Texture mapping a curved rectangle in OpenGL [python]

Question

I'm having some problems with the texture mapping in OpenGL in python. I'm trying to draw a rectangle that is curved on the top and on the bottom but so far I've been able to only get it curved on the bottom. Somehow the upper doesn't want to form a curved line. I'm using this function with a parameter of 0.2:

def DrawAWobble(y_wobble):
    R = y_wobble/2.0 - 1/(2.0*y_wobble)

    glBegin(GL_POLYGON)
    x = 0.0
    while x<2.1:
        glTexCoord2f(x*0.5, 1.0); glVertex2f(x/2 - 0.5, 0.5 + (R + math.sqrt(R**2 - (1 - x)**2 + 1)))
        x += 0.1

    x = 2.0
    while x>-0.1:
        glTexCoord2f(x*0.5, 0.0); glVertex2f(x/2 - 0.5, -0.5 + (R + math.sqrt(R**2 - (1 - x)**2 + 1)))
        x -= 0.1
    glEnd()

The result I'm getting is on the left, while I should get something like the right part of the image.

enter image description here

Don't know if this is related to your problem, but FYI GL_POLYGON only supports drawing **convex** polygons. Perhaps you're somehow confusing it with that concave shape. — Tim, Jun 23 '12 at 01:08

score 2 · Accepted Answer · answered Jun 23 '12 at 01:28

Tim, the commenteer, is right. The problem is GL_POLYGON. The issue is that the GPU has to figure out how to triangulate your arbitrary polygon, and it's doing in a way that's not preserving your mapping. What you probably want is to use a single quad strip or triangle strip for rendering this; instead of working around the edge of your polygon, alternate back and forth and work across. Something like this (obviously untested):

def DrawAWobble(y_wobble,step=0.1):
    R = y_wobble/2.0 - 1/(2.0*y_wobble)

    glBegin(GL_QUAD_STRIP)
    x = 0.0
    while x<2.0+0.5*step:
        glTexCoord2f(0.5*x,0.0); glVertex2f(0.5*(x-1), -0.5 + R + (R*R-(1-x)*(1-x)+1)**0.5)
        glTexCoord2f(0.5*x,1.0); glVertex2f(0.5*(x-1),  0.5 + R + (R*R-(1-x)*(1-x)+1)**0.5)
        x += step
    glEnd()

Wow, thanks, that works pretty well. Never would have thought of this on my own though. ^^ — lonelytransistor, Jun 23 '12 at 10:08
I recommend never using GL_POLYGON because the way it triangulates is also implementation-dependent. — geometrian, Jun 23 '12 at 23:58

Texture mapping a curved rectangle in OpenGL [python]

1 Answers1