Quad texture stretching on OpenGL

Question

So when drawing a rectangle on OpenGL, if you give the corners of the rectangle texture coordinates of (0,0), (1,0), (1,1) and (0, 1), you'll get the standard rectangle.

However, if you turn it into something that's not rectangular, you'll get a weird stretching effect. Just like the following:

I saw from this page below that this can be fixed, but the solution given is only for trapezoidal values only. Also, I have to be doing this over many rectangles.

And so, the questions is, what is the proper way, and most efficient way to get the right "4D" texture coordinates for drawing stretched quads?

Answer 1

Implementations are allowed to decompose quads into two triangles and if you visualize this as two triangles you can immediately see why it interpolates texture coordinates the way it does. That texture mapping is correct ... for two independent triangles.

That diagonal seam coincides with the edge of two independently interpolated triangles.

Projective texturing can help as you already know, but ultimately the real problem here is simply interpolation across two triangles instead of a single quad. You will find that while modifying the Q coordinate may help with mapping a texture onto your quadrilateral, interpolating other attributes such as colors will still have serious issues.

If you have access to fragment shaders and instanced vertex arrays (probably rules out OpenGL ES), there is a full implementation of quadrilateral vertex attribute interpolation here. (You can modify the shader to work without "instanced arrays", but it will require either 4x as much data in your vertex array or a geometry shader).

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Incidentally, texture coordinates in OpenGL are always "4D". It just happens that if you use something like glTexCoord2f (s, t) that r is assigned 0.0 and q is assigned 1.0. That behavior applies to all vertex attributes; vertex attributes are all 4D whether you explicitly define all 4 of the coordinates or not.