Fundamentals of Computer Graphics, 3rd Edition

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11

Texture Mapping

The shading models presented in Chapter 10 assume that a diffuse surface has

uniform reflectance c

r

.Thisisfine for surfaces such as blank paper or painted

walls, but it is inefficient for objects such as a printed sheet of paper. Such objects

have an appearance whose complexity arises from variation in reflectance prop-

erties. While we could use such small triangles that the variation is captured by

varying the reflectance properties of the triangles, this would be inefficient.

The common technique to handle variations of reflectance is to store the re-

flectance as a function or a a pixel-based image and “map” it onto a surface (Cat-

mull, 1975). The function or image is called a texture map, and the process of

controlling reflectance properties is called texture mapping. This is not hard to

implement once you understand the coordinate systems involved. Texture map-

ping can be classified by several different properties:

1. the dimensionality of the texture function,

2. the correspondences defined between points on the surface and points in the

texture function, and

3. whether the texture function is primarily procedural or primarily a table

look-up.

These items are usually closely related, so we will somewhat arbitrarily classify

textures by their dimension. We first cover 3D textures, often called solid tex-

tures or volume textures. We will then cover 2D textures, sometimes called image

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244 11. Texture Mapping

textures. When graphics programmers talk about textures without specifying di-

mension, they usually mean 2D textures. However, we begin with 3D textures

because, in many ways, they are easier to understand and implement. At the end

of the chapter we discuss bump mapping and displacement mapping which use

textures to change surface normals and position, respectively. Although those

methods modify properties other than reflectance, the images/functions they use

are still called textured. This is consistent with common usage where any image

used to modify object appearance is called a texture.

11.1 3D Texture Mapping

In previous chapters we used c

r

as the diffuse reflectance at a point on an object.

For an object that does not have a solid color, we can replace this with a function

c

r

(p) which maps 3D points to RGB colors (Peachey, 1985; Perlin, 1985). This

function might just return the reflectance of the object that contains p.Butfor

objects with texture, we should expect c

r

(p) to vary as p moves across a surface.

One way to do this is to create a 3D texture that defines an RGB value at every

point in 3D space. We will only call it for points p on the surface, but it is usually

easier to define it for all 3D points than a potentially strange 2D subset of points

that are on an arbitrary surface. Such a strategy is clearly suitable for surfaces that

are “carved” from a solid medium, such as a marble sculpture.

Note that in a ray-tracing program, we have immediate access to the point p

seen through a pixel. However, for a z-buffer or BSP-tree program, we only know

the point after projection into device coordinates. We will show how to resolve

this problem in Section 11.3.1.

11.1.1 3D Stripe Textures

There are a surprising number of ways to make a striped texture. Let’s assume we

have two colors c

0

and c

1

that we want to use to make the stripe color. We need

some oscillating function to switch between the two colors. An easy one is a sine:

RGB stripe( point p )

if (sin(x

p

) > 0) then

return c

0

else

return c

1