You're right. The spec is indeed self-contradictory regarding the orientation of cylindrical textures. My intuition was the opposite of yours; it seems more parsimonious that the first control point should correspond to "V=0" for both planar and cylindrical. But either way would be fine, we just need to pick one and amend the spec to make it clear.
Furthermore, the spec doesn't say in which direction the arctangents are computed (i.e., does the image appear in its natural orientation as viewed from the outside of the cylinder, or from the inside?) The obvious answer, to me, is that if
- the combined transformation matrix for the file in which the TEXMAP statement occurs has positive determinant;
- the value of "a" is positive; and
- we are viewing the cylinder from the outside;
then the image should appear in its natural orientation. If zero or two of the above conditions are satisfied, the image should appear flipped. However, the spec doesn't say so.
The spec is even less clear about spherical textures, as it doesn't say whether the third control point corresponds to the "left" or the "right" side of the texture. In my implementation I've been (somewhat arbitrarily) assuming that it goes on the right.
Furthermore, the spec doesn't say in which direction the arctangents are computed (i.e., does the image appear in its natural orientation as viewed from the outside of the cylinder, or from the inside?) The obvious answer, to me, is that if
- the combined transformation matrix for the file in which the TEXMAP statement occurs has positive determinant;
- the value of "a" is positive; and
- we are viewing the cylinder from the outside;
then the image should appear in its natural orientation. If zero or two of the above conditions are satisfied, the image should appear flipped. However, the spec doesn't say so.
The spec is even less clear about spherical textures, as it doesn't say whether the third control point corresponds to the "left" or the "right" side of the texture. In my implementation I've been (somewhat arbitrarily) assuming that it goes on the right.