/* OneLoneCoder - Geometry 2D v1.01 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A collection of 2D Geometric primitives and functions to work with and between them. License (OLC-3) ~~~~~~~~~~~~~~~ Copyright 2018 - 2022 OneLoneCoder.com Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions or derivations of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions or derivative works in binary form must reproduce the above copyright notice. This list of conditions and the following disclaimer must be reproduced in the documentation and/or other materials provided with the distribution. 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. Links ~~~~~ YouTube: https://www.youtube.com/javidx9 Discord: https://discord.gg/WhwHUMV Twitter: https://www.twitter.com/javidx9 Twitch: https://www.twitch.tv/javidx9 GitHub: https://www.github.com/onelonecoder Homepage: https://www.onelonecoder.com Author ~~~~~~ David Barr, aka javidx9, �OneLoneCoder 2019, 2020, 2021, 2022 Changes: v1.01: +Made constants inline +Header guards (lol... sigh...) */ #pragma once #include "olcPixelGameEngine.h" namespace olc::utils::geom2d { // Lemon Meringue inline const double pi = 3.141592653589793238462643383279502884; // Floating point error margin inline const double epsilon = 0.001; //https://stackoverflow.com/questions/1903954/is-there-a-standard-sign-function-signum-sgn-in-c-c template constexpr int sgn(T val) { return (T(0) < val) - (val < T(0)); } // Defines a line segment template struct line { olc::v2d_generic start; olc::v2d_generic end; inline line(const olc::v2d_generic& s = { T(0), T(0) }, const olc::v2d_generic& e = { T(0), T(0) }) : start(s), end(e) { } // Get length of line inline constexpr T length() { return (end - start).mag(); } // Get length of line^2 inline constexpr T length2() { return (end - start).mag2(); } inline constexpr olc::v2d_generic vector() const { return (end - start); } // Given a real distance, get point along line inline constexpr olc::v2d_generic rpoint(const T& distance) const { return start + (end - start).norm() * distance; } // Given a unit distance, get point along line inline constexpr olc::v2d_generic upoint(const T& distance) const { return start + (end - start) * distance; } // Return which side of the line does a point lie inline constexpr int32_t side(const olc::v2d_generic& point) const { double d = (end - start).cross(point - start); if (d < 0) return -1; else if (d > 0) return 1; else return 0; } }; template struct ray { olc::v2d_generic origin; olc::v2d_generic direction; }; template struct rect { olc::v2d_generic pos; olc::v2d_generic size; inline rect(const olc::v2d_generic& p = { T(0), T(0) }, const olc::v2d_generic& s = { T(1), T(1) }) : pos(p), size(s) { } inline olc::v2d_generic middle() const { return pos + (size * double(0.5)); } // Get line segment from top side of rectangle inline line top() const { return { pos, {pos.x + size.x, pos.y } }; } // Get line segment from bottom side of rectangle inline line bottom() const { return { {pos.x, pos.y + size.y}, pos + size }; } // Get line segment from left side of rectangle inline line left() const { return { pos, {pos.x, pos.y + size.y} }; } // Get line segment from right side of rectangle inline line right() const { return { {pos.x + size.x, pos.y }, pos + size }; } // Get a line from an indexed side, starting top, going clockwise inline line 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(); } // 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); } }; template struct ellipse { olc::v2d_generic pos; olc::v2d_generic radius; inline ellipse(const olc::v2d_generic& p = { T(0), T(0) }, const olc::v2d_generic r = {T(1),T(1)}) : pos(p), radius(r) { } // Get area of ellipse inline constexpr T area() const { return T(pi) * radius.x * radius.y; } // Get perimeter of an ellipse inline constexpr T perimeter() const { return T(2.0 * pi) * sqrt((radius.x*radius.x+radius.y*radius.y)/(2*1.0)); } // Get circumference of ellipse. Which is the same as a permieter of one. inline constexpr T circumference() const { return perimeter(); } }; template struct circle { olc::v2d_generic pos; T radius = T(0); inline circle(const olc::v2d_generic& 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 struct triangle { std::array, 3> pos; inline triangle( const olc::v2d_generic& p0 = { T(0), T(0) }, const olc::v2d_generic& p1 = { T(0), T(0) }, const olc::v2d_generic& p2 = { T(0), T(0) }) : pos{ p0,p1,p2 } { } // Get a line from an indexed side, starting top, going clockwise inline line 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(); } }; template struct polygon { std::vector> vPoints; }; // ========================================================================================================================= // Closest(shape, point) =================================================================================================== // Returns closest point to point template inline olc::v2d_generic closest(const olc::v2d_generic& p1, const olc::v2d_generic& p2) { return p1; } // Returns closest point on line to point template inline olc::v2d_generic closest(const line& l, const olc::v2d_generic& 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; } // Returns closest point on circle to point template inline olc::v2d_generic closest(const circle& c, const olc::v2d_generic& p) { return c.pos + olc::vd2d(p - c.pos).norm() * c.radius; } // Returns closest point on rectangle to point template inline olc::v2d_generic closest(const rect& r, const olc::v2d_generic& p) { // This could be a "constrain" function hmmmm // TODO: Not quite what i wanted, should restrain to boundary return olc::v2d_generic{ std::clamp(p.x, r.pos.x, r.pos.x + r.size.x), std::clamp(p.y, r.pos.y, r.pos.y + r.size.y) }; } // Returns closest point on triangle to point template inline olc::v2d_generic closest(const triangle& t, const olc::v2d_generic& p) { olc::utils::geom2d::line 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; } } // ================================================================================================================ // POINT ========================================================================================================== // Checks if point contains point template inline constexpr bool contains(const olc::v2d_generic& p1, const olc::v2d_generic& p2) { return (p1 - p2).mag2() < epsilon; } // Checks if line contains point template inline constexpr bool contains(const line& l, const olc::v2d_generic& 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; } // Checks if rectangle contains point template inline constexpr bool contains(const rect& r, const olc::v2d_generic& 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)); } // Checks if ellipse contains a point template inline constexpr bool contains(const ellipse& c, const olc::v2d_generic& p) { return std::pow(p.x-c.pos.x,2)/(c.radius.x*c.radius.x)+std::pow(p.y-c.pos.y,2)/(c.radius.y*c.radius.y)<1; } // Checks if circle contains a point template inline constexpr bool contains(const circle& c, const olc::v2d_generic& p) { return (c.pos - p).mag2() < (c.radius * c.radius); } // Checks if triangle contains a point template inline constexpr bool contains(const triangle& t, const olc::v2d_generic& 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; } // Check if point overlaps with point (analagous to contains()) template inline constexpr bool overlaps(const olc::v2d_generic& p1, const olc::v2d_generic& p2) { return contains(p1, p2); } // Checks if line segment overlaps with point template inline constexpr bool overlaps(const line& l, const olc::v2d_generic& p) { return contains(l, p); } // Checks if rectangle overlaps with point template inline constexpr bool overlaps(const rect& r, const olc::v2d_generic& p) { return contains(r, p); } // Checks if circle overlaps with point template inline constexpr bool overlaps(const circle& c, const olc::v2d_generic& p) { return contains(c, p); } // Checks if triangle overlaps with point template inline constexpr bool overlaps(const triangle& t, const olc::v2d_generic& p) { return contains(t, p); } // Get intersection points where point intersects with point template inline std::vector> intersects(const olc::v2d_generic& p1, const olc::v2d_generic& p2) { if (contains(p1, p2)) return { p1 }; else return {}; } // Get intersection points where line segment intersects with point template inline std::vector> intersects(const line& l, const olc::v2d_generic& p) { if (contains(l, p)) return { p }; else return {}; } // Get intersection points where rectangle intersects with point template inline std::vector> intersects(const rect& r, const olc::v2d_generic& p) { std::vector> vPoints; if (contains(r.top(), p)) vPoints.push_back(p); if (contains(r.bottom(), p)) vPoints.push_back(p); if (contains(r.left(), p)) vPoints.push_back(p); if (contains(r.right(), p)) vPoints.push_back(p); return vPoints; } // Get intersection points where circle intersects with point template inline std::vector> intersects(const circle& c, const olc::v2d_generic& p) { if (std::abs((p - c.pos).mag2() - (c.radius * c.radius)) <= epsilon) return { p }; else return {}; } // Get intersection points where triangle intersects with point template inline std::vector> intersects(const triangle& r, const olc::v2d_generic& p) { // TODO: return {}; } // ================================================================================================================ // LINE =========================================================================================================== // Check if point contains line segment template inline constexpr bool contains(const olc::v2d_generic& p, const line& l) { return false; // It can't! } // Check if line segment contains line segment template inline constexpr bool contains(const line& l1, const line& l2) { // TODO: Check if segments are colinear, and l1 exists within bounds of l2 return false; } // Check if rectangle contains line segment template inline constexpr bool contains(const rect& r, const line& l) { return contains(r, l.start) && contains(r, l.end); } // Check if circle contains line segment template inline constexpr bool contains(const circle& c1, const line& l) { return contains(c1, l.start) && contains(c1, l.end); } // Check if triangle contains line segment template inline constexpr bool contains(const triangle& t, const line& l) { return contains(t, l.start) && contains(t, l.end); } // Check if point overlaps line segment template inline constexpr bool overlaps(const olc::v2d_generic& p, const line& l) { return contains(l, p); } // Check if line segment overlaps line segment template inline constexpr bool overlaps(const line& l1, const line& l2) { // TODO: return false; } // Check if rectangle overlaps line segment template inline constexpr bool overlaps(const rect& r, const line& l) { return contains(r, l.start) || contains(r, l.end); // TODO: This method is no good, it cant detect lines whose start and end // points are outside the rectangle } // Check if circle overlaps line segment template inline constexpr bool overlaps(const circle& c, const line& l) { // TODO: return false; } // Check if triangle overlaps line segment template inline constexpr bool overlaps(const triangle& t, const line& l) { return overlaps(t, l.start) || overlaps(t, l.end); // TODO: This method is no good, it cant detect lines whose start and end // points are outside the triangle } // Get intersection points where point intersects with line segment template inline std::vector> intersects(const olc::v2d_generic& p, const line& l) { // TODO: return {}; } // Get intersection points where line segment intersects with line segment template inline std::vector> intersects(const line& l1, const line& l2) { // TODO: return {}; } // Get intersection points where rectangle intersects with line segment template inline std::vector> intersects(const rect& r, const line& l) { // TODO: return {}; } // Get intersection points where circle intersects with line segment template inline std::vector> intersects(const circle& c, const line& l) { // TODO: return {}; } // Get intersection points where triangle intersects with line segment template inline std::vector> intersects(const triangle& t, const line& l) { // TODO: return {}; } // ================================================================================================================ // RECTANGLE ====================================================================================================== // Check if point contains rectangle template inline constexpr bool contains(const olc::v2d_generic& p, const rect& r) { return false; // It can't! } // Check if line segment contains rectangle template inline constexpr bool contains(const line& l, const rect& r) { return false; // It can't } // Check if rectangle contains rectangle template inline constexpr bool contains(const rect& r1, const rect& 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); } // Check if circle contains rectangle template inline constexpr bool contains(const circle& c, const rect& r) { return contains(c, r.pos) && contains(c, olc::v2d_generic{ r.pos.x + r.size.x, r.pos.y }) && contains(c, olc::v2d_generic{ r.pos.x, r.pos.y + r.size.y }) && contains(c, r.pos + r.size); } // Check if triangle contains rectangle template inline constexpr bool contains(const triangle& t, const rect& r) { return contains(t, r.pos) && contains(t, r.pos + r.size) && contains(t, olc::v2d_generic{ r.pos.x + r.size.x,r.pos.y }) && contains(t, olc::v2d_generic{ r.pos.x, r.pos.y + r.size.y }); } // Check if point overlaps rectangle template inline constexpr bool overlaps(const olc::v2d_generic& p, const rect& r) { return overlaps(r, p); } // Check if line segment overlaps rectangle template inline constexpr bool overlaps(const line& l, const rect& r) { return overlaps(r, l); } // Check if rectangle overlaps rectangle template inline constexpr bool overlaps(const rect& r1, const rect& 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); } // Check if circle overlaps rectangle template inline constexpr bool overlaps(const circle& c, const rect& r) { // Inspired by this (very clever btw) // https://stackoverflow.com/questions/45370692/circle-rectangle-collision-response // But modified to work :P T2 overlap = (olc::v2d_generic{ 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 = T2(0); return (overlap - (c.radius * c.radius)) < T2(0); } // Check if triangle overlaps rectangle template inline constexpr bool overlaps(const triangle& t, const rect& r) { return contains(t, r.pos) || contains(t, r.pos + r.size) || contains(t, olc::v2d_generic{ r.pos.x + r.size.x, r.pos.y }) || contains(t, olc::v2d_generic{ r.pos.x, r.pos.y + r.size.y }); // TODO: This method is no good, consider rectangle with all vertices // outside of triangle, but edges still crossing } // Get intersection points where point intersects with rectangle template inline std::vector> intersects(const olc::v2d_generic& p, const rect& r) { return intersects(r, p); } // Get intersection points where line segment intersects with rectangle template inline std::vector> intersects(const line& l, const rect& r) { // TODO: return {}; } // Get intersection points where rectangle intersects with rectangle template inline std::vector> intersects(const rect& r1, const rect& r2) { // TODO: return {}; } // Get intersection points where circle intersects with rectangle template inline std::vector> intersects(const circle& c, const rect& r) { // TODO: return {}; } // Get intersection points where triangle intersects with rectangle template inline std::vector> intersects(const triangle& t, const rect& r) { // TODO: return {}; } // ================================================================================================================ // CIRCLE ========================================================================================================= // Check if point contains circle template inline constexpr bool contains(const olc::v2d_generic& p, const circle& c) { return false; // It can't! } // Check if line segment contains circle template inline constexpr bool contains(const line& l, const circle& c) { return false; // It can't! } // Check if rectangle contains circle template inline constexpr bool contains(const rect& r, const circle& c) { // TODO: return false; } // Check if circle contains circle template inline constexpr bool contains(const circle& c1, const circle& c2) { return (c1.pos - c2.pos).mag2() <= (c1.radius - c2.radius) * (c1.radius - c2.radius); } // Check if triangle contains circle template inline constexpr bool contains(const triangle& t, const circle& c) { // TODO: return false; } // Check if point overlaps circle template inline constexpr bool overlaps(const olc::v2d_generic& p, const circle& c) { return overlaps(c, p); } // Check if line segment overlaps circle template inline constexpr bool overlaps(const line& l, const circle& c) { return overlaps(c, l); } // Check if rectangle overlaps circle template inline constexpr bool overlaps(const rect& r, const circle& c) { return overlaps(c, r); } // Check if circle overlaps circle template inline constexpr bool overlaps(const circle& c1, const circle& c2) { return (c1.pos - c2.pos).mag2() <= (c1.radius + c2.radius) * (c1.radius + c2.radius); } // Check if triangle overlaps circle template inline constexpr bool overlaps(const triangle& t, const circle& c) { // TODO: return false; } // Get intersection points where point intersects with circle template inline std::vector> intersects(const olc::v2d_generic& p, const circle& c) { // TODO: return {}; } // Get intersection points where line segment intersects with circle template inline std::vector> intersects(const line& l, const circle& c) { // TODO: return {}; } // Get intersection points where rectangle intersects with circle template inline std::vector> intersects(const rect& r, const circle& c) { // TODO: return {}; } // Get intersection points where circle intersects with circle template inline std::vector> intersects(const circle& c1, const circle& c2) { // TODO: return {}; } // Get intersection points where triangle intersects with circle template inline std::vector> intersects(const triangle& t, const circle& c) { // TODO: return {}; } // ================================================================================================================ // TRIANGLE ======================================================================================================= // Check if point contains triangle template inline constexpr bool contains(const olc::v2d_generic& p, const triangle& t) { return false; // It can't! } // Check if line segment contains triangle template inline constexpr bool contains(const line& l, const triangle& t) { return false; // It can't } // Check if rectangle contains triangle template inline constexpr bool contains(const rect& r, const triangle& t) { // TODO: return false; } // Check if circle contains triangle template inline constexpr bool contains(const circle& c, const triangle& t) { // TODO: return false; } // Check if triangle contains triangle template inline constexpr bool contains(const triangle& t1, const triangle& t2) { // TODO: return false; } // Check if point overlaps triangle template inline constexpr bool overlaps(const olc::v2d_generic& p, const triangle& t) { return overlaps(t, p); } // Check if line segment overlaps triangle template inline constexpr bool overlaps(const line& l, const triangle& t) { return overlaps(t, l); } // Check if rectangle overlaps triangle template inline constexpr bool overlaps(const rect& r, const triangle& t) { return overlaps(t, r); } // Check if circle overlaps triangle template inline constexpr bool overlaps(const circle& c, const triangle& t) { return overlaps(t, c); } // Check if triangle overlaps triangle template inline constexpr bool overlaps(const triangle& t1, const triangle& t2) { // TODO: return false; } // Get intersection points where point intersects with triangle template inline std::vector> intersects(const olc::v2d_generic& p, const triangle& t) { // TODO: return {}; } // Get intersection points where line segment intersects with triangle template inline std::vector> intersects(const line& l, const triangle& t) { // TODO: return {}; } // Get intersection points where rectangle intersects with triangle template inline std::vector> intersects(const rect& r, const triangle& t) { // TODO: return {}; } // Get intersection points where circle intersects with triangle template inline std::vector> intersects(const circle& c, const triangle& t) { // TODO: return {}; } // Get intersection points where triangle intersects with triangle template inline std::vector> intersects(const triangle& t1, const triangle& t2) { // TODO: return {}; } } using namespace olc::utils;