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/*
OneLoneCoder.com - Programming Balls! #2 Circle Vs Edge Collisions
"...totally overkill for pong..." - @Javidx9
Disclaimer
~~~~~~~~~~
I don't care what you use this for. It's intended to be educational, and perhaps
to the oddly minded - a little bit of fun. Please hack this, change it and use it
in any way you see fit. BUT, you acknowledge that I am not responsible for anything
bad that happens as a result of your actions. However, if good stuff happens, I
would appreciate a shout out, or at least give the blog some publicity for me.
Cheers!
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.
Author
~~~~~~
Twitter: @javidx9
Blog: www.onelonecoder.com
Twitch: https://www.twitch.tv/javidx9
Discord: https://discord.gg/WhwHUMV
Video:
~~~~~~
Part #1 https://youtu.be/LPzyNOHY3A4
Part #2 https://youtu.be/ebq7L2Wtbl4
Last Updated: 18/02/2017
*/
#include <iostream>
#include <string>
#include <algorithm>
using namespace std;
#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);
}
public:
bool OnUserCreate()
{
float fBallRadius = 4.0f;
for (int i = 0; i <300; 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(640, 480, 2, 2))
game.Start();
else
wcout << L"Could not construct console" << endl;
return 0;
};