The Transformation between Positional Space and Texture Space

computer graphics, transformations, texture mapping In a 3D graphics application, a common operation is the binding of a 2D texture onto a triangle in a 3D positional space. For light-dependent or view-dependent texture mapping, a need may arise in the graphics pipeline to transform the light or view direction vector into texture space. The affine transformation is unique within the plane of the triangle because the texture coordinates and the position coordinates are specified at three vertices. In the direction perpendicular to this plane, the scale factor between positional and texture spaces is unconstrained and the solution is not unique. In particular, the choice of the scale factor is quite flexible when the texture is anisotropically scaled across the surface. This paper describes some ways to calculate a scale factor with desirable properties and a transformation between positional space and texture space given a triangle's positional coordinates and texture coordinates.