How do I subdivide a triangle in three dimensions? - c

Question

I have a function that takes 3 points and I will use these points to draw a triangle, as if I were using the glVertex function.
But since I want to texture map this triangle while avoiding perspective distortion, I have to subdivide it, and use the vertices for texture mapping and calculation of normals.
I managed to do this for rectangles, spheres, cylinders and torus, but I can't, for the life of me, figure out how to do a triangle.
Every example of triangle mapping I've managed to find is only for 2D space and with predefined points, using glVertex.
As for rectangles, the code I'm using is this one:
void Rectangle::draw(float texS, float texT)
{
float x1, x2, y1, y2;
x1 = v.at(0); x2 = v.at(2);
y1 = v.at(1); y2 = v.at(3);
//glRectf(x1,y1,x2,y2);
int _numDivisions = 100;
float _xDim = abs(x2 - x1);
float _yDim = abs(y2 - y1);
float texMultiS, texMultiT;
texMultiS = _xDim / texS;// / _xDim;
texMultiT = _yDim / texT;// / _yDim;
glPushMatrix();
glTranslatef(x1, y1, 0);
glRotatef(-90.0,1,0,0);
glScalef( _xDim * (1.0/(double) _numDivisions), 1 , _yDim * (1.0/(double) _numDivisions));
glNormal3f(0,-1,0);
for (int bx = 0; bx<_numDivisions; bx++)
{
glBegin(GL_TRIANGLE_STRIP);
glTexCoord2f((bx * 1.0/_numDivisions) * texMultiS, 0.0 * texMultiT);
glVertex3f(bx+x1, 0, 0+y1);
for (int bz = 0; bz<_numDivisions; bz++)
{
glTexCoord2f(((bx+1) * 1.0/_numDivisions) * texMultiS, (bz * 1.0/_numDivisions) * texMultiT);
glVertex3f((bx + 1)+x1, 0, bz+y1);
glTexCoord2f(((bx+1) * 1.0/_numDivisions) * texMultiS, ((bz+1) * 1.0/_numDivisions) * texMultiT);
glVertex3f(bx+x1, 0, (bz + 1)+y1);
}
glTexCoord2f(((bx+1) * 1.0/_numDivisions) * texMultiS, 1.0 * texMultiT);
glVertex3d((bx+1)+x1, 0, _numDivisions+y1);
glEnd();
}
glPopMatrix();
}
And this I get. It's simple enough, since it's in 2D space. I was aiming for the same kind of logic, but for a 3D space triangle.
But I can't figure out the calculations needed for the points in a triangle in 3D space.
FOR EXAMPLE:
P1->(0,0,1); P2->(1,0,0); P3->(0,1,0);
My best idea so far is to draw it in 2D space with P1 as origin, I can just make every point in the P1->P2 line converge towards P3, and then calculate the angle to rotate according to the x-axis and then the angle for a rotation in the y-axis, but is really this the best way to go at it?
EDIT:
As sugested below, a way to rephrase the question might be:
"How do I subdivide a general triangle in three dimensions"?
Since the objective is to get an algorithm that builds a triangle in 3D space in sections (triangle strip or quad strip) so I can use the vertices for texture mapping and normal calculation.

Answer 1

As suggested in the comments, you could slice up a triangle very similar to a quad. With some fancy ASCII art:
/|
/ |
----
/| /|
/ |/ |
-------
/| /| /|
/ |/ |/ |
----------
/| /| /| /|
/ |/ |/ |/ |
-------------
Decomposing this into triangle strips that run bottom to top, we would have 4 strips. The triangle counts of the strips for 4 strips are:
1, 3, 5, 7
or 2 * i + 1 for strip i, with i from 0 to n - 1.
To calculate the vertices needed for the subdivision, you can calculate the points along the bottom edge by linear interpolation between the corresponding two vertices. Same thing for the points along the edge that goes diagonal in the diagram. Then along each strip, you again do a linear interpolation between the corresponding two points, splitting the left side of strip i into i pieces, and the right side into i + 1 pieces.