Texture coordinate generation : cylinder map shape

A second shape used in texture mapping is a cylinder. An ( x,y,z ) value is converted to cylindrical coordinates of ( r, theta, height ). For texture mapping, we are only interested in theta and the heigh t. To find the color in two-dimensional texture map, theta is converted into an x-coordinate and height is converted into a y-coordinate. This wraps the two-dimensional texture map around the object.

The texture-mapped objects in this image have a cylindrical map shape, and the cylinder’s axis is parallel to the z-axis. At the smallest z-position on each object, note that the squares of the texture pattern become squeezed into "pie slices". This phenomenon occurs at the greatest zposition as well. When the cylinder’s axis is parallel to the z-axis, you’ll see "pie slices" radiating out along the x- and y- axes.

Source : Teaching Texture Mapping Visually by Rosalee Wolfe / DePaul University / wolfe@cs.depaul.edu