The professor describes 3D texture mapping as if you had a solid 3D block of texture that was then chiseled down into the expected features and geometry of the final model; this is not relaly projection, but simply the removal of existing texture in the original mapping to form the final product. However, 2D texture mapping in its various forms ultimately feels like projecting any 2D texture in a particular shape onto another 2D surface. In this sense, I wonder if 3D texture mapping can take other forms as well (e.g. spheres, rectangular prisms, or other regular shapes) and be somehow projected onto 3D volumes rather than simply casted through them with empty space chiseled away? I am unsure how this would mathematically work.
The professor describes 3D texture mapping as if you had a solid 3D block of texture that was then chiseled down into the expected features and geometry of the final model; this is not relaly projection, but simply the removal of existing texture in the original mapping to form the final product. However, 2D texture mapping in its various forms ultimately feels like projecting any 2D texture in a particular shape onto another 2D surface. In this sense, I wonder if 3D texture mapping can take other forms as well (e.g. spheres, rectangular prisms, or other regular shapes) and be somehow projected onto 3D volumes rather than simply casted through them with empty space chiseled away? I am unsure how this would mathematically work.