I need to be able to draw polynomial surfaces but I have
not found a way to do it with OpenGL. The problem is as
follows:
Given the polynomial: f(x,y) = sum(a_ijx^iy^j) i,j = 1,2,…,n
example: f(x,y) = 2.0x^2 + y^2 +3xy + x + 2.0y + 1.0
I want to be able to draw the 3D surface over a triangular domain:
example: I have the 2D triangle T2=(x1,y1, x2,y2, x3,y3).
If I say something like:
glBegin(GL_TRIANGLES)
glVertex3f(x1,y1,f(x1,y1));
glVertex3f(x2,y2,f(x2,y2));
glVertex3f(x3,y3,f(x3,y3));
glEnd();
I will see the the 3D triangle T3 whose vertices are
(xi,yi,f(xi,yi)) i=1,2,3 and all the points in the
2D triangle T2 have z coordinate such that it
lies inside the plane of the the triangle T3.
What I want to change is that each point P2(xp,zp) inside the
triangle T2 is mapped to a point P3(xp,yp,zp) where zp is given
by: zp = f(xp,yp).
How can I achieve that with OpenGL?
Thanks in advance!