I have came up to something like this:
float MinRe = -2.0f; // real
float MaxRe = 1.0f;
float MinIm = -1.0f; // imaginary
float MaxIm = MinIm + (MaxRe - MinRe) * WindowData.Height / WindowData.Width;
float Re_factor = (MaxRe - MinRe) / (WindowData.Width - 1);
float Im_factor = (MaxIm - MinIm) / (WindowData.Height - 1);
int MaxIterations = 50;
int iter=0;
for (int y = 0; y < WindowData.Height; ++y)
{
double c_im = MaxIm - y * Im_factor; // complex imaginary
for (int x = 0; x < WindowData.Width; ++x)
{
double c_re = MinRe + x * Re_factor; // complex real
// calculate mandelbrot set
double Z_re = c_re, Z_im = c_im; // Set Z = c
bool isInside = true;
for (iter=0; iter < MaxIterations; ++iter)
{
double Z_re2 = Z_re * Z_re, Z_im2 = Z_im * Z_im;
if (Z_re2 + Z_im2 > 4)
{
isInside = false;
break;
}
Z_im = 2 * Z_re * Z_im + c_im;
Z_re = Z_re2 - Z_im2 + c_re;
}
if(isInside)
{
GL.Color3(0, 0, 0);
GL.Vertex2(x, y);
}
}
}
I have tried in few ways, but most of the times ended with single color around set, or whole screen with the same color.
How to set up colors properly?
When I tried this, I just set the outside colour to RGB (value, value, 1) where value is (in your parlance) the fourth root of (iter / MaxIterations). That comes out as a quite nice fade from white to blue. Not so bright as duffymo's, though, but with less of a 'stripy' effect.
Here's how I did it: check out the Source Forge repository for source code.
http://craicpropagation.blogspot.com/2011/03/mandelbrot-set.html
I found empirically that if you use something like that: color(R,G,B) where R,G,B takes values from 0 to 255.
Then this function gives a really good looking result. f(x,f,p) = 255*(cos(sqrt(x)*f + p))^2 where x denotes the current iteration, f the frequency and p the phase.
And then apply the function for each color argument with a phase difference of 120:
color(f(iter,1,0),f(iter,1,120),f(iter,1,240)
try to display result of your computation. Check what input is required by your coloring function
See also
http://en.wikibooks.org/wiki/Fractals/Iterations_in_the_complex_plane/Mandelbrot_set
HTH
Adam
Related
I'm using the Visual Studio profiler for the first time and I'm trying to interpret the results. Looking at the percentages on the left, I found this subtraction's time cost a bit strange:
Other parts of the code contain more complex expressions, like:
Even a simple multiplication seems way faster than the subtraction :
Other multiplications take way longer and I really don't get why, like this :
So, I guess my question is if there is anything weird going on here.
Complex expressions take longer than that subtraction and some expressions take way longer than similar other ones. I run the profiler several times and the distribution of the percentages is always like this. Am I just interpreting this wrong?
Update:
I was asked to give the profile for the whole function so here it is, even though it's a bit big. I ran the function inside a for loop for 1 minute and got 50k samples. The function contains a double loop. I include the text first for ease, followed by the pictures of profiling. Note that the code in text is a bit updated.
for (int i = 0; i < NUMBER_OF_CONTOUR_POINTS; i++) {
vec4 contourPointV(contour3DPoints[i], 1);
float phi = angles[i];
float xW = pose[0][0] * contourPointV.x + pose[1][0] * contourPointV.y + contourPointV.z * pose[2][0] + pose[3][0];
float yW = pose[0][1] * contourPointV.x + pose[1][1] * contourPointV.y + contourPointV.z * pose[2][1] + pose[3][1];
float zW = pose[0][2] * contourPointV.x + pose[1][2] * contourPointV.y + contourPointV.z * pose[2][2] + pose[3][2];
float x = -G_FU_STRICT * xW / zW;
float y = -G_FV_STRICT * yW / zW;
x = (x + 1) * G_WIDTHo2;
y = (y + 1) * G_HEIGHTo2;
y = G_HEIGHT - y;
phi -= extraTheta;
if (phi < 0)phi += CV_PI2;
int indexForTable = phi * oneKoverPI;
//vec2 ray(cos(phi), sin(phi));
vec2 ray(cos_pre[indexForTable], sin_pre[indexForTable]);
vec2 ray2(-ray.x, -ray.y);
float outerStepX = ray.x * step;
float outerStepY = ray.y * step;
cv::Point2f outerPoint(x + outerStepX, y + outerStepY);
cv::Point2f innerPoint(x - outerStepX, y - outerStepY);
cv::Point2f contourPointCV(x, y);
cv::Point2f contourPointCVcopy(x, y);
bool cut = false;
if (!isInView(outerPoint.x, outerPoint.y) || !isInView(innerPoint.x, innerPoint.y)) {
cut = true;
}
bool outside2 = true; bool outside1 = true;
if (cut) {
outside2 = myClipLine(contourPointCV.x, contourPointCV.y, outerPoint.x, outerPoint.y, G_WIDTH - 1, G_HEIGHT - 1);
outside1 = myClipLine(contourPointCVcopy.x, contourPointCVcopy.y, innerPoint.x, innerPoint.y, G_WIDTH - 1, G_HEIGHT - 1);
}
myIterator innerRayMine(contourPointCVcopy, innerPoint);
myIterator outerRayMine(contourPointCV, outerPoint);
if (!outside1) {
innerRayMine.end = true;
innerRayMine.prob = true;
}
if (!outside2) {
outerRayMine.end = true;
innerRayMine.prob = true;
}
vec2 normal = -ray;
float dfdxTerm = -normal.x;
float dfdyTerm = normal.y;
vec3 point3D = vec3(xW, yW, zW);
cv::Point contourPoint((int)x, (int)y);
float Xc = point3D.x; float Xc2 = Xc * Xc; float Yc = point3D.y; float Yc2 = Yc * Yc; float Zc = point3D.z; float Zc2 = Zc * Zc;
float XcYc = Xc * Yc; float dfdxFu = dfdxTerm * G_FU; float dfdyFv = dfdyTerm * G_FU; float overZc2 = 1 / Zc2; float overZc = 1 / Zc;
pixelJacobi[0] = (dfdyFv * (Yc2 + Zc2) + dfdxFu * XcYc) * overZc2;
pixelJacobi[1] = (-dfdxFu * (Xc2 + Zc2) - dfdyFv * XcYc) * overZc2;
pixelJacobi[2] = (-dfdyFv * Xc + dfdxFu * Yc) * overZc;
pixelJacobi[3] = -dfdxFu * overZc;
pixelJacobi[4] = -dfdyFv * overZc;
pixelJacobi[5] = (dfdyFv * Yc + dfdxFu * Xc) * overZc2;
float commonFirstTermsSum = 0;
float commonFirstTermsSquaredSum = 0;
int test = 0;
while (!innerRayMine.end) {
test++;
cv::Point xy = innerRayMine.pos(); innerRayMine++;
int x = xy.x;
int y = xy.y;
float dx = x - contourPoint.x;
float dy = y - contourPoint.y;
vec2 dxdy(dx, dy);
float raw = -glm::dot(dxdy, normal);
float heavisideTerm = heaviside_pre[(int)raw * 100 + 1000];
float deltaTerm = delta_pre[(int)raw * 100 + 1000];
const Vec3b rgb = ante[y * 640 + x];
int red = rgb[0]; int green = rgb[1]; int blue = rgb[2];
red = red >> 3; red = red << 10; green = green >> 3; green = green << 5; blue = blue >> 3;
int colorIndex = red + green + blue;
pF = pFPointer[colorIndex];
pB = pBPointer[colorIndex];
float denAsMul = 1 / (pF + pB + 0.000001);
pF = pF * denAsMul;
float pfMinusPb = 2 * pF - 1;
float denominator = heavisideTerm * (pfMinusPb)+pB + 0.000001;
float commonFirstTerm = -pfMinusPb / denominator * deltaTerm;
commonFirstTermsSum += commonFirstTerm;
commonFirstTermsSquaredSum += commonFirstTerm * commonFirstTerm;
}
}
Visual Studio profiles by sampling: it interrupts execution often and records the value of the instruction pointer; it then maps it to the source and calculates the frequency of hitting that line.
There are few issues with that: it's not always possible to figure out which line produced a specific assembly instruction in the optimized code.
One trick I use is to move the code of interest into a separate function and declare it with __declspec(noinline) .
In your example, are you sure the subtraction was performed as many times as multiplication? I would be more puzzled by the difference in subsequent multiplication (0.39% and 0.53%)
Update:
I believe that the following lines:
float phi = angles[i];
and
phi -= extraTheta;
got moved together in assembly and the time spent getting angles[i] was added to that subtraction line.
I don't know much about multi-threading and I have no idea why this is happening so I'll just get to the point.
I'm processing an image and divide the image in 4 parts and pass each part to each thread(essentially I pass the indices of the first and last pixel rows of each part). For example, if the image has 1000 rows, each thread will process 250 of them. I can go in details about my implementation and what I'm trying to achieve in case it can help you. For now I provide the code executed by the threads in case you can detect why this is happening. I don't know if it's relevant but in both cases(1 thread or 4 threads) the process takes around 15ms and pfUMap and pbUMap are unordered maps.
void jacobiansThread(int start, int end,vector<float> &sJT,vector<float> &sJTJ) {
uchar* rgbPointer;
float* depthPointer;
float* sdfPointer;
float* dfdxPointer; float* dfdyPointer;
float fov = radians(45.0);
float aspect = 4.0 / 3.0;
float focal = 1 / (glm::tan(fov / 2));
float fu = focal * cols / 2 / aspect;
float fv = focal * rows / 2;
float strictFu = focal / aspect;
float strictFv = focal;
vector<float> pixelJacobi(6, 0);
for (int y = start; y <end; y++) {
rgbPointer = sceneImage.ptr<uchar>(y);
depthPointer = depthBuffer.ptr<float>(y);
dfdxPointer = dfdx.ptr<float>(y);
dfdyPointer = dfdy.ptr<float>(y);
sdfPointer = sdf.ptr<float>(y);
for (int x = roiX.x; x <roiX.y; x++) {
float deltaTerm;// = deltaPointer[x];
float raw = sdfPointer[x];
if (raw > 8.0)continue;
float dirac = (1.0f / float(CV_PI)) * (1.2f / (raw * 1.44f * raw + 1.0f));
deltaTerm = dirac;
vec3 rgb(rgbPointer[x * 3], rgbPointer[x * 3+1], rgbPointer[x * 3+2]);
vec3 bin = rgbToBin(rgb, numberOfBins);
int indexOfColor = bin.x * numberOfBins * numberOfBins + bin.y * numberOfBins + bin.z;
float s3 = glfwGetTime();
float pF = pfUMap[indexOfColor];
float pB = pbUMap[indexOfColor];
float heavisideTerm;
heavisideTerm = HEAVISIDE(raw);
float denominator = (heavisideTerm * pF + (1 - heavisideTerm) * pB) + 0.000001;
float commonFirstTerm = -(pF - pB) / denominator * deltaTerm;
if (pF == pB)continue;
vec3 pixel(x, y, depthPointer[x]);
float dfdxTerm = dfdxPointer[x];
float dfdyTerm = -dfdyPointer[x];
if (pixel.z == 1) {
cv::Point c = findClosestContourPoint(cv::Point(x, y), dfdxTerm, -dfdyTerm, abs(raw));
if (c.x == -1)continue;
pixel = vec3(c.x, c.y, depthBuffer.at<float>(cv::Point(c.x, c.y)));
}
vec3 point3D = pixel;
pixelToViewFast(point3D, cols, rows, strictFu, strictFv);
float Xc = point3D.x; float Xc2 = Xc * Xc; float Yc = point3D.y; float Yc2 = Yc * Yc; float Zc = point3D.z; float Zc2 = Zc * Zc;
pixelJacobi[0] = dfdyTerm * ((fv * Yc2) / Zc2 + fv) + (dfdxTerm * fu * Xc * Yc) / Zc2;
pixelJacobi[1] = -dfdxTerm * ((fu * Xc2) / Zc2 + fu) - (dfdyTerm * fv * Xc * Yc) / Zc2;
pixelJacobi[2] = -(dfdyTerm * fv * Xc) / Zc + (dfdxTerm * fu * Yc) / Zc;
pixelJacobi[3] = -(dfdxTerm * fu) / Zc;
pixelJacobi[4] = -(dfdyTerm * fv) / Zc;
pixelJacobi[5] = (dfdyTerm * fv * Yc) / Zc2 + (dfdxTerm * fu * Xc) / Zc2;
float weightingTerm = -1.0 / log(denominator);
for (int i = 0; i < 6; i++) {
pixelJacobi[i] *= commonFirstTerm;
sJT[i] += pixelJacobi[i];
}
for (int i = 0; i < 6; i++) {
for (int j = i; j < 6; j++) {
sJTJ[i * 6 + j] += weightingTerm * pixelJacobi[i] * pixelJacobi[j];
}
}
}
}
}
This is the part where I call each thread:
vector<std::thread> myThreads;
float step = (roiY.y - roiY.x) / numberOfThreads;
vector<vector<float>> tsJT(numberOfThreads, vector<float>(6, 0));
vector<vector<float>> tsJTJ(numberOfThreads, vector<float>(36, 0));
for (int i = 0; i < numberOfThreads; i++) {
int start = roiY.x+i * step;
int end = start + step;
if (end > roiY.y)end = roiY.y;
myThreads.push_back(std::thread(&pwp3dV2::jacobiansThread, this,start,end,std::ref(tsJT[i]), std::ref(tsJTJ[i])));
}
vector<float> sJT(6, 0);
vector<float> sJTJ(36, 0);
for (int i = 0; i < numberOfThreads; i++)myThreads[i].join();
Other Notes
To measure time I used glfwGetTime() before and right after the second code snippet. The measurements vary but the average is about 15ms as I mentioned, for both implementations.
Starting a thread has significant overhead, which might not be worth the time if you have only 15 milliseconds worth of work.
The common solution is to keep threads running in the background and send them data when you need them, instead of calling the std::thread constructor to create a new thread every time you have some work to do.
Pure spectaculation but two things might be preventing the full power of parallelization.
Processing speed is limited by the memory bus. Cores will wait until data is loaded before continuing.
Data sharing between cores. Some caches are core specific. If memory is shared between cores, data must traverse down to shared cache before loading.
On Linux you can use Perf to check for cache misses.
if you wanna better time you need to split a cycle runs from a counter, for this you need to do some preprocessing. some fast stuff like make an array of structures with headers for each segment or so. if say you can't mind anything better you can just do vector<int> with values of a counter. Then do for_each(std::execution::par,...) on that. way much faster.
for timings there's
auto t2 = std::chrono::system_clock::now();
std::chrono::milliseconds f = std::chrono::duration_cast<std::chrono::milliseconds>(t2 - t1);
Closed. This question needs debugging details. It is not currently accepting answers.
Edit the question to include desired behavior, a specific problem or error, and the shortest code necessary to reproduce the problem. This will help others answer the question.
Closed 8 years ago.
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I'm trying to implement a collision detection system, and it is working for the most part, no overlapping (or at most very little overlapping) of characters, and wall collisions. The problem is that i have a bunch of characters following a player and just run into it, and when there are about 15-20 of those characters all pushing at the player, it can lead to the player or other objects being pushed through walls.
My code works as follows, first I update all of the characters, and they check collisions against each other, then I check for any character collisions with the walls. I feel like the problem is that the eventual push of all the characters leads to pushing one or more of the characters large distances, but i'm not sure how to fix the problem. Code below if necessary, a thorough explanation of how to fix this is also sufficient.
Character update/collisions:
void CharacterManager::updateAll(float elapsedTime)
{
for(std::vector<std::shared_ptr<Character>>::iterator i = _characters.begin(); i != _characters.end(); i++) {
(*i)->update(elapsedTime);
}
collisions();
}
void CharacterManager::collisions()
{
for(std::vector<std::shared_ptr<Character>>::iterator i = _characters.begin(); i != _characters.end(); i++) {
for(std::vector<std::shared_ptr<Character>>::iterator j = _characters.begin(); j != _characters.end(); j++) {
if(i == j) continue;
float xi = (*i)->position().x;
float yi = (*i)->position().y;
float xj = (*j)->position().x;
float yj = (*j)->position().y;
float dx = xi - xj;
float dy = yi - yj;
float distSquared = dx * dx + dy * dy;
float ri = (*i)->xRect().width/2;
float rj = (*j)->xRect().width/2;
if(distSquared < (ri + rj) * (ri + rj)) {
// fix collisions
float angle = atan2f(dy,dx);
float overlap = (ri + rj) - sqrt(distSquared);
if(xi < xj) {
if(yi < yj) {
(*i)->position(xi - cosf(angle) * overlap/2, yi - sinf(angle) * overlap/2);
(*j)->position(xj + cosf(angle) * overlap/2, yj + sinf(angle) * overlap/2);
} else {
(*i)->position(xi - cosf(angle) * overlap/2, yi + sinf(angle) * overlap/2);
(*j)->position(xj + cosf(angle) * overlap/2, yj - sinf(angle) * overlap/2);
}
} else {
if(yi < yj) {
(*i)->position(xi + cosf(angle) * overlap/2, yi - sinf(angle) * overlap/2);
(*j)->position(xj - cosf(angle) * overlap/2, yj + sinf(angle) * overlap/2);
} else {
(*i)->position(xi + cosf(angle) * overlap/2, yi + sinf(angle) * overlap/2);
(*j)->position(xj - cosf(angle) * overlap/2, yj - sinf(angle) * overlap/2);
}
}
// calc new velocities
float vxi = (*i)->velocity().x;
float vyi = (*i)->velocity().y;
float vxj = (*j)->velocity().x;
float vyj = (*j)->velocity().y;
float vx = vxj - vxi;
float vy = vyj - vyi;
float dotProduct = dx * vx + dy * vy;
if(dotProduct >= 0) {
float collisionScale = dotProduct / distSquared;
float xCollision = dx * collisionScale;
float yCollision = dy * collisionScale;
float combinedMass = (*i)->weight() + (*j)->weight();
float collisionWeightA = 2 * (*j)->weight() / combinedMass;
float collisionWeightB = 2 * (*i)->weight() / combinedMass;
(*i)->velocity(vxi + collisionWeightA * xCollision, vyi + collisionWeightA * yCollision);
(*j)->velocity(vxj - collisionWeightB * xCollision, vyj - collisionWeightB * yCollision);
}
}
}
}
}
Wall collisions:
void Stage::characterCrossCollisions(std::shared_ptr<Character> character)
{
for(std::vector<std::shared_ptr<Tile>>::iterator tile = tiles.begin(); tile != tiles.end(); tile++) {
if(!(*tile)->walkable) {
sf::Rect<float> cxr = character->xRect();
sf::Rect<float> cyr = character->yRect();
sf::Rect<float> tr = (*tile)->getRect();
if(!(cxr.left > tr.left + tr.width ||
cxr.left + cxr.width < tr.left ||
cxr.top > tr.top + tr.height ||
cxr.top + cxr.height < tr.top)) {
float ox = 0;
if(character->position().x > (*tile)->position().x) {
ox = cxr.left - (tr.left + tr.width);
}
else {
ox = cxr.left + cxr.width - tr.left;
}
character->position(character->position().x - ox, character->position().y);
}
if(!(cyr.left > tr.left + tr.width ||
cyr.left + cyr.width < tr.left ||
cyr.top > tr.top + tr.height ||
cyr.top + cyr.height < tr.top)) {
float oy = 0;
if(character->position().y > (*tile)->position().y) {
oy = cyr.top - (tr.top + tr.height);
}
else {
oy = cyr.top + cyr.height - tr.top;
}
character->position(character->position().x, character->position().y - oy);
}
}
}
}
Generally you run the collision code for two objects when the two objects intersect each other. Two objects intersect each other if they share at least one point in space. But the problem with this is that if objects are intersecting that means that there was a collision in the past and not that there is a collision right now.
Ideal collision code should calculate the energy transfer and modify the velocity of the objects at the exact moment when the objects touch each other. Good collision code would roll back time and try to find out the moment when the collision happened, calculate the new velocities based on that moment and roll the time forward. However these are rather hard to do and might be overkill for a simple computer game.
The easy but robust solution that I can recommend to you is:
move the objects forward
check for collision, if no collision repeat from beginning
move the objects away from each other until they don't collide proportional to their mass. Since walls don't move you can consider that they have infinite mass and only move the characters
recalculate the velocity of the colliding objects after the objects don't intersect anymore
repeat
You can also use a constraint like 'objects can never intersect the wall' and you apply this constraint by checking if a new position is valid when moving the characters. And you only move the character if the new position is valid.
This small example should exemplify validation. Make the position only updatable with the MoveTo() method and inside the MoveTo() method you can validate the new position and return whether the move was successful. If the move wasn't successful, the caller will probably want to take a different action. (move the object less until exactly the contact position and this would be the perfect opportunity to process the collision)
class Character{
bool MoveTo(float x, float y)
{
if (this.isValidPosition(x,y))
{
this.x = x;
this.y = y;
return true;
}
return false;
}
void Update(float deltaTime)
{
float new_x = x + velocity_x*deltaTime;
float new_y = y + velocity_y*deltaTime;
if (!this.MoveTo(new_x, new_y))
{
Console.Write("cannot move " + this + " to the new position, something is already there\n");
}
}
}
I copied this ellipse code directly from the opengl textbook:
void ellipseMidpoint (int xCenter, int yCenter, int Rx, int Ry)
{
int Rx2 = Rx * Rx;
int Ry2 = Ry * Ry;
int twoRx2 = 2 * Rx2;
int twoRy2 = 2 * Ry2;
int p;
int x = 0;
int y = Ry;
int px = 0;
int py = twoRx2 * y;
//initial points in both quadrants
ellipsePlotPoints (xCenter, yCenter, x, y);
//Region 1
p = round (Ry2 - (Rx2 * Ry) + (0.25 * Rx2));
while (px < py) {
x++;
px += twoRy2;
if (p < 0)
p += Ry2 + px;
else {
y--;
py -= twoRx2;
p += Ry2 + px - py;
}
ellipsePlotPoints (xCenter, yCenter, x, y);
}
//Region 2
p = round (Ry2 * (x+0.5) * (x+0.5) + Rx2 * (y-1) * (y-1) - Rx2 * Ry2);
while (y > 0) {
y--;
py -= twoRx2;
if (p > 0)
p += Rx2 - py;
else {
x++;
px += twoRy2;
p += Rx2 - py + px;
}
ellipsePlotPoints (xCenter, yCenter, x, y);
}
}
void ellipsePlotPoints (int xCenter, int yCenter, int x, int y)
{
setPixel (xCenter + x, yCenter + y);
setPixel (xCenter - x, yCenter + y);
setPixel (xCenter + x, yCenter - y);
setPixel (xCenter - x, yCenter - y);
}
void setPixel (GLint xPos, GLint yPos)
{
glBegin (GL_POINTS);
glVertex2i(xPos, yPos);
glEnd();
}
The smaller ellipses seem to be fine but the larger ones are pointy and sort of flat at the ends.
Any ideas why?
Here is a current screenshot:
I think you're encountering overflow. I played with your code. While I never saw exactly the same "lemon" type shapes from your pictures, things definitely fell apart at large sizes, and it was caused by overflowing the range of the int variables used in the code.
For example, look at one of the first assignments:
int py = twoRx2 * y;
If you substitute, this becomes:
int py = 2 * Rx * Rx * Ry;
If you use a value of 1000 each for Rx and Ry, this is 2,000,000,000. Which is very close to the 2^31 - 1 top of the range of a 32-bit int.
If you want to use this algorithm for larger sizes, you could use 64-bit integer variables. Depending on your system, the type would be long or long long. Or more robustly, int64_t after including <stdint.h>.
Now, if all you want to do is draw an ellipsis with OpenGL, there are much better ways. The Bresenham type algorithms used in your code are ideal if you need to draw a curve pixel by pixel. But OpenGL is a higher level API, which knows how to render more complex primitives than just pixels. For a curve, you will most typically use a connected set of line segments to approximate the curve. OpenGL will then take care of turning those line segments into pixels.
The simplest way to draw an ellipsis is to directly apply the parametric representation. With phi an angle between 0 and PI, and using the naming from your code, the points on the ellipsis are:
x = xCenter + Rx * cos(phi)
y = yCenter + Ry * sin(phi)
You can use an increment for phi that meets your precision requirements, and the code will look something to generate an ellipsis approximated by DIV_COUNT points will look something like this:
float angInc = 2.0f * m_PI / (float)DIV_COUNT;
float ang = 0.0f;
glBegin(GL_LINE_LOOP);
for (int iDiv = 0; iDiv < DIV_COUNT; ++iDiv) {
ang += angInc;
float x = xCenter + Rx * cos(ang);
float y = yCenter + Ry * sin(ang);
glVertex2f(x, y);
glEnd();
If you care about efficiency, you can avoid calculating the trigonometric functions for each point, and apply an incremental rotation to calculate each point from the previous one:
float angInc = 2.0f * M_PI / (float)DIV_COUNT;
float cosInc = cos(angInc);
float sinInc = sin(angInc);
float cosAng = 1.0f;
float sinAng = 0.0f
glBegin(GL_LINE_LOOP);
for (int iDiv = 0; iDiv < DIV_COUNT; ++iDiv) {
float newCosAng = cosInc * cosAng - sinInc * sinAng;
sinAng = sinInc * cosAng + cosInc * sinAng;
cosAng = newCosAng;
float x = xCenter + Rx * cosAng;
float y = yCenter + Ry * sinAng;
glVertex2f(x, y);
glEnd();
This code is of course just for illustrating the math, and to get you started. In reality, you should use current OpenGL rendering methods, which includes vertex buffers, etc.
i am working on an implementation of the Separting Axis Theorem for use in 2D games. It kind of works but just kind of.
I use it like this:
bool penetration = sat(c1, c2) && sat(c2, c1);
Where c1 and c2 are of type Convex, defined as:
class Convex
{
public:
float tx, ty;
public:
std::vector<Point> p;
void translate(float x, float y) {
tx = x;
ty = y;
}
};
(Point is a structure of float x, float y)
The points are typed in clockwise.
My current code (ignore Qt debug):
bool sat(Convex c1, Convex c2, QPainter *debug)
{
//Debug
QColor col[] = {QColor(255, 0, 0), QColor(0, 255, 0), QColor(0, 0, 255), QColor(0, 0, 0)};
bool ret = true;
int c1_faces = c1.p.size();
int c2_faces = c2.p.size();
//For every face in c1
for(int i = 0; i < c1_faces; i++)
{
//Grab a face (face x, face y)
float fx = c1.p[i].x - c1.p[(i + 1) % c1_faces].x;
float fy = c1.p[i].y - c1.p[(i + 1) % c1_faces].y;
//Create a perpendicular axis to project on (axis x, axis y)
float ax = -fy, ay = fx;
//Normalize the axis
float len_v = sqrt(ax * ax + ay * ay);
ax /= len_v;
ay /= len_v;
//Debug graphics (ignore)
debug->setPen(col[i]);
//Draw the face
debug->drawLine(QLineF(c1.tx + c1.p[i].x, c1.ty + c1.p[i].y, c1.p[(i + 1) % c1_faces].x + c1.tx, c1.p[(i + 1) % c1_faces].y + c1.ty));
//Draw the axis
debug->save();
debug->translate(c1.p[i].x, c1.p[i].y);
debug->drawLine(QLineF(c1.tx, c1.ty, ax * 100 + c1.tx, ay * 100 + c1.ty));
debug->drawEllipse(QPointF(ax * 100 + c1.tx, ay * 100 + c1.ty), 10, 10);
debug->restore();
//Carve out the min and max values
float c1_min = FLT_MAX, c1_max = FLT_MIN;
float c2_min = FLT_MAX, c2_max = FLT_MIN;
//Project every point in c1 on the axis and store min and max
for(int j = 0; j < c1_faces; j++)
{
float c1_proj = (ax * (c1.p[j].x + c1.tx) + ay * (c1.p[j].y + c1.ty)) / (ax * ax + ay * ay);
c1_min = min(c1_proj, c1_min);
c1_max = max(c1_proj, c1_max);
}
//Project every point in c2 on the axis and store min and max
for(int j = 0; j < c2_faces; j++)
{
float c2_proj = (ax * (c2.p[j].x + c2.tx) + ay * (c2.p[j].y + c2.ty)) / (ax * ax + ay * ay);
c2_min = min(c2_proj, c2_min);
c2_max = max(c2_proj, c2_max);
}
//Return if the projections do not overlap
if(!(c1_max >= c2_min && c1_min <= c2_max))
ret = false; //return false;
}
return ret; //return true;
}
What am i doing wrong? It registers collision perfectly but is over sensitive on one edge (in my test using a triangle and a diamond):
//Triangle
push_back(Point(0, -150));
push_back(Point(0, 50));
push_back(Point(-100, 100));
//Diamond
push_back(Point(0, -100));
push_back(Point(100, 0));
push_back(Point(0, 100));
push_back(Point(-100, 0));
I am getting this mega-adhd over this, please help me out :)
http://u8999827.fsdata.se/sat.png
OK, I was wrong the first time. Looking at your picture of a failure case it is obvious a separating axis exists and is one of the normals (the normal to the long edge of the triangle). The projection is correct, however, your bounds are not.
I think the error is here:
float c1_min = FLT_MAX, c1_max = FLT_MIN;
float c2_min = FLT_MAX, c2_max = FLT_MIN;
FLT_MIN is the smallest normal positive number representable by a float, not the most negative number. In fact you need:
float c1_min = FLT_MAX, c1_max = -FLT_MAX;
float c2_min = FLT_MAX, c2_max = -FLT_MAX;
or even better for C++
float c1_min = std::numeric_limits<float>::max(), c1_max = -c1_min;
float c2_min = std::numeric_limits<float>::max(), c2_max = -c2_min;
because you're probably seeing negative projections onto the axis.