Rosalee Wolfe
DePaul University
wolfe@cs.depaul.edu
| 7: In two-dimensional texture mapping, we have to decide how to paste the image on to an object. In other words, for each pixel in an object, we encounter the question, "Where do I have to look in the texture map to find the color?" To answer this question, we consider two things: map shape and map entity. | |
| 8: We’ll discuss map shapes first. For a map shape that’s planar, we take an (x,y,z) value from the object and throw away (project) one of the components, which leaves us with a two-dimensional (planar) coordinate. We use the planar coordinate to look up the color in the texture map. | |
| 9: This slide shows several textured-mapped objects that have a planar map shape. None of the objects have been rotated. In this case, the component that was thrown away was the z-coordinate. You can determine which component was projected by looking for color changes in coordinate directions. When moving parallel to the x-axis, an object’s color changes. When moving up and down along the y-axis, the object’s color also changes. However, movement along the z-axis does not produce a change in color. This is how you can tell that the z-component was eliminated. | |
| 10: In the left image, an objects color changes when there’s a change in y, or when there’s a change in z, but the color remains constant when x changes. Which component was projected? In the right image, which component was projected? | |
| 11: 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 height. 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. | |
| 12: 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 z position 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. | |
| 13:On the left squares of the texture map are squeezed into pie slices that radiate out along the x- and z-axes. Which coordinate axis is parallel to the cylinder’s axis? | |
| 14: When using a sphere as the map shape, the (x,y,z) value of a point is converted into spherical coordinates. For purposes of texture mapping, we keep just the latitude and the longitude information. To find the color in the texture map, the latitude is converted into an x-coordinate and the longitude is converted into a y-coordinate. | |
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