Teaching Texture MappingVisuallyRosalee WolfeDePaul [email protected] demonstrating the behavior of texturemapping is beneficial to both computer science andart students. For computer science students it canserve as prelude to delving into the mathematicalunderpinnings of the topic, while in an art class it canbe the main vehicle of explanation for studentslearning to use a rendering package as a medium ofcreative expression. The SIGGRAPH 97 EducationSlide set covers not only the techniques of two- andthree-dimensional texture mapping, but proceduraltextures, bump mapping, and environment mappingas well. In addition it discusses aliasing in texturemapping, and what can be done to counteract it.The following is a reprint of an article that appearedin the November 1997 issue of Computer Grapics andcontains thumbnails and accompanying narrative forthe slide set. To order the full color 35mm slide set,call ACM Member Services at 800 342 6626 in the U.S.and Canada, and +1 212 626 0500 for the greater NewYork area and all other countries. The ACM ordernumber of the education slide set is 434975 (ISBN 089791 956-4) and the price is $35.00 forACM/SIGGRAPH members and $45 for non-members.1. Mapping techniquesadd realism and interestto computer graphicsimages. Texture mappingapplies a pattern of colorto an object. Bumpmapping alters thesurface of an object so that it appears rough, dentedor pitted. In this example, the umbrella, background,beachball and beach blanket have texture maps. Thesand has been bump mapped. These and othermapping techniques are the subject of this slide set.2: When creating imagedetail, it is cheaper toemploy mappingtechniques that it is to usemyriads of tiny polygons.The image on the rightportrays a brick wall, alawn and the sky. In actuality the wall was modeledas a rectangular solid, and the lawn and the sky werecreated from rectangles. The entire image containseight polygons.Imagine the number of polygon itwould require to model the blades of grass in thelawn! Texture mapping creates the appearance ofgrass without the cost of rendering thousands ofpolygons.3: Knowing the differencebetween world coordinatesand object coordinates isimportant when usingmapping techniques. Inobject coordinates theorigin and coordinate axesremain fixed relative to an object no matter how theobject’s position and orientation change. Mostmapping techniques use object coordinates.Normally, if a teapot’s spout is painted yellow, thespout should remain yellow as the teapot flies andtumbles through space. When using worldcoordinates, the pattern shifts on the object as theobject moves through space.4: Depending on themapping situation, we mayneed to bound an objectwith a box, a cylinder, or asphere. It’s often useful totransform the boundinggeometry so its coordinatesrange between zero and one. Transformed boundingboxes have coordinates that range from (0,0,0) to(1,1,1). For a bounding cylinder, we set thecircumference to one and the height to one. For asphere, we scale the latitude and the longitude so thatthey both range between zero and one.5: Texture mapping can bedivided into two-dimensional and three-dimensional techniques.Two-dimensionaltechniques place a two-dimensional (flat) imageonto an object using methods similar to pastingwallpaper onto an object. Three-dimensionaltechniques are analogous to carving the object from ablock of marble.26: Two-dimensionalmappings use pre-existing images. Thisslide shows some imagesthat might be used fortexture mapping. Theimages on the left areeither scanned photographs or images created in apaint or drawing package. POVRay, a raytracer,created the images on the right.7: In two-dimensionaltexture mapping, wehave to decide how topaste the image on to anobject. In other words,for each pixel in anobject, we encounter thequestion, “Where do I have to look in the texture mapto find the color?” To answer this question, weconsider two things: map shape and map entity.8: We’ll discuss mapshapes first. For a mapshape that’s planar, wetake an (x,y,z) value fromthe object and throwaway (project) one of thecomponents, whichleaves us with a two-dimensional (planar) coordinate.We use the planar coordinate to look up the color inthe texture map.9: This slide showsseveral textured-mappedobjects that have a planarmap shape. None of theobjects have been rotated.In this case, thecomponent that wasthrown away was the z-coordinate. You candetermine which component was projected bylooking for color changes in coordinate directions.When moving parallel to the x-axis, an object’s colorchanges. 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 changein color. This is how you can tell that the z-component was eliminated.10: In the left image, anobjects color changeswhen there’s a change iny, or when there’s achange in z, but the colorremains constant when xchanges. Whichcomponent was projected? In the right image, whichcomponent was projected?11: A second shape usedin texture mapping is acylinder. An (x,y,z) valueis converted to cylindricalcoordinates of (r, theta,height). For texturemapping, we are onlyinterested in theta and the height. To find the colorin two-dimensional texture map, theta is convertedinto an x-coordinate and height is converted into a y-coordinate. This wraps the two-dimensional texturemap around the object.12: The texture-mappedobjects in this image havea cylindrical map shape,and the cylinder’s axis isparallel to the z-axis. Atthe smallest z-position oneach object, note that thesquares of the texture pattern become squeezed into“pie slices”. This phenomenon occurs at the greatest zposition as well. When the cylinder’s axis is parallelto the z-axis, you’ll see “pie slices” radiating out alongthe x- and y- axes.13:On the left squares ofthe texture map aresqueezed into pie slicesthat radiate out along thex- and z-axes. Whichcoordinate axis is parallelto the cylinder’s axis?14: When using a sphereas the map shape, the(x,y,z) value of a point isconverted into sphericalcoordinates. Forpurposes of texturemapping, we keep justthe latitude and the longitude information. To findthe color in the texture map, the latitude is convertedinto an x-coordinate and the longitude is convertedinto a y-coordinate.315: The objects have amap shape of a sphere,and the poles of