I am trying to find the common intersection(x,y) of 3 circles using c++. But i'm not getting the proper output. What am i doing wrong in my code? Here i my program i'm using to calculate the common intersection point. Here first i have calculated the intersection of two pixels which comes from quadric equation,as (x0,y0), (x1,y1). After that considering that 3rd circle intersects at atleast one point, i have used those two intersection points in 3rd circle, whichever satisfies the 3rd circle it is considered as the common intersection point of 3 circle. Am i doing anything wrong?
vector<pix> obj; struct pix { int x; int y; };
auto p0 = obj[stoi(r[2])][stoi(r[0])];
auto p1 = obj[stoi(r[2])][stoi(r[1])];
int ax = p1.x-p0.x; int ay = p1.y-p0.y;
int bx = -ay; int by = ax;
pix pv;
pv.x = p1.x+bx; pv.y = p1.y+by;
OrigImg.copyTo(cv_ptr->image);
for(auto pi : obj[stoi(r[2])]) {
float p0pi = sqrt(pow(p0.x-pi.x,2)+pow(p0.y-pi.y,2));
float p1pi = sqrt(pow(p1.x-pi.x,2)+pow(p1.y-pi.y,2));
float pvpi = sqrt(pow(pv.x-pi.x,2)+pow(pv.y-pi.y,2));
float a1 = 2*(p1.x-p0.x);
float b1 = 2*(p1.y-p0.y);
float c1 = p0.x*p0.x-p1.x*p1.x+p0.y*p0.y-p1.y*p1.y-p0pi*p0pi+p1pi*p1pi;
float a = a1*a1+b1*b1;
float b = 2*(b1*c1 + b1*a1*p0.x - p0.y*a1*a1);
float c = c1*c1+2*c1*p0.x*a1 + a1*a1*(p0.x*p0.x + p0.y*p0.y - p0pi*p0pi);
int y0 = -(b+sqrt(b*b-4*a*c))/2*a;
int y1 = (b+sqrt(b*b-4*a*c))/2*a;
int x0 = -(b1*y0+c1)/a1;
int x1 = -(b1*y1+c1)/a1;
int x,y;
cout<<"hello"<<x0<<"\t"<<y0<<"\t"<<x1<<"\t"<<y1<<endl;
cout<<pow(x0-pv.x,2)+pow(y0-pv.y,2)<<"\t"<<pvpi*pvpi<<"\t"<<
pow(x1-pv.x,2)+pow(y1-pv.y,2)<<"\t"<<pvpi*pvpi<<endl;
if(sqrt(pow(x0-pv.x,2)+pow(y0-pv.y,2))==pvpi) {
x = x0; y = y0;
}
else if(sqrt(pow(x1-pv.x,2)+pow(y1-pv.y,2))==pvpi) {
x = x1; y = y1;
}
if(x>=0 && x<OrigImg.rows && y>=0 && y<OrigImg.cols) {
cv_ptr->image.at<cv::Vec3b>( y, x )[2] = 0;
cv_ptr->image.at<cv::Vec3b>( y, x )[1] = 0;
cv_ptr->image.at<cv::Vec3b>( y, x )[0] = 0;
}
}
}
image_pub_.publish(cv_ptr->toImageMsg());
Here p0, p1, pv are the position of 3 circles which are at different position. Here what i'm trying to do it, i have saved the pixels belonging to one object in a map obj[obj_index][pixel_index] where pixel index is index for each unique pixel belonging to that pixel and obj_index is index for each unique object.
After applying some pattern matching algorithm i get the r[0]=obj_index, r[1]=p0 index, r[2]=p1 index of object. Now what i'm trying to do it to visualize and check which pixels are present in current analysed object w.r.t previously saved object.
Here the output comes like:
hello 150492 150336 -150180 -150336
4.51763e+10 873 4.52274e+10 873
Related
Problem
I am writing a ray tracer as a use case for a specific machine learning approach in Computer Graphics.
My problem is that, when I try to find the intersection between a ray and a surface, the result is not exact.
Basically, if I am scattering a ray from point O towards a surface located at (x,y,z), where z = 81, I would expect the solution to be something like S = (x,y,81). The problem is: I get a solution like (x,y,81.000000005).
This is of course a problem, because following operations depend on that solution, and it needs to be the exact one.
Question
My question is: how do people in Computer Graphics deal with this problem? I tried to change my variables from float to double and it does not solve the problem.
Alternative solutions
I tried to use the function std::round(). This can only help in specific situations, but not when the exact solution contains one or more significant digits.
Same for std::ceil() and std::floor().
EDIT
This is how I calculate the intersection with a surface (rectangle) parallel to the xz axes.
First of all, I calculate the distance t between the origin of my Ray and the surface. In case my Ray, in that specific direction, does not hit the surface, t is returned as 0.
class Rectangle_xy: public Hitable {
public:
float x1, x2, y1, y2, z;
...
float intersect(const Ray &r) const { // returns distance, 0 if no hit
float t = (y - r.o.y) / r.d.y; // ray.y = t* dir.y
const float& x = r.o.x + r.d.x * t;
const float& z = r.o.z + r.d.z * t;
if (x < x1 || x > x2 || z < z1 || z > z2 || t < 0) {
t = 0;
return 0;
} else {
return t;
}
....
}
Specifically, given a Ray and the id of an object in the list (that I want to hit):
inline Vec hittingPoint(const Ray &r, int &id) {
float t; // distance to intersection
if (!intersect(r, t, id))
return Vec();
const Vec& x = r.o + r.d * t;// ray intersection point (t calculated in intersect())
return x ;
}
The function intersect() in the previous snippet of code checks for every Rectangle in the List rect if I intersect some object:
inline bool intersect(const Ray &r, float &t, int &id) {
const float& n = NUMBER_OBJ; //Divide allocation of byte of the whole scene, by allocation in byte of one single element
float d;
float inf = t = 1e20;
for (int i = 0; i < n; i++) {
if ((d = rect[i]->intersect(r)) && d < t) { // Distance of hit point
t = d;
id = i;
}
}
// Return the closest intersection, as a bool
return t < inf;
}
The coordinate is then obtained using the geometric interpolation between a line and a surface in the 3D space:
Vec& x = r.o + r.d * t;
where:
r.o: it represents the ray origin. It's defined as a r.o : Vec(float a, float b, float c)
r.d : this is the direction of the ray. As before: r.d: Vec(float d, float e, float f).
t: float representing the distance between the object and the origin.
You could look into using std::numeric_limits<T>::epsilon for your float/double comparison. And see if your result is in the region +-epsilon.
An alternative would be to not ray trace towards a point. Maybe just place relatively small box or sphere there.
Issue
I'm trying to implement the Perlin Noise algorithm in 2D with a single octave with a size of 16x16. I'm using this as heightmap data for a terrain, however it only seems to work in one axis. Whenever the sample point moves to a new Y section in the Perlin Noise grid, the gradient is very different from what I expect (for example, it often flips from 0.98 to -0.97, which is a very sudden change).
This image shows the staggered terrain in the z direction (which is the y axis in the 2D Perlin Noise grid)
Code
I've put the code that calculates which sample point to use at the end since it's quite long and I believe it's not where the issue is, but essentially I scale down the terrain to match the Perlin Noise grid (16x16) and then sample through all the points.
Gradient At Point
So the code that calculates out the gradient at a sample point is the following:
// Find the gradient at a certain sample point
float PerlinNoise::gradientAt(Vector2 point)
{
// Decimal part of float
float relativeX = point.x - (int)point.x;
float relativeY = point.y - (int)point.y;
Vector2 relativePoint = Vector2(relativeX, relativeY);
vector<float> weights(4);
// Find the weights of the 4 surrounding points
weights = surroundingWeights(point);
float fadeX = fadeFunction(relativePoint.x);
float fadeY = fadeFunction(relativePoint.y);
float lerpA = MathUtils::lerp(weights[0], weights[1], fadeX);
float lerpB = MathUtils::lerp(weights[2], weights[3], fadeX);
float lerpC = MathUtils::lerp(lerpA, lerpB, fadeY);
return lerpC;
}
Surrounding Weights of Point
I believe the issue is somewhere here, in the function that calculates the weights for the 4 surrounding points of a sample point, but I can't seem to figure out what is wrong since all the values seem sensible in the function when stepping through it.
// Find the surrounding weight of a point
vector<float> PerlinNoise::surroundingWeights(Vector2 point){
// Produces correct values
vector<Vector2> surroundingPoints = surroundingPointsOf(point);
vector<float> weights;
for (unsigned i = 0; i < surroundingPoints.size(); ++i) {
// The corner to the sample point
Vector2 cornerToPoint = surroundingPoints[i].toVector(point);
// Getting the seeded vector from the grid
float x = surroundingPoints[i].x;
float y = surroundingPoints[i].y;
Vector2 seededVector = baseGrid[x][y];
// Dot product between the seededVector and corner to the sample point vector
float dotProduct = cornerToPoint.dot(seededVector);
weights.push_back(dotProduct);
}
return weights;
}
OpenGL Setup and Sample Point
Setting up the heightmap and getting the sample point. Variables 'wrongA' and 'wrongA' is an example of when the gradient flips and changes suddenly.
void HeightMap::GenerateRandomTerrain() {
int perlinGridSize = 16;
PerlinNoise perlin_noise = PerlinNoise(perlinGridSize, perlinGridSize);
numVertices = RAW_WIDTH * RAW_HEIGHT;
numIndices = (RAW_WIDTH - 1) * (RAW_HEIGHT - 1) * 6;
vertices = new Vector3[numVertices];
textureCoords = new Vector2[numVertices];
indices = new GLuint[numIndices];
float perlinScale = RAW_HEIGHT/ (float) (perlinGridSize -1);
float height = 50;
float wrongA = perlin_noise.gradientAt(Vector2(0, 68.0f / perlinScale));
float wrongB = perlin_noise.gradientAt(Vector2(0, 69.0f / perlinScale));
for (int x = 0; x < RAW_WIDTH; ++x) {
for (int z = 0; z < RAW_HEIGHT; ++z) {
int offset = (x* RAW_WIDTH) + z;
float xVal = (float)x / perlinScale;
float yVal = (float)z / perlinScale;
float noise = perlin_noise.gradientAt(Vector2( xVal , yVal));
vertices[offset] = Vector3(x * HEIGHTMAP_X, noise * height, z * HEIGHTMAP_Z);
textureCoords[offset] = Vector2(x * HEIGHTMAP_TEX_X, z * HEIGHTMAP_TEX_Z);
}
}
numIndices = 0;
for (int x = 0; x < RAW_WIDTH - 1; ++x) {
for (int z = 0; z < RAW_HEIGHT - 1; ++z) {
int a = (x * (RAW_WIDTH)) + z;
int b = ((x + 1)* (RAW_WIDTH)) + z;
int c = ((x + 1)* (RAW_WIDTH)) + (z + 1);
int d = (x * (RAW_WIDTH)) + (z + 1);
indices[numIndices++] = c;
indices[numIndices++] = b;
indices[numIndices++] = a;
indices[numIndices++] = a;
indices[numIndices++] = d;
indices[numIndices++] = c;
}
}
BufferData();
}
Turned out the issue was in the interpolation stage:
float lerpA = MathUtils::lerp(weights[0], weights[1], fadeX);
float lerpB = MathUtils::lerp(weights[2], weights[3], fadeX);
float lerpC = MathUtils::lerp(lerpA, lerpB, fadeY);
I had the interpolation in the y axis the wrong way around, so it should have been:
lerp(lerpB, lerpA, fadeY)
Instead of:
lerp(lerpA, lerpB, fadeY)
I am building a raytracer and my texture mapping isn't quite right. Its very close though. I build a cup in blender and did a UV unwrap to display a texture. I exported the object and loaded it into my raytracer with the same texture. Here are two pictures:
As you can see the textures look very close, but something is off. If you look at the bottom of the cup on the sides you can see they aren't the same, but the textures are all aligned correctly so it does look somewhat right. The way the textures are calculated is by using barycentric coordinates.
Vect n = getTriangleNormal();
Vect ba = B.add(A.negative()).negative();
Vect ca = C.add(A.negative()).negative();
Vect ap = A.add(point.negative()).negative();
Vect bp = B.add(point.negative()).negative();
Vect cp = C.add(point.negative()).negative();
double areaABC = n.dotProduct(ba.crossProduct(ca));
double areaPBC = n.dotProduct(bp.crossProduct(cp));
double areaPCA = n.dotProduct(cp.crossProduct(ap));
if(areaABC < 0){areaABC = -areaABC;}
if(areaPBC < 0){areaPBC = -areaPBC;}
if(areaPCA < 0){areaPCA = -areaPCA;}
double u = areaPBC / areaABC ; // alpha
double v = areaPCA / areaABC ; // beta
double w = 1.0f - u - v ; // gamma
Then to find the color I take the new point and map it onto the image
Vect uv = (textA.mult(u)).add(textB.mult(v)).add(textC.mult(w));
int width = texture ->columns();
int height = texture ->rows();
double x = width * (uv.getX()) ; x = (int) x;
double y = height * (1-uv.getY()) ; y = (int) y;
//vector<unsigned int> c = texture -> getPixel(x,y);
//return Color(c[0]/255.0,c[1]/255.0,c[2]/255.0,0);
int row = y;
int column = x;
Magick::PixelPacket *pixels = texture->getPixels(0, 0, width, height);
Magick::Color color = pixels[width * row + column];
double range = pow(2, texture -> modulusDepth());
double r = color.redQuantum()/range ;
double g = color.greenQuantum()/range ;
double b = color.blueQuantum()/range ;
return Color(r, g, b, 0);
I'm trying to do terrain following, and I get a negative camera position in the xz plane. Now I get an out of boundary exception, because the row or the col is negative. How would I transform the cell of the grid to the origin correctly, giving negative camera coordinates.
Here is the two functions
int cGrid::getHeightmapEntry(int row, int col)
{
return m_heightmap[row * 300 + col];
}
float cGrid::getHeight(float x, float z, float _width, float _depth, int _cellSpacing)
{
// Translate on xz-plane by the transformation that takes
// the terrain START point to the origin.
x = ((float)_width / 2.0f) + x;
z = ((float)_depth / 2.0f) - z;
// Scale down by the transformation that makes the
// cellspacing equal to one. This is given by
// 1 / cellspacing since; cellspacing * 1 / cellspacing = 1.
x /= (float)_cellSpacing;
z /= (float)_cellSpacing;
// From now on, we will interpret our positive z-axis as
// going in the 'down' direction, rather than the 'up' direction.
// This allows to extract the row and column simply by 'flooring'
// x and z:
float col = ::floorf(x);
float row = ::floorf(z);
if (row < 0 || col<0)
{
row = 0;
}
// get the heights of the quad we're in:
//
// A B
// *---*
// | / |
// *---*
// C D
float A = getHeightmapEntry(row, col);
float B = getHeightmapEntry(row, col + 1);
float C = getHeightmapEntry(row + 1, col);
float D = getHeightmapEntry(row + 1, col + 1);
//
// Find the triangle we are in:
//
// Translate by the transformation that takes the upper-left
// corner of the cell we are in to the origin. Recall that our
// cellspacing was nomalized to 1. Thus we have a unit square
// at the origin of our +x -> 'right' and +z -> 'down' system.
float dx = x - col;
float dz = z - row;
// Note the below compuations of u and v are unneccessary, we really
// only need the height, but we compute the entire vector to emphasis
// the books discussion.
float height = 0.0f;
if (dz < 1.0f - dx) // upper triangle ABC
{
float uy = B - A; // A->B
float vy = C - A; // A->C
// Linearly interpolate on each vector. The height is the vertex
// height the vectors u and v originate from {A}, plus the heights
// found by interpolating on each vector u and v.
height = A + Lerp(0.0f, uy, dx) + Lerp(0.0f, vy, dz);
}
else // lower triangle DCB
{
float uy = C - D; // D->C
float vy = B - D; // D->B
// Linearly interpolate on each vector. The height is the vertex
// height the vectors u and v originate from {D}, plus the heights
// found by interpolating on each vector u and v.
height = D + Lerp(0.0f, uy, 1.0f - dx) + Lerp(0.0f, vy, 1.0f - dz);
}
return height;
}
float height = m_Grid.getHeight(position.x, position.y, 49 * 300, 49 * 300, 6.1224489795918367f);
if (height != 0)
{
position.y = height + 10.0f;
}
m_Camera.SetPosition(position.x, position.y, position.z);
bool cGrid::readRawFile(std::string fileName, int m, int n)
{
// A height for each vertex
std::vector<BYTE> in(m*n);
std::ifstream inFile(fileName.c_str(), std::ios_base::binary);
if (!inFile)
return false;
inFile.read(
(char*)&in[0], // buffer
in.size());// number of bytes to read into buffer
inFile.close();
// copy BYTE vector to int vector
m_heightmap.resize(n*m);
for (int i = 0; i < in.size(); i++)
m_heightmap[i] = (float)((in[i])/255)*50.0f;
return true;
}
m_Grid.readRawFile("castlehm257.raw", 50, 50);
I infer that you’re storing a 50 by 50 matrix inside a 300 by 300 matrix, to represent a grid of 49 by 49 cells. I also infer that m_Grid is an object of type cGrid. Your code appears to contain the following errors:
Argument(2) of call m_Grid.getHeight is not a z value.
Argument(3) of call m_Grid.getHeight is inconsistent with argument(5).
Argument(4) of call m_Grid.getHeight is inconsistent with argument(5).
Implicit cast of literal float to int in argument(5) of call m_Grid.getHeight - the value will be truncated.
Try changing your function call to this:
float height = m_Grid.getHeight(position.x, position.z, 49 * cellspacing, 49 * cellspacing, cellspacing);
-- where cellspacing is as defined in your diagram.
Also, try changing parameter(5) of cGrid::getHeight from int _cellSpacing to float _cellSpacing.
(I have edited this answer a couple of times as my understanding of your code has evolved.)
I have line that is defined as two points.
start = (xs,ys)
end = (xe, ye)
Drawing function that I'm using Only accepts lines that are fully in screen coordinates.
Screen size is (xSize, ySize).
Top left corner is (0,0). Bottom right corner is (xSize, ySize).
Some other funcions gives me line that that is defined for example as start(-50, -15) end(5000, 200). So it's ends are outside of screen size.
In C++
struct Vec2
{
int x, y
};
Vec2 start, end //This is all little bit pseudo code
Vec2 screenSize;//You can access coordinates like start.x end.y
How can I calculate new start and endt that is at the screen edge, not outside screen.
I know how to do it on paper. But I can't transfer it to c++.
On paper I'm sershing for point that belongs to edge and line. But it is to much calculations for c++.
Can you help?
There are many line clipping algorithms like:
Cohen–Sutherland wikipedia page with implementation
Liang–Barsky wikipedia page
Nicholl–Lee–Nicholl (NLN)
and many more. see Line Clipping on wikipedia
[EDIT1]
See below figure:
there are 3 kinds of start point:
sx > 0 and sy < 0 (red line)
sx < 0 and sy > 0 (yellow line)
sx < 0 and sy < 0 (green and violet lines)
In situations 1 and 2 simply find Xintersect and Yintersect respectively and choose them as new start point.
As you can see, there are 2 kinds of lines in situation 3. In this situation find Xintersect and Yintersect and choose the intersect point near the end point which is the point that has minimum distance to endPoint.
min(distance(Xintersect, endPoint), distance(Yintersect, endPoint))
[EDIT2]
// Liang-Barsky function by Daniel White # http://www.skytopia.com/project/articles/compsci/clipping.html
// This function inputs 8 numbers, and outputs 4 new numbers (plus a boolean value to say whether the clipped line is drawn at all).
//
bool LiangBarsky (double edgeLeft, double edgeRight, double edgeBottom, double edgeTop, // Define the x/y clipping values for the border.
double x0src, double y0src, double x1src, double y1src, // Define the start and end points of the line.
double &x0clip, double &y0clip, double &x1clip, double &y1clip) // The output values, so declare these outside.
{
double t0 = 0.0; double t1 = 1.0;
double xdelta = x1src-x0src;
double ydelta = y1src-y0src;
double p,q,r;
for(int edge=0; edge<4; edge++) { // Traverse through left, right, bottom, top edges.
if (edge==0) { p = -xdelta; q = -(edgeLeft-x0src); }
if (edge==1) { p = xdelta; q = (edgeRight-x0src); }
if (edge==2) { p = -ydelta; q = -(edgeBottom-y0src);}
if (edge==3) { p = ydelta; q = (edgeTop-y0src); }
r = q/p;
if(p==0 && q<0) return false; // Don't draw line at all. (parallel line outside)
if(p<0) {
if(r>t1) return false; // Don't draw line at all.
else if(r>t0) t0=r; // Line is clipped!
} else if(p>0) {
if(r<t0) return false; // Don't draw line at all.
else if(r<t1) t1=r; // Line is clipped!
}
}
x0clip = x0src + t0*xdelta;
y0clip = y0src + t0*ydelta;
x1clip = x0src + t1*xdelta;
y1clip = y0src + t1*ydelta;
return true; // (clipped) line is drawn
}
Here is a function I wrote. It cycles through all 4 planes (left, top, right, bottom) and clips each point by the plane.
// Clips a line segment to an axis-aligned rectangle
// Returns true if clipping is successful
// Returns false if line segment lies outside the rectangle
bool clipLineToRect(int a[2], int b[2],
int xmin, int ymin, int xmax, int ymax)
{
int mins[2] = {xmin, ymin};
int maxs[2] = {xmax, ymax};
int normals[2] = {1, -1};
for (int axis=0; axis<2; axis++) {
for (int plane=0; plane<2; plane++) {
// Check both points
for (int pt=1; pt<=2; pt++) {
int* pt1 = pt==1 ? a : b;
int* pt2 = pt==1 ? b : a;
// If both points are outside the same plane, the line is
// outside the rectangle
if ( (a[0]<xmin && b[0]<xmin) || (a[0]>xmax && b[0]>xmax) ||
(a[1]<ymin && b[1]<ymin) || (a[1]>ymax && b[1]>ymax)) {
return false;
}
const int n = normals[plane];
if ( (n==1 && pt1[axis]<mins[axis]) || // check left/top plane
(n==-1 && pt1[axis]>maxs[axis]) ) { // check right/bottom plane
// Calculate interpolation factor t using ratio of signed distance
// of each point from the plane
const float p = (n==1) ? mins[axis] : maxs[axis];
const float q1 = pt1[axis];
const float q2 = pt2[axis];
const float d1 = n * (q1-p);
const float d2 = n * (q2-p);
const float t = d1 / (d1-d2);
// t should always be between 0 and 1
if (t<0 || t >1) {
return false;
}
// Interpolate to find the new point
pt1[0] = (int)(pt1[0] + (pt2[0] - pt1[0]) * t );
pt1[1] = (int)(pt1[1] + (pt2[1] - pt1[1]) * t );
}
}
}
}
return true;
}
Example Usage:
void testClipLineToRect()
{
int screenWidth = 320;
int screenHeight = 240;
int xmin=0;
int ymin=0;
int xmax=screenWidth-1;
int ymax=screenHeight-1;
int a[2] = {-10, 10};
int b[2] = {300, 250};
printf("Before clipping:\n\ta={%d, %d}\n\tb=[%d, %d]\n",
a[0], a[1], b[0], b[1]);
if (clipLineToRect(a, b, xmin, ymin, xmax, ymax)) {
printf("After clipping:\n\ta={%d, %d}\n\tb=[%d, %d]\n",
a[0], a[1], b[0], b[1]);
}
else {
printf("clipLineToRect returned false\n");
}
}
Output:
Before clipping:
a={-10, 10}
b=[300, 250]
After clipping:
a={0, 17}
b=[285, 239]