest point on line to circle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const line<T1>& l, const circle<T2>& c)
|
|
{
|
|
const auto p1 = closest(c, l); // Closest point on circle to line
|
|
return closest(l, p1);
|
|
}
|
|
|
|
// closest(r,c)
|
|
// Returns closest point on rectangle to circle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const rect<T1>& r, const circle<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
// closest(c,c)
|
|
// Returns closest point on circle to circle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const circle<T1>& c, const circle<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
// closest(t,c)
|
|
// Returns closest point on triangle to circle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const triangle<T1>& r, const circle<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
|
|
// Closest location on [SHAPE] to Triangle
|
|
|
|
// closest(l,t)
|
|
// Returns closest point on line to triangle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const line<T1>& l, const triangle<T2>& c)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
// closest(r,t)
|
|
// Returns closest point on rectangle to triangle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const rect<T1>& r, const triangle<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
// closest(c,t)
|
|
// Returns closest point on circle to triangle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const circle<T1>& c, const triangle<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
// closest(t,t)
|
|
// Returns closest point on triangle to triangle
|
|
template<typename T1, typename T2>
|
|
inline olc::v_2d<T1> closest(const triangle<T1>& r, const triangle<T2>& l)
|
|
{
|
|
// TODO:
|
|
return {};
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
// ================================================================================================================
|
|
// POINT ==========================================================================================================
|
|
|
|
// contains(p,p)
|
|
// Checks if point contains point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const olc::v_2d<T1>& p1, const olc::v_2d<T2>& p2)
|
|
{
|
|
return (p1 - p2).mag2() < epsilon;
|
|
}
|
|
|
|
// contains(l,p)
|
|
// Checks if line contains point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const line<T1>& l, const olc::v_2d<T2>& p)
|
|
{
|
|
double d = ((p.x - l.start.x) * (l.end.y - l.start.y) - (p.y - l.start.y) * (l.end.x - l.start.x));
|
|
if (std::abs(d) < epsilon)
|
|
{
|
|
// point is on line
|
|
double u = l.vector().dot(p - l.start) / l.vector().mag2();
|
|
return (u >= double(0.0) && u <= double(1.0));
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
// contains(r,p)
|
|
// Checks if rectangle contains point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const rect<T1>& r, const olc::v_2d<T2>& p)
|
|
{
|
|
return !(p.x < r.pos.x || p.y < r.pos.y ||
|
|
p.x > (r.pos.x + r.size.x) || p.y > (r.pos.y + r.size.y));
|
|
}
|
|
|
|
// contains(c,p)
|
|
// Checks if circle contains a point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const circle<T1>& c, const olc::v_2d<T2>& p)
|
|
{
|
|
return (c.pos - p).mag2() <= (c.radius * c.radius);
|
|
}
|
|
|
|
// contains(t,p)
|
|
// Checks if triangle contains a point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const triangle<T1>& t, const olc::v_2d<T2>& p)
|
|
{
|
|
// http://jsfiddle.net/PerroAZUL/zdaY8/1/
|
|
T2 A = T2(0.5) * (-t.pos[1].y * t.pos[2].x + t.pos[0].y * (-t.pos[1].x + t.pos[2].x) + t.pos[0].x * (t.pos[1].y - t.pos[2].y) + t.pos[1].x * t.pos[2].y);
|
|
T2 sign = A < T2(0) ? T2(-1) : T2(1);
|
|
T2 s = (t.pos[0].y * t.pos[2].x - t.pos[0].x * t.pos[2].y + (t.pos[2].y - t.pos[0].y) * p.x + (t.pos[0].x - t.pos[2].x) * p.y) * sign;
|
|
T2 v = (t.pos[0].x * t.pos[1].y - t.pos[0].y * t.pos[1].x + (t.pos[0].y - t.pos[1].y) * p.x + (t.pos[1].x - t.pos[0].x) * p.y) * sign;
|
|
return s >= T2(0) && v >= T2(0) && (s + v) <= T2(2) * A * sign;
|
|
}
|
|
|
|
|
|
|
|
// overlaps(p,p)
|
|
// Check if point overlaps with point (analagous to contains())
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const olc::v_2d<T1>& p1, const olc::v_2d<T2>& p2)
|
|
{
|
|
return contains(p1, p2);
|
|
}
|
|
|
|
// overlaps(l,p)
|
|
// Checks if line segment overlaps with point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const line<T1>& l, const olc::v_2d<T2>& p)
|
|
{
|
|
return contains(l, p);
|
|
}
|
|
|
|
// overlaps(r,p)
|
|
// Checks if rectangle overlaps with point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const rect<T1>& r, const olc::v_2d<T2>& p)
|
|
{
|
|
return contains(r, p);
|
|
}
|
|
|
|
// overlaps(c,p)
|
|
// Checks if circle overlaps with point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const circle<T1>& c, const olc::v_2d<T2>& p)
|
|
{
|
|
return contains(c, p);
|
|
}
|
|
|
|
// overlaps(t,p)
|
|
// Checks if triangle overlaps with point
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const triangle<T1>& t, const olc::v_2d<T2>& p)
|
|
{
|
|
return contains(t, p);
|
|
}
|
|
|
|
|
|
|
|
|
|
// intersects(p,p)
|
|
// Get intersection points where point intersects with point
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const olc::v_2d<T1>& p1, const olc::v_2d<T2>& p2)
|
|
{
|
|
if (contains(p1, p2))
|
|
return { p1 };
|
|
|
|
return {};
|
|
}
|
|
|
|
// intersects(l,p)
|
|
// Get intersection points where line segment intersects with point
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const line<T1>& l, const olc::v_2d<T2>& p)
|
|
{
|
|
if (contains(l, p))
|
|
return { p };
|
|
|
|
return {};
|
|
}
|
|
|
|
// intersects(r,p)
|
|
// Get intersection points where rectangle intersects with point
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const rect<T1>& r, const olc::v_2d<T2>& p)
|
|
{
|
|
for (size_t i = 0; i < r.side_count(); i++)
|
|
if (contains(r.side(i), p))
|
|
return { p };
|
|
|
|
return {};
|
|
}
|
|
|
|
// intersects(c,p)
|
|
// Get intersection points where circle intersects with point
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const circle<T1>& c, const olc::v_2d<T2>& p)
|
|
{
|
|
if (std::abs((p - c.pos).mag2() - (c.radius * c.radius)) <= epsilon)
|
|
return { p };
|
|
|
|
return {};
|
|
}
|
|
|
|
// intersects(t,p)
|
|
// Get intersection points where triangle intersects with point
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const triangle<T1>& t, const olc::v_2d<T2>& p)
|
|
{
|
|
for (size_t i = 0; i < t.side_count(); i++)
|
|
if (contains(t.side(i), p))
|
|
return { p };
|
|
|
|
return {};
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// ================================================================================================================
|
|
// LINE ===========================================================================================================
|
|
|
|
// contains(p,l)
|
|
// Check if point contains line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains([[maybe_unused]] const olc::v_2d<T1>& p, [[maybe_unused]] const line<T2>& l)
|
|
{
|
|
return false; // It can't!
|
|
}
|
|
|
|
// contains(l,l)
|
|
// Check if line segment contains line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const line<T1>& l1, const line<T2>& l2)
|
|
{
|
|
return overlaps(l1, l2.start) && overlaps(l1, l2.end);
|
|
}
|
|
|
|
// contains(r,l)
|
|
// Check if rectangle contains line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const rect<T1>& r, const line<T2>& l)
|
|
{
|
|
return contains(r, l.start) && contains(r, l.end);
|
|
}
|
|
|
|
// contains(c,l)
|
|
// Check if circle contains line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const circle<T1>& c1, const line<T2>& l)
|
|
{
|
|
return contains(c1, l.start) && contains(c1, l.end);
|
|
}
|
|
|
|
// contains(t,l)
|
|
// Check if triangle contains line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const triangle<T1>& t, const line<T2>& l)
|
|
{
|
|
return contains(t, l.start) && contains(t, l.end);
|
|
}
|
|
|
|
|
|
|
|
// overlaps(p,l)
|
|
// Check if point overlaps line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const olc::v_2d<T1>& p, const line<T2>& l)
|
|
{
|
|
return contains(l, p);
|
|
}
|
|
|
|
// overlaps(l,l)
|
|
// Check if line segment overlaps line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const line<T1>& l1, const line<T2>& l2)
|
|
{
|
|
double D = ((l2.end.y - l2.start.y) * (l1.end.x - l1.start.x) - (l2.end.x - l2.start.x) * (l1.end.y - l1.start.y));
|
|
double uA = ((l2.end.x-l2.start.x)*(l1.start.y-l2.start.y) - (l2.end.y-l2.start.y)*(l1.start.x-l2.start.x)) / D;
|
|
double uB = ((l1.end.x-l1.start.x)*(l1.start.y-l2.start.y) - (l1.end.y-l1.start.y)*(l1.start.x-l2.start.x)) / D;
|
|
return uA >= 0 && uA <= 1 && uB >= 0 && uB <= 1;
|
|
}
|
|
|
|
// overlaps(r,l)
|
|
// Check if rectangle overlaps line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const rect<T1>& r, const line<T2>& l)
|
|
{
|
|
return contains(r, l.start)
|
|
|| overlaps(r.top(), l)
|
|
|| overlaps(r.bottom(), l)
|
|
|| overlaps(r.left(), l)
|
|
|| overlaps(r.right(), l);
|
|
}
|
|
|
|
// overlaps(c,l)
|
|
// Check if circle overlaps line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const circle<T1>& c, const line<T2>& l)
|
|
{
|
|
auto vClosest = closest(l, c.pos);
|
|
return ((c.pos - vClosest).mag2() <= (c.radius * c.radius));
|
|
}
|
|
|
|
// overlaps(t,l)
|
|
// Check if triangle overlaps line segment
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const triangle<T1>& t, const line<T2>& l)
|
|
{
|
|
return overlaps(t, l.start) || overlaps(t.side(0), l) || overlaps(t.side(1), l) || overlaps(t.side(2), l);
|
|
}
|
|
|
|
|
|
|
|
// intersects(p,l)
|
|
// Get intersection points where point intersects with line segment
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const olc::v_2d<T1>& p, const line<T2>& l)
|
|
{
|
|
return intersects(l, p);
|
|
}
|
|
|
|
// intersects(l,l)
|
|
// Get intersection points where line segment intersects with line segment
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const line<T1>& l1, const line<T2>& l2)
|
|
{
|
|
float rd = l1.vector().cross(l2.vector());
|
|
if (rd == 0) return {}; // Parallel or Colinear TODO: Return two points
|
|
|
|
//Inverse rd product
|
|
rd = 1.f / rd;
|
|
|
|
//Cross products:
|
|
//rn = (b1b2 x b1a1)
|
|
float rn = ((l2.end.x - l2.start.x) * (l1.start.y - l2.start.y) - (l2.end.y - l2.start.y) * (l1.start.x - l2.start.x)) * rd;
|
|
//sn = (a1a2 x b1a1)
|
|
float sn = ((l1.end.x - l1.start.x) * (l1.start.y - l2.start.y) - (l1.end.y - l1.start.y) * (l1.start.x - l2.start.x)) * rd;
|
|
|
|
//Return the intersection depth
|
|
//if (d) *d = rn;
|
|
|
|
if (rn < 0.f || rn > 1.f || sn < 0.f || sn > 1.f)
|
|
return {}; // Intersection not within line segment
|
|
|
|
return { l1.start + rn * l1.vector()};
|
|
}
|
|
|
|
// intersects(r,l)
|
|
// Get intersection points where rectangle intersects with line segment
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const rect<T1>& r, const line<T2>& l)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < r.side_count(); i++)
|
|
{
|
|
auto v = intersects(r.side(i), l);
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
// intersects(c,l)
|
|
// Get intersection points where circle intersects with line segment
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const circle<T1>& c, const line<T2>& l)
|
|
{
|
|
const auto closestPointToSegment = closest(l, c.pos);
|
|
if (!overlaps(c, closestPointToSegment))
|
|
{
|
|
// Circle is too far away
|
|
return {};
|
|
}
|
|
|
|
// Compute point closest to the circle on the line
|
|
const auto d = l.vector();
|
|
const auto uLine = d.dot(c.pos - l.start) / d.mag2();
|
|
const auto closestPointToLine = l.start + uLine * d;
|
|
const auto distToLine = (c.pos - closestPointToLine).mag2();
|
|
|
|
if (std::abs(distToLine - c.radius * c.radius) < epsilon)
|
|
{
|
|
// Circle "kisses" the line
|
|
return { closestPointToLine };
|
|
}
|
|
|
|
// Circle intersects the line
|
|
const auto length = std::sqrt(c.radius * c.radius - distToLine);
|
|
const auto p1 = closestPointToLine + l.vector().norm() * length;
|
|
const auto p2 = closestPointToLine - l.vector().norm() * length;
|
|
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
intersections.reserve(2);
|
|
|
|
if ((p1 - closest(l, p1)).mag2() < epsilon * epsilon)
|
|
intersections.push_back(p1);
|
|
if ((p2 - closest(l, p2)).mag2() < epsilon * epsilon)
|
|
intersections.push_back(p2);
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
// intersects(t,l)
|
|
// Get intersection points where triangle intersects with line segment
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const triangle<T1>& t, const line<T2>& l)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < t.side_count(); i++)
|
|
{
|
|
auto v = intersects(t.side(i), l);
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// ================================================================================================================
|
|
// RECTANGLE ======================================================================================================
|
|
|
|
// contains(p,r)
|
|
// Check if point contains rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains([[maybe_unused]] const olc::v_2d<T1>& p, [[maybe_unused]] const rect<T2>& r)
|
|
{
|
|
return false; // It can't!
|
|
}
|
|
|
|
// contains(l,r)
|
|
// Check if line segment contains rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains([[maybe_unused]] const line<T1>& l, [[maybe_unused]] const rect<T2>& r)
|
|
{
|
|
return false; // It can't
|
|
}
|
|
|
|
// contains(r,r)
|
|
// Check if rectangle contains rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const rect<T1>& r1, const rect<T2>& r2)
|
|
{
|
|
return (r2.pos.x >= r1.pos.x) && (r2.pos.x + r2.size.x <= r1.pos.x + r1.size.x) &&
|
|
(r2.pos.y >= r1.pos.y) && (r2.pos.y + r2.size.y <= r1.pos.y + r1.size.y);
|
|
}
|
|
|
|
// contains(c,r)
|
|
// Check if circle contains rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const circle<T1>& c, const rect<T2>& r)
|
|
{
|
|
return contains(c, r.pos)
|
|
&& contains(c, olc::v_2d<T2>{ r.pos.x + r.size.x, r.pos.y })
|
|
&& contains(c, olc::v_2d<T2>{ r.pos.x, r.pos.y + r.size.y })
|
|
&& contains(c, r.pos + r.size);
|
|
}
|
|
|
|
// contains(t,r)
|
|
// Check if triangle contains rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const triangle<T1>& t, const rect<T2>& r)
|
|
{
|
|
return contains(t, r.pos)
|
|
&& contains(t, r.pos + r.size)
|
|
&& contains(t, olc::v_2d<T2>{ r.pos.x + r.size.x,r.pos.y })
|
|
&& contains(t, olc::v_2d<T2>{ r.pos.x, r.pos.y + r.size.y });
|
|
}
|
|
|
|
|
|
|
|
// overlaps(p,r)
|
|
// Check if point overlaps rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const olc::v_2d<T1>& p, const rect<T2>& r)
|
|
{
|
|
return overlaps(r, p);
|
|
}
|
|
|
|
// overlaps(l,r)
|
|
// Check if line segment overlaps rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const line<T1>& l, const rect<T2>& r)
|
|
{
|
|
return overlaps(r, l);
|
|
}
|
|
|
|
// overlaps(r,r)
|
|
// Check if rectangle overlaps rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const rect<T1>& r1, const rect<T2>& r2)
|
|
{
|
|
return (r1.pos.x <= r2.pos.x + r2.size.x && r1.pos.x + r1.size.x >= r2.pos.x &&
|
|
r1.pos.y <= r2.pos.y + r2.size.y && r1.pos.y + r1.size.y >= r2.pos.y);
|
|
}
|
|
|
|
// overlaps(c,r)
|
|
// Check if circle overlaps rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const circle<T1>& c, const rect<T2>& r)
|
|
{
|
|
// Inspired by this (very clever btw)
|
|
// https://stackoverflow.com/questions/45370692/circle-rectangle-collision-response
|
|
// But modified to work :P
|
|
double overlap = (olc::v_2d<T2>{ std::clamp(c.pos.x, r.pos.x, r.pos.x + r.size.x), std::clamp(c.pos.y, r.pos.y, r.pos.y + r.size.y) } - c.pos).mag2();
|
|
if (std::isnan(overlap)) overlap = 0;
|
|
return (overlap - (c.radius * c.radius)) < 0;
|
|
}
|
|
|
|
// overlaps(t,r)
|
|
// Check if triangle overlaps rectangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const triangle<T1>& t, const rect<T2>& r)
|
|
{
|
|
return overlaps(t, r.top())
|
|
|| overlaps(t, r.bottom())
|
|
|| overlaps(t, r.left())
|
|
|| overlaps(t, r.right())
|
|
|| contains(r, t.pos[0]);
|
|
}
|
|
|
|
|
|
|
|
// intersects(p,r)
|
|
// Get intersection points where point intersects with rectangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const olc::v_2d<T1>& p, const rect<T2>& r)
|
|
{
|
|
return intersects(r, p);
|
|
}
|
|
|
|
// intersects(l,r)
|
|
// Get intersection points where line segment intersects with rectangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const line<T1>& l, const rect<T2>& r)
|
|
{
|
|
return intersects(r,l);
|
|
}
|
|
|
|
// intersects(r,r)
|
|
// Get intersection points where rectangle intersects with rectangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const rect<T1>& r1, const rect<T2>& r2)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < r2.side_count(); i++) {
|
|
auto v = intersects(r1, r2.side(i));
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
// intersects(c,r)
|
|
// Get intersection points where circle intersects with rectangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const circle<T1>& c, const rect<T2>& r)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < r.side_count(); i++)
|
|
{
|
|
auto v = intersects(c, r.side(i));
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
// intersects(t,r)
|
|
// Get intersection points where triangle intersects with rectangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const triangle<T1>& t, const rect<T2>& r)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < r.side_count(); i++) {
|
|
auto v = intersects(t, r.side(i));
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// ================================================================================================================
|
|
// CIRCLE =========================================================================================================
|
|
|
|
// contains(p,c)
|
|
// Check if point contains circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains([[maybe_unused]] const olc::v_2d<T1>& p, [[maybe_unused]] const circle<T2>& c)
|
|
{
|
|
return false; // It can't!
|
|
}
|
|
|
|
// contains(l,c)
|
|
// Check if line segment contains circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains([[maybe_unused]] const line<T1>& l, [[maybe_unused]] const circle<T2>& c)
|
|
{
|
|
return false; // It can't!
|
|
}
|
|
|
|
// contains(r,c)
|
|
// Check if rectangle contains circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const rect<T1>& r, const circle<T2>& c)
|
|
{
|
|
return r.pos.x + c.radius <= c.pos.x
|
|
&& c.pos.x <= r.pos.x + r.size.x - c.radius
|
|
&& r.pos.y + c.radius <= c.pos.y
|
|
&& c.pos.y <= r.pos.y + r.size.y - c.radius;
|
|
}
|
|
|
|
// contains(c,c)
|
|
// Check if circle contains circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const circle<T1>& c1, const circle<T2>& c2)
|
|
{
|
|
return (std::sqrt(std::pow(c2.pos.x - c1.pos.x, 2) + std::pow(c2.pos.y - c1.pos.y, 2)) + c2.radius) <= c1.radius;
|
|
|
|
}
|
|
|
|
// contains(t,c)
|
|
// Check if triangle contains circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const triangle<T1>& t, const circle<T2>& c)
|
|
{
|
|
return contains(t, c.pos) && (c.pos - closest(t, c.pos)).mag2() >= c.radius * c.radius;
|
|
}
|
|
|
|
|
|
|
|
// overlaps(p,c)
|
|
// Check if point overlaps circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const olc::v_2d<T1>& p, const circle<T2>& c)
|
|
{
|
|
return overlaps(c, p);
|
|
}
|
|
|
|
// overlaps(l,c)
|
|
// Check if line segment overlaps circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const line<T1>& l, const circle<T2>& c)
|
|
{
|
|
return overlaps(c, l);
|
|
}
|
|
|
|
// overlaps(r,c)
|
|
// Check if rectangle overlaps circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const rect<T1>& r, const circle<T2>& c)
|
|
{
|
|
return overlaps(c, r);
|
|
}
|
|
|
|
// overlaps(c,c)
|
|
// Check if circle overlaps circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const circle<T1>& c1, const circle<T2>& c2)
|
|
{
|
|
return (c1.pos - c2.pos).mag2() <= (c1.radius + c2.radius) * (c1.radius + c2.radius);
|
|
}
|
|
|
|
// overlaps(t,c)
|
|
// Check if triangle overlaps circle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const triangle<T1>& t, const circle<T2>& c)
|
|
{
|
|
return contains(t, c.pos) || (c.pos - closest(t, c.pos)).mag2() <= c.radius * c.radius;
|
|
}
|
|
|
|
|
|
|
|
// intersects(p,c)
|
|
// Get intersection points where point intersects with circle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const olc::v_2d<T1>& p, const circle<T2>& c)
|
|
{
|
|
return intersects(c, p);
|
|
}
|
|
|
|
// intersects(l,c)
|
|
// Get intersection points where line segment intersects with circle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const line<T1>& l, const circle<T2>& c)
|
|
{
|
|
return intersects(c, l);
|
|
}
|
|
|
|
// intersects(r,c)
|
|
// Get intersection points where rectangle intersects with circle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const rect<T1>& r, const circle<T2>& c)
|
|
{
|
|
return intersects(c, r);
|
|
}
|
|
|
|
// intersects(c,c)
|
|
// Get intersection points where circle intersects with circle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const circle<T1>& c1, const circle<T2>& c2)
|
|
{
|
|
if (c1.pos == c2.pos) return {}; // circles are either within one another so cannot intersect, or are
|
|
// identical so share all points which there's no good way to represent in return value.
|
|
v_2d<T1> between = c2.pos - c1.pos;
|
|
float dist2 = between.mag2();
|
|
float radiusSum = c1.radius + c2.radius;
|
|
if (dist2 > radiusSum*radiusSum) return {}; // circles are too far apart to be touching.
|
|
if (contains(c1, c2) || contains(c2, c1)) return {}; // one circle is inside of the other, they can't be intersecting.
|
|
if (dist2 == radiusSum) return {c1.pos + between.norm() * c1.radius}; // circles are touching at exactly 1 point
|
|
// otherwise they're touching at 2 points.
|
|
//
|
|
// ______ ________
|
|
// .'' ''.X' ''. X = intersections
|
|
// / / |\ \ O = chordCenter
|
|
// | | | | | In order to find the intersections we first find O.
|
|
// ( c1--(--O-)--c2 ) To do this, we find the distance c1->O by solving for the
|
|
// | | | | | two right triangles formed by the chord and c1->c2 (L).
|
|
// \ \ |/ / . Pythagorean theorem:
|
|
// '. .'X ,' .'|\ (L-x)^2 + h^2 = c1.r^2
|
|
// ''----'' ''------'' c1.r / | \ c2.radius x^2 + h^2 = c2.r^2
|
|
// .' h| \ Subtract 1 equation from the other and solve:
|
|
// /_____|___\ (L-x)^2 + h^2 - (x^2 + h^2) = c1.r^2 - c2.r^2
|
|
// x L-x (L-x)^2 - x^2 = c1.r^2 - c2.r^2
|
|
// L^2 - 2Lx = c1.r^2 - c2.r^2
|
|
// 2Lx - L^2 = c2.r^2 - c1.r^2
|
|
// v------------<-----------------<-----------------<-----. x = (L^2 + c2.r^2 - c1.r^2)/2 -.
|
|
// Next, we have to solve for the height h, and move '-------<--------------------<-----'
|
|
// that distance from O, perpendicular to c1->c2.
|
|
//
|
|
// Pythagorean theorem: x^2 + h^2 = c1.r^2 -> c1.r^2 - x^2 = h^2 -> h = sqrt(c1.r^2 - x^2)
|
|
//
|
|
// x is ccDist and h is halfChord.
|
|
//
|
|
float dist = std::sqrt(dist2);
|
|
float ccDist = (dist2 + c1.radius * c1.radius - c2.radius * c2.radius)/(2*dist);
|
|
v_2d<T1> chordCenter = c1.pos + between.norm() * ccDist;
|
|
v_2d<T1> halfChord = between.norm().perp() * std::sqrt(c1.radius * c1.radius - ccDist * ccDist);
|
|
return {chordCenter + halfChord, chordCenter - halfChord};
|
|
}
|
|
|
|
// intersects(t,c)
|
|
// Get intersection points where triangle intersects with circle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const triangle<T1>& t, const circle<T2>& c)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < t.side_count(); i++) {
|
|
auto v = intersects(c, t.side(i));
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// ================================================================================================================
|
|
// TRIANGLE =======================================================================================================
|
|
|
|
// contains(p,t)
|
|
// Check if point contains triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains([[maybe_unused]] const olc::v_2d<T1>& p, [[maybe_unused]] const triangle<T2>& t)
|
|
{
|
|
return false; // It can't!
|
|
}
|
|
|
|
// contains(l,t)
|
|
// Check if line segment contains triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains([[maybe_unused]] const line<T1>& l, [[maybe_unused]] const triangle<T2>& t)
|
|
{
|
|
return false; // It can't
|
|
}
|
|
|
|
// contains(r,t)
|
|
// Check if rectangle contains triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const rect<T1>& r, const triangle<T2>& t)
|
|
{
|
|
return contains(r, t.side(0))
|
|
&& contains(r, t.side(1))
|
|
&& contains(r, t.side(2));
|
|
}
|
|
|
|
// contains(c,t)
|
|
// Check if circle contains triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const circle<T1>& c, const triangle<T2>& t)
|
|
{
|
|
return contains(c, t.pos[0])
|
|
&& contains(c, t.pos[1])
|
|
&& contains(c, t.pos[2]);
|
|
}
|
|
|
|
// contains(t,t)
|
|
// Check if triangle contains triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool contains(const triangle<T1>& t1, const triangle<T2>& t2)
|
|
{
|
|
return contains(t1, t2.pos[0])
|
|
&& contains(t1, t2.pos[1])
|
|
&& contains(t1, t2.pos[2]);
|
|
}
|
|
|
|
|
|
|
|
// overlaps(p,t)
|
|
// Check if point overlaps triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const olc::v_2d<T1>& p, const triangle<T2>& t)
|
|
{
|
|
return overlaps(t, p);
|
|
}
|
|
|
|
// overlaps(l,t)
|
|
// Check if line segment overlaps triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const line<T1>& l, const triangle<T2>& t)
|
|
{
|
|
return overlaps(t, l);
|
|
}
|
|
|
|
// overlaps(r,t)
|
|
// Check if rectangle overlaps triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const rect<T1>& r, const triangle<T2>& t)
|
|
{
|
|
return overlaps(t, r);
|
|
}
|
|
|
|
// overlaps(c,t)
|
|
// Check if circle overlaps triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const circle<T1>& c, const triangle<T2>& t)
|
|
{
|
|
return overlaps(t, c);
|
|
}
|
|
|
|
// overlaps(t,t)
|
|
// Check if triangle overlaps triangle
|
|
template<typename T1, typename T2>
|
|
inline constexpr bool overlaps(const triangle<T1>& t1, const triangle<T2>& t2)
|
|
{
|
|
return overlaps(t1, t2.side(0))
|
|
|| overlaps(t1, t2.side(1))
|
|
|| overlaps(t1, t2.side(2))
|
|
|| overlaps(t2, t1.pos[0]);
|
|
}
|
|
|
|
|
|
|
|
// intersects(p,t)
|
|
// Get intersection points where point intersects with triangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const olc::v_2d<T1>& p, const triangle<T2>& t)
|
|
{
|
|
return intersects(t, p);
|
|
}
|
|
|
|
// intersects(l,t)
|
|
// Get intersection points where line segment intersects with triangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const line<T1>& l, const triangle<T2>& t)
|
|
{
|
|
return intersects(t, l);
|
|
}
|
|
|
|
// intersects(r,t)
|
|
// Get intersection points where rectangle intersects with triangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const rect<T1>& r, const triangle<T2>& t)
|
|
{
|
|
return intersects(t, r);
|
|
}
|
|
|
|
// intersects(c,t)
|
|
// Get intersection points where circle intersects with triangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const circle<T1>& c, const triangle<T2>& t)
|
|
{
|
|
return intersects(t, c);
|
|
}
|
|
|
|
// intersects(t,t)
|
|
// Get intersection points where triangle intersects with triangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const triangle<T1>& t1, const triangle<T2>& t2)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < t2.side_count(); i++) {
|
|
auto v = intersects(t1, t2.side(i));
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
|
|
// envelope_c(c)
|
|
// Return circle that fully encapsulates a point
|
|
template<typename T1>
|
|
inline constexpr circle<T1> envelope_c(const olc::v_2d<T1>& p)
|
|
{
|
|
return circle<T1>(p, 0);
|
|
}
|
|
|
|
|
|
|
|
// envelope_c(l)
|
|
// Return circle that fully encapsulates a line
|
|
template<typename T1>
|
|
inline constexpr circle<T1> envelope_c(const line<T1>& l)
|
|
{
|
|
return {l.upoint(0.5),l.vector().mag()/2};
|
|
}
|
|
|
|
// envelope_c(r)
|
|
// Return circle that fully encapsulates a rectangle
|
|
template<typename T1>
|
|
inline constexpr circle<T1> envelope_c(const rect<T1>& r)
|
|
{
|
|
// Construct the circle from the rectangle's diagonal
|
|
return envelope_c(line<T1>(r.pos, r.pos + r.size));
|
|
}
|
|
|
|
// envelope_c(c)
|
|
// Return circle that fully encapsulates a circle
|
|
template<typename T1>
|
|
inline constexpr circle<T1> envelope_c(const circle<T1>& c)
|
|
{
|
|
return c;
|
|
}
|
|
|
|
// envelope_c(t)
|
|
// Return circle that fully encapsulates a triangle
|
|
template<typename T1>
|
|
inline constexpr circle<T1> envelope_c(const triangle<T1>& t)
|
|
{
|
|
olc::v_2d<T1> circumcenter;
|
|
|
|
double D = 2 * (t.pos[0].x * (t.pos[1].y - t.pos[2].y) + t.pos[1].x * (t.pos[2].y - t.pos[0].y) + t.pos[2].x * (t.pos[0].y - t.pos[1].y));
|
|
circumcenter.x = T1(double(
|
|
(t.pos[0].x * t.pos[0].x + t.pos[0].y * t.pos[0].y) * (t.pos[1].y - t.pos[2].y) +
|
|
(t.pos[1].x * t.pos[1].x + t.pos[1].y * t.pos[1].y) * (t.pos[2].y - t.pos[0].y) +
|
|
(t.pos[2].x * t.pos[2].x + t.pos[2].y * t.pos[2].y) * (t.pos[0].y - t.pos[1].y)
|
|
) / D);
|
|
circumcenter.y = T1(double(
|
|
(t.pos[0].x * t.pos[0].x + t.pos[0].y * t.pos[0].y) * (t.pos[2].x - t.pos[1].x) +
|
|
(t.pos[1].x * t.pos[1].x + t.pos[1].y * t.pos[1].y) * (t.pos[0].x - t.pos[2].x) +
|
|
(t.pos[2].x * t.pos[2].x + t.pos[2].y * t.pos[2].y) * (t.pos[1].x - t.pos[0].x)
|
|
) / D);
|
|
|
|
double r = 0;
|
|
for (auto& point : t.pos) {
|
|
r = std::max(r, double(std::hypot(circumcenter.x - point.x, circumcenter.y - point.y)));
|
|
}
|
|
|
|
return {circumcenter, T1(r)};
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
// envelope_r(p)
|
|
// Return rectangle that fully encapsulates a point
|
|
template<typename T1>
|
|
inline constexpr rect<T1> envelope_r(const olc::v_2d<T1>& p)
|
|
{
|
|
return rect<T1>(p, { 0,0 });
|
|
}
|
|
|
|
// envelope_r(l)
|
|
// Return rectangle that fully encapsulates a line
|
|
template<typename T1>
|
|
inline constexpr rect<T1> envelope_r(const line<T1>& l)
|
|
{
|
|
T1 min_x=std::min(l.start.x,l.end.x);
|
|
T1 min_y=std::min(l.start.y,l.end.y);
|
|
T1 size_x=std::abs(l.start.x-l.end.x);
|
|
T1 size_y=std::abs(l.start.y-l.end.y);
|
|
return {{min_x,min_y},{size_x,size_y}};
|
|
}
|
|
|
|
// envelope_r(r)
|
|
// Return rectangle that fully encapsulates a rectangle
|
|
template<typename T1>
|
|
inline constexpr rect<T1> envelope_r(const rect<T1>& r)
|
|
{
|
|
return r;
|
|
}
|
|
|
|
// envelope_r(c)
|
|
// Return rectangle that fully encapsulates a circle
|
|
template<typename T1>
|
|
inline constexpr rect<T1> envelope_r(const circle<T1>& c)
|
|
{
|
|
return rect<T1>(c.pos - v_2d<T1>{c.radius, c.radius}, { c.radius * 2, c.radius * 2 });
|
|
}
|
|
|
|
// envelope_r(t)
|
|
// Return rectangle that fully encapsulates a triangle
|
|
template<typename T1>
|
|
inline constexpr rect<T1> envelope_r(const triangle<T1>& t)
|
|
{
|
|
auto vMin = t.pos[0].min(t.pos[1].min(t.pos[2]));
|
|
auto vMax = t.pos[0].max(t.pos[1].max(t.pos[2]));
|
|
return rect<T1>(vMin, vMax - vMin);
|
|
}
|
|
|
|
template<typename T>
|
|
inline constexpr auto bounding_box(T&& t)
|
|
{
|
|
return envelope_r(std::forward<T>(t));
|
|
}
|
|
|
|
template<typename T>
|
|
inline constexpr auto bounding_circle(T&& t)
|
|
{
|
|
return envelope_c(std::forward<T>(t));
|
|
}
|
|
|
|
|
|
// PROJECTIONS ==========================================================================================================
|
|
|
|
// project(c,p)
|
|
// project a circle, onto a point, via a ray (i.e. how far along the ray can the circle travel until it contacts the point?)
|
|
template<typename T1, typename T2, typename T3>
|
|
inline std::optional<olc::v_2d<T1>> project(const circle<T1>& c, const olc::v_2d<T2>& p, const ray<T3>& q)
|
|
{
|
|
return project(c, circle<T2>(p, 0), q);
|
|
}
|
|
|
|
|
|
// project(c,c)
|
|
// project a circle, onto a circle, via a ray (i.e. how far along the ray can the circle travel until it contacts the other circle?)
|
|
template<typename T1, typename T2, typename T3>
|
|
inline std::optional<olc::v_2d<T1>> project(const circle<T1>& c1, const circle<T2>& c2, const ray<T3>& q)
|
|
{
|
|
// Inspired by https://math.stackexchange.com/a/929240
|
|
|
|
double A = q.direction.mag2();
|
|
double B = 2.0 * (q.origin.dot(q.direction) - c2.pos.dot(q.direction));
|
|
double C = c2.pos.mag2() + q.origin.mag2() - (2.0 * c2.pos.x * q.origin.x) - (2.0 * c2.pos.y * q.origin.y) - ((c1.radius + c2.radius) * (c1.radius + c2.radius));
|
|
double D = B * B - 4.0 * A * C;
|
|
|
|
if (D < 0.0)
|
|
return std::nullopt;
|
|
else
|
|
{
|
|
const auto sD = std::sqrt(D);
|
|
const auto s1 = (-B + sD) / (2.0 * A);
|
|
const auto s2 = (-B - sD) / (2.0 * A);
|
|
|
|
if (s1 < 0 && s2 < 0)
|
|
return std::nullopt;
|
|
if (s1 < 0)
|
|
return q.origin + q.direction * s2;
|
|
if (s2 < 0)
|
|
return q.origin + q.direction * s1;
|
|
|
|
return q.origin + q.direction * std::min(s1, s2);
|
|
}
|
|
}
|
|
|
|
// project(c,l)
|
|
// project a circle, onto a line segment, via a ray
|
|
template<typename T1, typename T2, typename T3>
|
|
inline std::optional<olc::v_2d<T2>> project(const circle<T1>& c, const line<T2>& l, const ray<T3>& q)
|
|
{
|
|
// Treat line segment as capsule with radius that of the circle
|
|
// and treat the circle as a point
|
|
|
|
// First do we hit ends of line segment, inflated to be circles
|
|
const auto vHitsStartCirc = intersects(q, circle<T2>(l.start, c.radius));
|
|
const auto vHitsEndCirc = intersects(q, circle<T2>(l.end, c.radius));
|
|
|
|
// Now create two line segments in parallel to the original, that join
|
|
// up the end circles to form the sides of the capsule
|
|
const auto displace = l.vector().norm().perp() * c.radius;
|
|
const auto vHitsSide1 = intersects(q, line<T2>(l.start + displace, l.end + displace));
|
|
const auto vHitsSide2 = intersects(q, line<T2>(l.start - displace, l.end - displace));
|
|
|
|
// Bring the multitude of points to one place
|
|
std::vector<olc::v_2d<T2>> vAllIntersections;
|
|
vAllIntersections.insert(vAllIntersections.end(), vHitsStartCirc.begin(), vHitsStartCirc.end());
|
|
vAllIntersections.insert(vAllIntersections.end(), vHitsEndCirc.begin(), vHitsEndCirc.end());
|
|
vAllIntersections.insert(vAllIntersections.end(), vHitsSide1.begin(), vHitsSide1.end());
|
|
vAllIntersections.insert(vAllIntersections.end(), vHitsSide2.begin(), vHitsSide2.end());
|
|
|
|
if (vAllIntersections.size() == 0)
|
|
{
|
|
// No intersections at all, so
|
|
return std::nullopt;
|
|
}
|
|
|
|
// Find closest
|
|
double dClosest = std::numeric_limits<double>::max();
|
|
olc::v_2d<T2> vClosest;
|
|
for (const auto& vContact : vAllIntersections)
|
|
{
|
|
double dDistance = (vContact - c.pos).mag2();
|
|
if (dDistance < dClosest)
|
|
{
|
|
dClosest = dDistance;
|
|
vClosest = vContact;
|
|
}
|
|
}
|
|
|
|
return vClosest;
|
|
}
|
|
|
|
// project(c,r)
|
|
// project a circle, onto a rectangle, via a ray
|
|
template<typename T1, typename T2, typename T3>
|
|
inline std::optional<olc::v_2d<T2>> project(const circle<T1>& c, const rect<T2>& r, const ray<T3>& q)
|
|
{
|
|
// TODO:
|
|
return std::nullopt;
|
|
}
|
|
|
|
// project(c,t)
|
|
// project a circle, onto a triangle, via a ray
|
|
template<typename T1, typename T2, typename T3>
|
|
inline std::optional<olc::v_2d<T2>> project(const circle<T1>& c, const triangle<T2>& t, const ray<T3>& q)
|
|
{
|
|
// TODO:
|
|
return std::nullopt;
|
|
}
|
|
|
|
|
|
// RAYS =================================================================================================================
|
|
|
|
// intersects(q,q)
|
|
// return intersection point (if it exists) of a ray and a ray
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const ray<T1>& q1, const ray<T2>& q2)
|
|
{
|
|
const auto origin_diff = q2.origin - q1.origin;
|
|
const auto cp1 = q1.direction.cross(q2.direction);
|
|
const auto cp2 = origin_diff.cross(q2.direction);
|
|
|
|
if (cp1 == 0) // Early rejection
|
|
{
|
|
if (cp2 == 0)
|
|
return { q1.origin }; // co-linear
|
|
else
|
|
return {}; // parallel
|
|
}
|
|
|
|
const auto cp3 = origin_diff.cross(q1.direction);
|
|
const auto t1 = cp2 / cp1; // distance along q1 to intersection
|
|
const auto t2 = cp3 / cp1; // distance along q2 to intersection
|
|
|
|
if (t1 >= 0 && t2 >= 0)
|
|
return { q1.origin + q1.direction * t1 }; // Intersection, both rays positive
|
|
else
|
|
return {}; // Intersection, but behind a rays origin, so not really an intersection in context
|
|
}
|
|
|
|
// intersects(q,p)
|
|
// return intersection point (if it exists) of a ray and a point
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const ray<T1>& q, const v_2d<T2>& p)
|
|
{
|
|
const line<T1> l = { q.origin, q.origin + q.direction };
|
|
|
|
if (std::abs(l.side(p)) < epsilon )
|
|
return { p }; // Intersection
|
|
else
|
|
return {};
|
|
}
|
|
|
|
// intersects(q,l)
|
|
// return intersection point (if it exists) of a ray and a line segment
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const ray<T1>& q, const line<T2>& l)
|
|
{
|
|
const auto line_direction = l.vector();
|
|
const auto origin_diff = l.start - q.origin;
|
|
const auto cp1 = q.direction.cross(line_direction);
|
|
const auto cp2 = origin_diff.cross(line_direction);
|
|
|
|
if (cp1 == 0) // Early rejection
|
|
{
|
|
if (cp2 == 0)
|
|
return { q.origin }; // co-linear
|
|
else
|
|
return {}; // parallel
|
|
}
|
|
|
|
const auto cp3 = origin_diff.cross(q.direction);
|
|
const auto t1 = cp2 / cp1; // distance along ray to intersection
|
|
const auto t2 = cp3 / cp1; // distance along line segment to intersection
|
|
|
|
if (t1 >= 0 && t2 >= 0 && t2 <= 1)
|
|
return { q.origin + q.direction * t1 }; // Intersection, both rays positive
|
|
else
|
|
return {}; // Intersection, but behind a rays origin, or outside line segment bounds.
|
|
// so not really an intersection in context
|
|
}
|
|
|
|
// collision(q,l)
|
|
// optionally returns collision point and collision normal of ray and a line segment, if it collides
|
|
template<typename T1, typename T2>
|
|
inline std::optional<std::pair<olc::v_2d<T2>, olc::v_2d<T2>>> collision(const ray<T1>& q, const line<T2>& l)
|
|
{
|
|
const auto vIntersection = intersects(q, l);
|
|
if (vIntersection.size() > 0)
|
|
{
|
|
return { {vIntersection[0], l.vector().perp().norm() * l.side(q.origin)} };
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// reflect(q,l)
|
|
// optionally returns a ray reflected off a line segement if collision occurs
|
|
template<typename T1, typename T2>
|
|
inline std::optional<ray<T1>> reflect(const ray<T1>& q, const line<T2>& l)
|
|
{
|
|
const auto vCollision = collision(q, l);
|
|
if (vCollision.has_value())
|
|
{
|
|
return { ray<T1>{vCollision.value().first, q.direction.reflect(vCollision.value().second)} };
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// reflect(q,p)
|
|
// optionally returns a ray reflected off a point if collision occurs
|
|
template<typename T1, typename T2>
|
|
inline std::optional<ray<T1>> reflect(const ray<T1>& q, const olc::v_2d<T2>& p)
|
|
{
|
|
// TODO:
|
|
return std::nullopt;
|
|
}
|
|
|
|
// collision(q,r)
|
|
// optionally returns collision point and collision normal of ray and a line segment, if it collides
|
|
template<typename T1, typename T2>
|
|
inline std::optional<std::pair<olc::v_2d<T1>, olc::v_2d<T1>>> collision(const ray<T1>& q, const rect<T2>& r)
|
|
{
|
|
olc::v_2d<T1> vClosestIntersection;
|
|
olc::v_2d<T1> vIntersectionNormal;
|
|
double dClosestDistance2 = std::numeric_limits<double>::max();
|
|
bool bCollide = false;
|
|
|
|
for (size_t i = 0; i < r.side_count(); i++)
|
|
{
|
|
auto v = intersects(q, r.side(i));
|
|
if (v.size() > 0)
|
|
{
|
|
bCollide = true;
|
|
double d = (v[0] - q.origin).mag2();
|
|
if (d < dClosestDistance2)
|
|
{
|
|
dClosestDistance2 = d;
|
|
vClosestIntersection = v[0];
|
|
vIntersectionNormal = r.side(i).vector().perp().norm();
|
|
}
|
|
}
|
|
}
|
|
|
|
if (bCollide)
|
|
{
|
|
return { {vClosestIntersection, vIntersectionNormal} };
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// reflect(q,r)
|
|
// optionally returns a ray reflected off a rectangle if collision occurs
|
|
template<typename T1, typename T2>
|
|
inline std::optional<ray<T1>> reflect(const ray<T1>& q, const rect<T2>& r)
|
|
{
|
|
const auto vCollision = collision(q, r);
|
|
if (vCollision.has_value())
|
|
{
|
|
return { ray<T1>{vCollision.value().first, q.direction.reflect(vCollision.value().second)} };
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// collision(q,c)
|
|
// optionally returns collision point and collision normal of ray and a circle, if it collides
|
|
template<typename T1, typename T2>
|
|
inline std::optional<std::pair<olc::v_2d<T2>, olc::v_2d<T2>>> collision(const ray<T1>& q, const circle<T2>& c)
|
|
{
|
|
const auto vIntersection = intersects(q, c);
|
|
if (vIntersection.size() > 0)
|
|
{
|
|
return { {vIntersection[0], (vIntersection[0] - c.pos).norm()}};
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// reflect(q,c)
|
|
// optionally returns a ray reflected off a circle if collision occurs
|
|
template<typename T1, typename T2>
|
|
inline std::optional<ray<T1>> reflect(const ray<T1>& q, const circle<T2>& c)
|
|
{
|
|
const auto vCollision = collision(q, c);
|
|
if (vCollision.has_value())
|
|
{
|
|
return { ray<T1>{vCollision.value().first, q.direction.reflect(vCollision.value().second)} };
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// collision(q,r)
|
|
// optionally returns collision point and collision normal of ray and a triangle, if it collides
|
|
template<typename T1, typename T2>
|
|
inline std::optional<std::pair<olc::v_2d<T1>, olc::v_2d<T1>>> collision(const ray<T1>& q, const triangle<T2>& t)
|
|
{
|
|
olc::v_2d<T1> vClosestIntersection;
|
|
olc::v_2d<T1> vIntersectionNormal;
|
|
double dClosestDistance2 = std::numeric_limits<double>::max();
|
|
bool bCollide = false;
|
|
|
|
for (size_t i = 0; i < t.side_count(); i++)
|
|
{
|
|
auto v = intersects(q, t.side(i));
|
|
if (v.size() > 0)
|
|
{
|
|
bCollide = true;
|
|
double d = (v[0] - q.origin).mag2();
|
|
if (d < dClosestDistance2)
|
|
{
|
|
dClosestDistance2 = d;
|
|
vClosestIntersection = v[0];
|
|
vIntersectionNormal = t.side(i).vector().perp().norm();
|
|
}
|
|
}
|
|
}
|
|
|
|
if (bCollide)
|
|
{
|
|
return { {vClosestIntersection, vIntersectionNormal} };
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// reflect(q,t)
|
|
// optionally returns a ray reflected off a triangle if collision occurs
|
|
template<typename T1, typename T2>
|
|
inline std::optional<ray<T1>> reflect(const ray<T1>& q, const triangle<T2>& t)
|
|
{
|
|
const auto vCollision = collision(q, t);
|
|
if (vCollision.has_value())
|
|
{
|
|
return { ray<T1>{vCollision.value().first, q.direction.reflect(vCollision.value().second)} };
|
|
}
|
|
|
|
return std::nullopt;
|
|
}
|
|
|
|
// reflect(q,r)
|
|
// can't reflect a ray of a ray
|
|
template<typename T1, typename T2>
|
|
inline std::optional<ray<T1>> reflect(const ray<T1>& q1, const ray<T2>& q2)
|
|
{
|
|
// Can't reflect!
|
|
return std::nullopt;
|
|
}
|
|
|
|
|
|
// intersects(q,c)
|
|
// Get intersection points where a ray intersects a circle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const ray<T1>& q, const circle<T2>& c)
|
|
{
|
|
// Look familiar?
|
|
double A = q.direction.mag2();
|
|
double B = 2.0 * (q.origin.dot(q.direction) - c.pos.dot(q.direction));
|
|
double C = c.pos.mag2() + q.origin.mag2() - (2.0 * c.pos.x * q.origin.x) - (2.0 * c.pos.y * q.origin.y) - (c.radius * c.radius);
|
|
double D = B * B - 4.0 * A * C;
|
|
|
|
if (D < 0.0)
|
|
return {};
|
|
else
|
|
{
|
|
const auto sD = std::sqrt(D);
|
|
const auto s1 = (-B + sD) / (2.0 * A);
|
|
const auto s2 = (-B - sD) / (2.0 * A);
|
|
|
|
if (s1 < 0 && s2 < 0)
|
|
return {};
|
|
if (s1 < 0)
|
|
return { q.origin + q.direction * s2 };
|
|
if (s2 < 0)
|
|
return { q.origin + q.direction * s1 };
|
|
|
|
return { q.origin + q.direction * std::min(s1, s2) };
|
|
}
|
|
}
|
|
|
|
// intersects(q,r)
|
|
// Get intersection points where a ray intersects a rectangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const ray<T1>& q, const rect<T2>& r)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < r.side_count(); i++)
|
|
{
|
|
auto v = intersects(q, r.side(i));
|
|
intersections.insert(intersections.end(), v.begin(), v.end());
|
|
}
|
|
|
|
return internal::filter_duplicate_points(intersections);
|
|
}
|
|
|
|
// intersects(q,t)
|
|
// Get intersection points where a ray intersects a triangle
|
|
template<typename T1, typename T2>
|
|
inline std::vector<olc::v_2d<T2>> intersects(const ray<T1>& q, const triangle<T2>& t)
|
|
{
|
|
std::vector<olc::v_2d<T2>> intersections;
|
|
|
|
for (size_t i = 0; i < t.side_count(); i++)
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{
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auto v = intersects(q, t.side(i));
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intersections.insert(intersections.end(), v.begin(), v.end());
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}
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|
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return internal::filter_duplicate_points(intersections);
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}
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|
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template<typename T>
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inline const bool operator ==(const rect<T>&r1,const rect<T>&r2){
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return r1.pos==r2.pos&&r1.size==r2.size;
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|
}
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|
}
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|
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using namespace olc;
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using namespace olc::utils; |