You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
500 lines
16 KiB
500 lines
16 KiB
/*
|
|
OneLoneCoder.com - Programming Balls! #2 Circle Vs Edge Collisions
|
|
"...totally overkill for pong..." - @Javidx9
|
|
|
|
|
|
Background
|
|
~~~~~~~~~~
|
|
Collision detection engines can get quite complicated. This program shows the interactions
|
|
between circular objects of different sizes and masses. Use Left mouse button to select
|
|
and drag a ball to examin static collisions, and use Right mouse button to apply velocity
|
|
to the balls as if using a pool/snooker/billiards cue.
|
|
|
|
License (OLC-3)
|
|
~~~~~~~~~~~~~~~
|
|
|
|
Copyright 2018 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
|
|
|
|
Relevant Videos
|
|
~~~~~~~~~~~~~~~
|
|
Part #1 https://youtu.be/LPzyNOHY3A4
|
|
Part #2 https://youtu.be/ebq7L2Wtbl4
|
|
|
|
Author
|
|
~~~~~~
|
|
David Barr, aka javidx9, ©OneLoneCoder 2018
|
|
*/
|
|
|
|
|
|
#include <iostream>
|
|
#include <string>
|
|
#include <algorithm>
|
|
using namespace std;
|
|
|
|
#define OLC_PGE_APPLICATION
|
|
#include "olcPixelGameEngine.h"
|
|
|
|
struct sBall
|
|
{
|
|
float px, py;
|
|
float vx, vy;
|
|
float ax, ay;
|
|
float ox, oy;
|
|
float radius;
|
|
float mass;
|
|
float friction;
|
|
int score;
|
|
int id;
|
|
float fSimTimeRemaining;
|
|
olc::Pixel col;
|
|
};
|
|
|
|
struct sLineSegment
|
|
{
|
|
float sx, sy;
|
|
float ex, ey;
|
|
float radius;
|
|
};
|
|
|
|
|
|
|
|
class CirclePhysics : public olc::PixelGameEngine
|
|
{
|
|
public:
|
|
CirclePhysics()
|
|
{
|
|
sAppName = "Circles V Edges";
|
|
}
|
|
|
|
private:
|
|
vector<sBall> vecBalls;
|
|
vector<sLineSegment> vecLines;
|
|
vector<pair<float, float>> modelCircle;
|
|
sBall* pSelectedBall = nullptr;
|
|
olc::Sprite *spriteBalls = nullptr;
|
|
sLineSegment* pSelectedLine = nullptr;
|
|
bool bSelectedLineStart = false;
|
|
|
|
void AddBall(float x, float y, float r = 5.0f, int s = 0)
|
|
{
|
|
sBall b;
|
|
b.px = x; b.py = y;
|
|
b.vx = 0; b.vy = 0;
|
|
b.ax = 0; b.ay = 0;
|
|
b.ox = 0; b.oy = 0;
|
|
b.radius = r;
|
|
b.mass = r * 10.0f;
|
|
b.friction = 0.0f;
|
|
b.score = s;
|
|
b.fSimTimeRemaining = 0.0f;
|
|
b.id = vecBalls.size();
|
|
b.col = olc::Pixel(rand() % 200 + 55, rand() % 200 + 55, rand() % 200 + 55);
|
|
vecBalls.emplace_back(b);
|
|
}
|
|
|
|
olc::Sprite spr;
|
|
|
|
public:
|
|
bool OnUserCreate()
|
|
{
|
|
|
|
float fBallRadius = 4.0f;
|
|
for (int i = 0; i <100; i++)
|
|
AddBall(((float)rand()/(float)RAND_MAX) * ScreenWidth(), ((float)rand() / (float)RAND_MAX) * ScreenHeight(), fBallRadius);
|
|
|
|
AddBall(28.0f, 33.0, fBallRadius * 3);
|
|
AddBall(28.0f, 35.0, fBallRadius * 2);
|
|
|
|
float fLineRadius = 4.0f;
|
|
vecLines.push_back({ 12.0f, 4.0f, 64.0f, 4.0f, fLineRadius });
|
|
vecLines.push_back({ 76.0f, 4.0f, 132.0f, 4.0f, fLineRadius });
|
|
vecLines.push_back({ 12.0f, 68.0f, 64.0f, 68.0f, fLineRadius });
|
|
vecLines.push_back({ 76.0f, 68.0f, 132.0f, 68.0f, fLineRadius });
|
|
vecLines.push_back({ 4.0f, 12.0f, 4.0f, 60.0f, fLineRadius });
|
|
vecLines.push_back({ 140.0f, 12.0f, 140.0f, 60.0f, fLineRadius });
|
|
return true;
|
|
}
|
|
|
|
bool OnUserUpdate(float fElapsedTime)
|
|
{
|
|
|
|
auto DoCirclesOverlap = [](float x1, float y1, float r1, float x2, float y2, float r2)
|
|
{
|
|
return fabs((x1 - x2)*(x1 - x2) + (y1 - y2)*(y1 - y2)) <= ((r1 + r2) * (r1 + r2));
|
|
};
|
|
|
|
auto IsPointInCircle = [](float x1, float y1, float r1, float px, float py)
|
|
{
|
|
return fabs((x1 - px)*(x1 - px) + (y1 - py)*(y1 - py)) < (r1 * r1);
|
|
};
|
|
|
|
if (GetMouse(0).bPressed)
|
|
{
|
|
// Check for selected ball
|
|
pSelectedBall = nullptr;
|
|
for (auto &ball : vecBalls)
|
|
{
|
|
if (IsPointInCircle(ball.px, ball.py, ball.radius, GetMouseX(), GetMouseY()))
|
|
{
|
|
pSelectedBall = &ball;
|
|
break;
|
|
}
|
|
}
|
|
|
|
// Check for selected line segment end
|
|
pSelectedLine = nullptr;
|
|
for (auto &line : vecLines)
|
|
{
|
|
if (IsPointInCircle(line.sx, line.sy, line.radius, GetMouseX(), GetMouseY()))
|
|
{
|
|
pSelectedLine = &line;
|
|
bSelectedLineStart = true;
|
|
break;
|
|
}
|
|
|
|
if (IsPointInCircle(line.ex, line.ey, line.radius, GetMouseX(), GetMouseY()))
|
|
{
|
|
pSelectedLine = &line;
|
|
bSelectedLineStart = false;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (GetMouse(0).bHeld)
|
|
{
|
|
if (pSelectedLine != nullptr)
|
|
{
|
|
if (bSelectedLineStart)
|
|
{
|
|
pSelectedLine->sx = GetMouseX();
|
|
pSelectedLine->sy = GetMouseY();
|
|
}
|
|
else
|
|
{
|
|
pSelectedLine->ex = GetMouseX();
|
|
pSelectedLine->ey = GetMouseY();
|
|
}
|
|
}
|
|
}
|
|
|
|
if (GetMouse(0).bReleased)
|
|
{
|
|
if (pSelectedBall != nullptr)
|
|
{
|
|
// Apply velocity
|
|
pSelectedBall->vx = 5.0f * ((pSelectedBall->px) - GetMouseX());
|
|
pSelectedBall->vy = 5.0f * ((pSelectedBall->py) - GetMouseY());
|
|
}
|
|
|
|
pSelectedBall = nullptr;
|
|
pSelectedLine = nullptr;
|
|
}
|
|
|
|
if (GetMouse(1).bHeld)
|
|
{
|
|
for (auto &ball : vecBalls)
|
|
{
|
|
ball.vx += (GetMouseX() - ball.px) * 0.01f;
|
|
ball.vy += (GetMouseY() - ball.py) * 0.01f;
|
|
}
|
|
}
|
|
|
|
|
|
|
|
vector<pair<sBall*, sBall*>> vecCollidingPairs;
|
|
vector<sBall*> vecFakeBalls;
|
|
|
|
// Threshold indicating stability of object
|
|
float fStable = 0.005f;
|
|
|
|
// Multiple simulation updates with small time steps permit more accurate physics
|
|
// and realistic results at the expense of CPU time of course
|
|
int nSimulationUpdates = 4;
|
|
|
|
// Multiple collision trees require more steps to resolve. Normally we would
|
|
// continue simulation until the object has no simulation time left for this
|
|
// epoch, however this is risky as the system may never find stability, so we
|
|
// can clamp it here
|
|
int nMaxSimulationSteps = 15;
|
|
|
|
// Break up the frame elapsed time into smaller deltas for each simulation update
|
|
float fSimElapsedTime = fElapsedTime / (float)nSimulationUpdates;
|
|
|
|
// Main simulation loop
|
|
for (int i = 0; i < nSimulationUpdates; i++)
|
|
{
|
|
// Set all balls time to maximum for this epoch
|
|
for (auto &ball : vecBalls)
|
|
ball.fSimTimeRemaining = fSimElapsedTime;
|
|
|
|
// Erode simulation time on a per objec tbasis, depending upon what happens
|
|
// to it during its journey through this epoch
|
|
for (int j = 0; j < nMaxSimulationSteps; j++)
|
|
{
|
|
// Update Ball Positions
|
|
for (auto &ball : vecBalls)
|
|
{
|
|
if (ball.fSimTimeRemaining > 0.0f)
|
|
{
|
|
ball.ox = ball.px; // Store original position this epoch
|
|
ball.oy = ball.py;
|
|
|
|
ball.ax = -ball.vx * 0.8f; // Apply drag and gravity
|
|
ball.ay = -ball.vy * 0.8f + 100.0f;
|
|
|
|
ball.vx += ball.ax * ball.fSimTimeRemaining; // Update Velocity
|
|
ball.vy += ball.ay * ball.fSimTimeRemaining;
|
|
|
|
ball.px += ball.vx * ball.fSimTimeRemaining; // Update position
|
|
ball.py += ball.vy * ball.fSimTimeRemaining;
|
|
|
|
// Crudely wrap balls to screen - note this cause issues when collisions occur on screen boundaries
|
|
if (ball.px < 0) ball.px += (float)ScreenWidth();
|
|
if (ball.px >= ScreenWidth()) ball.px -= (float)ScreenWidth();
|
|
if (ball.py < 0) ball.py += (float)ScreenHeight();
|
|
if (ball.py >= ScreenHeight()) ball.py -= (float)ScreenHeight();
|
|
|
|
// Stop ball when velocity is neglible
|
|
if (fabs(ball.vx*ball.vx + ball.vy*ball.vy) < fStable)
|
|
{
|
|
ball.vx = 0;
|
|
ball.vy = 0;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
// Work out static collisions with walls and displace balls so no overlaps
|
|
for (auto &ball : vecBalls)
|
|
{
|
|
float fDeltaTime = ball.fSimTimeRemaining;
|
|
|
|
// Against Edges
|
|
for (auto &edge : vecLines)
|
|
{
|
|
// Check that line formed by velocity vector, intersects with line segment
|
|
float fLineX1 = edge.ex - edge.sx;
|
|
float fLineY1 = edge.ey - edge.sy;
|
|
|
|
float fLineX2 = ball.px - edge.sx;
|
|
float fLineY2 = ball.py - edge.sy;
|
|
|
|
float fEdgeLength = fLineX1 * fLineX1 + fLineY1 * fLineY1;
|
|
|
|
// This is nifty - It uses the DP of the line segment vs the line to the object, to work out
|
|
// how much of the segment is in the "shadow" of the object vector. The min and max clamp
|
|
// this to lie between 0 and the line segment length, which is then normalised. We can
|
|
// use this to calculate the closest point on the line segment
|
|
float t = std::max(0.0f, std::min(fEdgeLength, (fLineX1 * fLineX2 + fLineY1 * fLineY2))) / fEdgeLength;
|
|
|
|
// Which we do here
|
|
float fClosestPointX = edge.sx + t * fLineX1;
|
|
float fClosestPointY = edge.sy + t * fLineY1;
|
|
|
|
// And once we know the closest point, we can check if the ball has collided with the segment in the
|
|
// same way we check if two balls have collided
|
|
float fDistance = sqrtf((ball.px - fClosestPointX)*(ball.px - fClosestPointX) + (ball.py - fClosestPointY)*(ball.py - fClosestPointY));
|
|
|
|
if (fDistance <= (ball.radius + edge.radius))
|
|
{
|
|
// Collision has occurred - treat collision point as a ball that cannot move. To make this
|
|
// compatible with the dynamic resolution code below, we add a fake ball with an infinite mass
|
|
// so it behaves like a solid object when the momentum calculations are performed
|
|
sBall *fakeball = new sBall();
|
|
fakeball->radius = edge.radius;
|
|
fakeball->mass = ball.mass * 0.8f;
|
|
fakeball->px = fClosestPointX;
|
|
fakeball->py = fClosestPointY;
|
|
fakeball->vx = -ball.vx; // We will use these later to allow the lines to impart energy into ball
|
|
fakeball->vy = -ball.vy; // if the lines are moving, i.e. like pinball flippers
|
|
|
|
// Store Fake Ball
|
|
vecFakeBalls.push_back(fakeball);
|
|
|
|
// Add collision to vector of collisions for dynamic resolution
|
|
vecCollidingPairs.push_back({ &ball, fakeball });
|
|
|
|
// Calculate displacement required
|
|
float fOverlap = 1.0f * (fDistance - ball.radius - fakeball->radius);
|
|
|
|
// Displace Current Ball away from collision
|
|
ball.px -= fOverlap * (ball.px - fakeball->px) / fDistance;
|
|
ball.py -= fOverlap * (ball.py - fakeball->py) / fDistance;
|
|
}
|
|
}
|
|
|
|
// Against other balls
|
|
for (auto &target : vecBalls)
|
|
{
|
|
if (ball.id != target.id) // Do not check against self
|
|
{
|
|
if (DoCirclesOverlap(ball.px, ball.py, ball.radius, target.px, target.py, target.radius))
|
|
{
|
|
// Collision has occured
|
|
vecCollidingPairs.push_back({ &ball, &target });
|
|
|
|
// Distance between ball centers
|
|
float fDistance = sqrtf((ball.px - target.px)*(ball.px - target.px) + (ball.py - target.py)*(ball.py - target.py));
|
|
|
|
// Calculate displacement required
|
|
float fOverlap = 0.5f * (fDistance - ball.radius - target.radius);
|
|
|
|
// Displace Current Ball away from collision
|
|
ball.px -= fOverlap * (ball.px - target.px) / fDistance;
|
|
ball.py -= fOverlap * (ball.py - target.py) / fDistance;
|
|
|
|
// Displace Target Ball away from collision - Note, this should affect the timing of the target ball
|
|
// and it does, but this is absorbed by the target ball calculating its own time delta later on
|
|
target.px += fOverlap * (ball.px - target.px) / fDistance;
|
|
target.py += fOverlap * (ball.py - target.py) / fDistance;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Time displacement - we knew the velocity of the ball, so we can estimate the distance it should have covered
|
|
// however due to collisions it could not do the full distance, so we look at the actual distance to the collision
|
|
// point and calculate how much time that journey would have taken using the speed of the object. Therefore
|
|
// we can now work out how much time remains in that timestep.
|
|
float fIntendedSpeed = sqrtf(ball.vx * ball.vx + ball.vy * ball.vy);
|
|
float fIntendedDistance = fIntendedSpeed * ball.fSimTimeRemaining;
|
|
float fActualDistance = sqrtf((ball.px - ball.ox)*(ball.px - ball.ox) + (ball.py - ball.oy)*(ball.py - ball.oy));
|
|
float fActualTime = fActualDistance / fIntendedSpeed;
|
|
|
|
// After static resolution, there may be some time still left for this epoch, so allow simulation to continue
|
|
ball.fSimTimeRemaining = ball.fSimTimeRemaining - fActualTime;
|
|
}
|
|
|
|
// Now work out dynamic collisions
|
|
float fEfficiency = 1.00f;
|
|
for (auto c : vecCollidingPairs)
|
|
{
|
|
sBall *b1 = c.first, *b2 = c.second;
|
|
|
|
// Distance between balls
|
|
float fDistance = sqrtf((b1->px - b2->px)*(b1->px - b2->px) + (b1->py - b2->py)*(b1->py - b2->py));
|
|
|
|
// Normal
|
|
float nx = (b2->px - b1->px) / fDistance;
|
|
float ny = (b2->py - b1->py) / fDistance;
|
|
|
|
// Tangent
|
|
float tx = -ny;
|
|
float ty = nx;
|
|
|
|
// Dot Product Tangent
|
|
float dpTan1 = b1->vx * tx + b1->vy * ty;
|
|
float dpTan2 = b2->vx * tx + b2->vy * ty;
|
|
|
|
// Dot Product Normal
|
|
float dpNorm1 = b1->vx * nx + b1->vy * ny;
|
|
float dpNorm2 = b2->vx * nx + b2->vy * ny;
|
|
|
|
// Conservation of momentum in 1D
|
|
float m1 = fEfficiency * (dpNorm1 * (b1->mass - b2->mass) + 2.0f * b2->mass * dpNorm2) / (b1->mass + b2->mass);
|
|
float m2 = fEfficiency * (dpNorm2 * (b2->mass - b1->mass) + 2.0f * b1->mass * dpNorm1) / (b1->mass + b2->mass);
|
|
|
|
// Update ball velocities
|
|
b1->vx = tx * dpTan1 + nx * m1;
|
|
b1->vy = ty * dpTan1 + ny * m1;
|
|
b2->vx = tx * dpTan2 + nx * m2;
|
|
b2->vy = ty * dpTan2 + ny * m2;
|
|
}
|
|
|
|
// Remove collisions
|
|
vecCollidingPairs.clear();
|
|
|
|
// Remove fake balls
|
|
for (auto &b : vecFakeBalls) delete b;
|
|
vecFakeBalls.clear();
|
|
}
|
|
}
|
|
|
|
// Clear Screen
|
|
FillRect(0, 0, ScreenWidth(), ScreenHeight(), olc::Pixel(0, 0, 0));
|
|
|
|
// Draw Lines
|
|
for (auto line : vecLines)
|
|
{
|
|
FillCircle(line.sx, line.sy, line.radius, olc::Pixel(255,255,255));
|
|
FillCircle(line.ex, line.ey, line.radius, olc::Pixel(128, 128, 128));
|
|
|
|
float nx = -(line.ey - line.sy);
|
|
float ny = (line.ex - line.sx);
|
|
float d = sqrt(nx*nx + ny * ny);
|
|
nx /= d;
|
|
ny /= d;
|
|
|
|
DrawLine((line.sx + nx * line.radius), (line.sy + ny * line.radius), (line.ex + nx * line.radius), (line.ey + ny * line.radius), olc::Pixel(255, 255, 255));
|
|
DrawLine((line.sx - nx * line.radius), (line.sy - ny * line.radius), (line.ex - nx * line.radius), (line.ey - ny * line.radius), olc::Pixel(255, 255, 255));
|
|
}
|
|
|
|
// Draw Balls
|
|
for (auto ball : vecBalls)
|
|
{
|
|
FillCircle(ball.px, ball.py, ball.radius, ball.col);
|
|
|
|
}
|
|
|
|
// Draw Cue
|
|
if (pSelectedBall != nullptr)
|
|
DrawLine(pSelectedBall->px, pSelectedBall->py, GetMouseX(), GetMouseY(), olc::Pixel(0, 0, 255));
|
|
|
|
|
|
|
|
|
|
return true;
|
|
}
|
|
|
|
};
|
|
|
|
|
|
int main()
|
|
{
|
|
|
|
CirclePhysics game;
|
|
if (game.Construct(320, 240, 4, 4))
|
|
game.Start();
|
|
else
|
|
wcout << L"Could not construct console" << endl;
|
|
|
|
return 0;
|
|
};
|
|
|
|
|