Calculating points on a 3D angle between two lines [closed] - opengl

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I'm trying to calculate multiple points on an angle (circle segment) so that I can store it as a VBO of Vector3 and render it in OpenGL.
Imagine each of those points on the dotted line as a coordinate I want to calculate
I know I can find the magnitude of the angle using the dot product, and in 2 dimensions I would be able to calculate the points on the angle just using sin and cos of this angle. But how do I apply this in 3 dimensions?
I thought maybe I should split the angle down into components, but then wasn't sure how to calculate magnitudes in that situation.
So what is the best method for calculating those points, and how do I do it?
I'm working in C# but of course pseudo code or just methods would do.

Answer 1

normalize and scale both vectors and then slerp between them
slerp stands for spherical linear interpolation and is referenced mostly for quaternions but is valid here as well
vec3 slerp(vec3 a, vec3 b, float t){
float dotp = dot(a,b);
if (dotp > DOT_THRESHOLD) {
// If the inputs are too close for comfort, linearly interpolate
// and normalize the result to avoid division by near 0
vec3 result = v0 + t*(v1 – v0);
result.normalize();
return result;
}
float theta = acos(dotp);
return (sin(theta*(1-t))*a + sin(theta*t)*b)/sin(theta);
}

Answer 2

The trick is to compute the dots as if your two vectors are the unit vectors. Just a half circle. But then instead of writing it as (x,y) = (0,0,1)*x + (0,1,0)*y... just put in your two red and green vectors as a new base.
Compute your 2d x,y circle points. Then the 3d point is redvector*x + greenvector*y.

Answer 3

Here is a C++ DLL for your C# project(tested but angles are not uniform but there is no division by zero as long as vectors have a magnitude):
Usage:
[DllImport("angle.dll")]
extern static void anglePoints(
float x1,
float y1,
float z1,
float x2,
float y2,
float z2,
float [] points
);
İnside of DLL:
class float3
{
public:
float x,y,z;
float3(float X, float Y, float Z)
{
x=X; y=Y; z=Z;
}
float3 sub(float X, float Y, float Z)
{
float3 tmp(0,0,0);
tmp.x=x-X;
tmp.y=y-Y;
tmp.z=z-Z;
return tmp;
}
float3 sub(float3 b)
{
float3 tmp(0,0,0);
tmp.x=x-b.x;
tmp.y=y-b.y;
tmp.z=z-b.z;
return tmp;
}
float3 add(float3 b)
{
float3 tmp(0,0,0);
tmp.x=x+b.x;
tmp.y=y+b.y;
tmp.z=z+b.z;
return tmp;
}
void normalize()
{
float r=sqrt(x*x+y*y+z*z);
x/=r;
y/=r;
z/=r;
}
void scale(float s)
{
x*=s;y*=s;z*=s;
}
void set(float3 v)
{
x=v.x;y=v.y;z=v.z;
}
};
extern "C" __declspec(dllexport) void anglePoints(
float x1,
float y1,
float z1,
float x2,
float y2,
float z2,
float * points
)
{
float3 A(x1,y1,z1);
float3 B(x2,y2,z2);
float3 tmp(0,0,0);
float3 diff(0,0,0);
for(int i=0;i<10;i++)
{
tmp.set(A);
diff.set(B.sub(A));
diff.scale(0.1*((float)i)); // simple and not efficient :P
diff.set(diff.add(tmp));
diff.normalize(); // normalized values so you can
points[i*3+0]=diff.x; // simply use them
points[i*3+1]=diff.y;
points[i*3+2]=diff.z;
}
}
Example:
float[] tmp = new float[30];
anglePoints(0,1,1,10,10,10,tmp);
for (int i = 0; i < 30; i++)
{
Console.WriteLine(tmp[i]);
}
Output:
0 // starts as 0,1,1 normalized
0,7071068
0,7071068
0,34879
0,6627011
0,6627011
0,4508348
0,6311687
0,6311687
0,4973818
0,6134375
0,6134375
0,5237828
0,6023502
0,6023502
0,540738
0,5948119
0,5948119
0,5525321
0,5893675
0,5893675
0,5612046
0,5852562
0,5852562
0,5678473
0,5820435
0,5820435
0,5730973 //ends as 10,10,10 but normalized
0,579465
0,579465