Textures and Texture Transforms
Textured objects are shown in the display at the upper right. Use the pop-up menus to select the texture and the object that you want to view. You can use your mouse to rotate the objects.
The display on the upper left shows the st-plane, where the texture lives. In the display, s and t range from −1 to 2. A box is drawn around the original texture image, with s and t ranging from 0 to 1. The point (0,0) is at the lower left corner of that box. Note that (0,0) is not at the center of the display.
Four sliders allow you apply texture transformations. The transform can be seen as a coordinate transformation in the st-plane, or as a modeling transformation that applies to the box. As a modeling transform, the box is first scaled, then rotated, then translated.
The same transform is also applied as a texture transformation on the textured object. The result is easiest to see on the cube: Each face of the cube shows a copy of the part of the st-plane that is inside the box.
Try adjusting just one slider while the others are at their default values. (Click "Reset" between experiments.) Note that when the box is translated to the left, the image on the cube moves to the right. When the box grows, the image on the cube shrinks (because you are seeing a larger region in the st-plane mapped to the same area on the cube). When the box rotates counterclockwise, the image on the cube rotates clockwise.
Although the effect is easiest to understand on the cube, it's fun to watch a texture moving around on an object. Try it! I especially like a rotating texture on the torus.