Original Post
I'm using the following code to calculate barycentric coordinates for a point on triangle t1/t2/t3 and use those to gather the related point position on a second triangle T1/T2/T3.
It seems to work but sometimes I'm not totally sure about it, and I'd be more confident if you guys could check on that.
Do you see any possible trouble or issue with it? Do you perhaps have other C++ code to share?
Thanks for any help.
It seems to work but sometimes I'm not totally sure about it, and I'd be more confident if you guys could check on that.
Do you see any possible trouble or issue with it? Do you perhaps have other C++ code to share?
Thanks for any help.
// compute the area of a triangle using Heron's formula
double triarea(double a, double b, double c)
{
double s = (a + b + c)/2.0;
double area=sqrt(fabs(s*(s-a)*(s-b)*(s-c)));
return area;
}
// compute the distance between two 2d points
double dist(double x0, double y0, double z0, double x1, double y1, double z1)
{
double a = x1 - x0;
double b = y1 - y0;
double c = z1 - z0;
return sqrt(a*a + b*b + c*c);
}
// calculate barycentric coordinates
// triangle 1st vertex: x0,y0,z0
// triangle 2nd vertex: x1,y1,z1
// triangle 3rd vertex: x2,y2,z2
// point inside triangle: vx, vy,vz
// *u,*v,*w are the coordinates returned
void barycent(double x0, double y0, double z0, double x1, double y1, double z1, double x2, double y2, double z2,
double vx, double vy, double vz,
double *u, double *v, double *w)
{
// compute the area of the big triangle
double a = dist(x0, y0, z0, x1, y1, z1);
double b = dist(x1, y1, z1, x2, y2, z2);
double c = dist(x2, y2, z2, x0, y0, z0);
double totalarea = triarea(a, b, c);
// compute the distances from the outer vertices to the inner vertex
double length0 = dist(x0, y0, z0, vx, vy, vz);
double length1 = dist(x1, y1, z1, vx, vy, vz);
double length2 = dist(x2, y2, z2, vx, vy, vz);
// divide the area of each small triangle by the area of the big triangle
*u = triarea(b, length1, length2)/totalarea;
*v = triarea(c, length0, length2)/totalarea;
*w = triarea(a, length0, length1)/totalarea;
}
void main()
{
double r1,r2,r3; // barycentric coordinates
barycent(t1.x, t1.y, t1.z, t2.x, t2.y, t2.z, t3.x, t3.y, t3.z, firstPoint.x, firstPoint.y, firstPoint.z, &r1, &r2, &r3);
Point3d newPoint(T1.x*r1 + T2.x*r2 + T3.x*r3, T1.y*r1 + T2.y*r2 + T3.y*r3, T1.z*r1 + T2.z*r2 + T3.z*r3); // T1,T2,T3 are the coordinates of another triangle
}
