6. Texturing (11/11)

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6.7. Bump Mapping 197

changing heightﬁelds. Schroeders and Gulik [1134] present quadtree relief

mapping, a hierarchical method to skip over volumes during traversal. Tevs

et al. [1264] use “maximum mipmaps” to allow skipping while minimizing

precomputation costs.

Although this is an active area of research and is highly sensitive to

particular GPU architectures, in preliminary testing, one of the most time-

and space-eﬃcient methods for relief mapping at the time of printing is

Tatarchuk’s [1244] linear ray-marching with single-step secant correction.

That said, newer methods, such as cone-stepping and quadtree relief map-

ping, were not part of this informal survey. Unquestionably, research will

continue to improve algorithms in this area.

One problem with relief mapping methods is that the illusion breaks

down along the silhouette edges of objects, which will show the original

surface’s smooth outlines. See Figure 6.35.

The key idea is that the triangles rendered deﬁne which pixels should

be evaluated by the pixel shader program, not where the surface actually

is located. In addition, for curved surfaces, the problem of silhouettes be-

comes more involved. One approach is described and developed by Oliveira

and Policarpo [964, 1334], which uses a quadratic silhouette approximation

technique. Jeschke et al. [610] and Dachsbacher et al. [223] both give a more

general and robust method (and review previous work) for dealing with sil-

houettes and curved surfaces correctly. First explored by Hirche [552], the

general idea is to extrude each polygon in the mesh outwards and form a

prism. Rendering this prism forces evaluation of all pixels in which the

heightﬁeld could possibly appear. This type of approach is called shell

Figure 6.36. Parallax occlusion mapping, a.k.a. relief mapping, used on a path to make

the stones look more realistic. (Image from “Crysis” courtesy of Crytek.)

198 6. Texturing

mapping, as the expanded mesh forms a separate shell over the original

model. By preserving the nonlinear nature of prisms when intersecting

them with rays, artifact-free rendering of heightﬁelds becomes possible,

though expensive to compute.

To conclude, an impressive use of this type of technique is shown in

Figure 6.36.

6.7.5 Heightﬁeld Texturing

One obvious method of rendering bumps is to model the bumps as true

geometry, in a very ﬁne mesh. A space-eﬃcient alternative is to use the

vertex texture fetch feature (introduced in Shader Model 3.0) to have a

ﬂat meshed polygon access a heightﬁeld texture. The height retrieved from

the texture is used by the vertex shading program to modify the vertex’s

location. This method is usually called displacement mapping,andthe

heightﬁeld is therefore called a displacement texture in this context. Us-

ing a texture allows for faster manipulation of data for wave simulations

and other animations to apply to the mesh. These techniques can be ex-

pensive in both memory and in processing power, as each vertex in the

mesh requires three additional ﬂoating-point numbers, all of which must

be accessed (the less memory touched, the better). For large expanses

(e.g., terrain or ocean rendering [703]), where level of detail techniques can

be brought to bear to keep complexity down, such an approach can be

suitable. See Section 12.5.2. With the evolution of GPUs towards uniﬁed

shaders

and performing tessellation on the ﬂy, the scale appears to be

tipping towards this being the preferred method in general. It is simple

to program and on newer GPUs has few drawbacks. We consider it likely

that this will be the preferred method once the minimum GPU required

for an application supports fast vertex texture access. Szirmay-Kalos and

Umenhoﬀer [1235] have an excellent, thorough survey of relief mapping and

displacement methods.

While relief and displacement mapping oﬀer additional realism at a

generally reasonable cost, these techniques do have some drawbacks. The

fact that the base surface is unperturbed makes collision detection, and

therefore object interaction, more challenging. For example, if a displace-

ment map is used to model a rock protruding out of the ground, it will

be additional work to have a character’s foot properly stop at the correct

height at this location. Instead of a simple test against a mesh, the mesh

height will also need to be accessed.

Other surfaces than simple quadrilaterals can use displacement map-

ping. Its use with subdivision surfaces is discussed in Section 13.5.6. In

The original vertex texture fetch was slow compared to the pixel shader’s. With

uniﬁed shaders there is no diﬀerence.

6.7. Bump Mapping 199

Section 13.6, we present hardware tessellation where displacement mapping

also can be used.

Table of Contents for 6. Texturing (11/11)

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6. Texturing (11/11)