## Further Reading

Burley’s article (2012) on a material model developed at Disney for feature films is an excellent read. It includes extensive discussion of features of real-world reflection functions that can be observed in Matusik et al.’s (2003b) measurements of one hundred BRDFs and analyzes the ways that existing BRDF models do and do not fit these features well. These insights are then used to develop an “artist-friendly” material model that can express a wide range of surface appearances. The model describes reflection with a single color and ten scalar parameters, all of which are in the range and have fairly predictable effects on the appearance of the resulting material.

Blinn (1978) invented the bump-mapping technique. Kajiya (1985)
generalized the idea of bump mapping the normal to *frame mapping*,
which also perturbs the surface’s primary tangent vector and is useful
for controlling the appearance of anisotropic reflection
models. Mikkelsen’s thesis (2008) carefully investigates a number of the
assumptions underlying bump mapping, proposes generalizations, and
addresses a number of subtleties with respect to its application to real-time
rendering.

Snyder and Barr (1987) noted the light leak problem from per-vertex shading normals and proposed a number of work-arounds. The method we have used in this chapter is from Section 5.3 of Veach’s thesis (1997); it is a more robust solution than those of Snyder and Barr.

Shading normals introduce a number of subtle problems for physically based light transport algorithms that we have not addressed in this chapter. For example, they can easily lead to surfaces that reflect more energy than was incident upon them, which can wreak havoc with light transport algorithms that are designed under the assumption of energy conservation. Veach (1996) investigated this issue in depth and developed a number of solutions. Section 16.1 of this book will return to this issue.

One visual shortcoming of bump mapping is that it doesn’t naturally account
for self-shadowing, where bumps cast shadows on the surface and prevent
light from reaching nearby points. These shadows can have a significant
impact on the appearance of rough surfaces. Max (1988) developed the
*horizon mapping* technique, which performs a preprocess on bump maps
stored in image maps to compute a term to account for this
effect. This approach isn’t directly applicable to
procedural textures, however. Dana et al. (1999) measured spatially varying
reflection properties from real-world surfaces, including these
self-shadowing effects; they convincingly demonstrate this effect’s
importance for accurate image synthesis.

Another difficult issue related to bump mapping is that antialiasing bump
maps that have higher frequency detail than can be represented in the image
is quite difficult. In particular, it is not enough to remove
high-frequency detail from the bump map function, but in general the BSDF
needs to be modified to account for this detail. Fournier (1992) applied
*normal distribution functions* to this problem, where the surface
normal was generalized to represent a distribution of normal directions.
Becker and Max (1993) developed algorithms for blending between bump maps
and BRDFs that represented higher-frequency details. Schilling (1997, 2001) investigated this issue particularly for application to graphics
hardware. More recently, effective approaches to filtering bump maps were
developed by Han et al. (2007) and Olano and Baker (2010). Recent
work by Dupuy et al. (2013) and Hery et al. (2014) addressed this issue by
developing techniques that convert displacements into anisotropic
distributions of Beckmann microfacets.

An alternative to bump mapping is displacement mapping, where the bump function is used to actually modify the surface geometry, rather than just perturbing the normal (Cook 1984; Cook et al. 1987). Advantages of displacement mapping include geometric detail on object silhouettes and the possibility of accounting for self-shadowing. Patterson and collaborators described an innovative algorithm for displacement mapping with ray tracing where the geometry is unperturbed but the ray’s direction is modified such that the intersections that are found are the same as would be found with the displaced geometry (Patterson et al. 1991; Logie and Patterson 1994). Heidrich and Seidel (1998) developed a technique for computing direct intersections with procedurally defined displacement functions.

As computers have become faster, another viable approach for displacement
mapping has been to use an implicit function to define the displaced surface and
to then take steps along rays until they find a zero crossing with the
implicit function. At this point, an intersection has been found. This
approach was first introduced by Hart (1996); see Donnelly (2005) for
information about using this approach for displacement mapping on the
GPU. This approach was recently popularized by Quilez on the
*shadertoy* Web site (Quilez 2015).

With the advent of increased memory on computers and caching algorithms, the option of finely tessellating geometry and displacing its vertices for ray tracing has become feasible. Pharr and Hanrahan (1996) described an approach to this problem based on geometry caching, and Wang et al. (2000) described an adaptive tessellation algorithm that reduces memory requirements. Smits, Shirley, and Stark (2000) lazily tessellate individual triangles, saving a substantial amount of memory.

Measuring fine-scale surface geometry of real surfaces to acquire bump or displacement maps can be challenging. Johnson et al. (2011) developed a novel hand-held system that can measure detail down to a few microns, which more than suffices for these uses.

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