# Ray Tracing Displacement Mapped Surface

Logie, James R (1995) Ray Tracing Displacement Mapped Surface. PhD thesis, University of Glasgow.

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## Abstract

Displacement mapping is a technique in computer graphics which allows a simple base surface to be deformed into a more complex surface by applying a texture to change the geometry. This is achieved by applying to each point on the surface a displacement, specified by a displacement function, with a magnitude specified by a height field. This technique makes it possible to transform the simple primitives used in computer graphics today into visually rich and geometrically complex surfaces. Displacement mapping is a texture mapping technique in which the texture is the height field defining the displacement magnitudes. But, unlike any other form of texture mapping, displacement mapping alters the surface geometry. This has many implications for the rendering of displacement mapped surfaces. It must be considered early in the rendering process during the visibility calculations (since it defines the actual geometry of the surface). This is in contrast to other forms of texture mapping which are applied after the visibility of the surface is known. This fact accounts for much of the power and complexity involved in rendering displacement mapped surfaces This thesis provides an investigation into ways to render such surfaces by the use of ray tracing. It is commonly believed that displacement mapped surfaces are too complex to be ray-traced due to the complex nature of the geometry they define. This myth is disproved by the algorithms contained herein. Three algorithms are presented which tackle the ray-surface intersection problem for displacement mapped surfaces (this being the core calculation in a ray tracer). The first algorithm tackles the problem geometrically by analysing the geometry of the intersection calculation. This approach provides a fast algorithm but with limited applicability. It is only suitable for simple base surfaces where the underlying geometry can be easily analysed. The second algorithm reduced the intersection calculation to a system of non-linear equations and applies existing numerical techniques to solve these. This approach, although very general, proves to unsuccessful due to the enormous amount of computation involved. The third approach polygonalises the displacement-mapped surface as it is rendered and calculates the intersections with the generated polygons. This, combined with a system to allow the efficient generation, storage and processing of the generated polygons, provides the first practical system for ray tracing displacement mapped surfaces.

Item Type: Thesis (PhD) Doctoral Adviser: John W Patterson Computer science 1995 Enlighten Team glathesis:1995-76302 Copyright of this thesis is held by the author. 19 Nov 2019 16:09 19 Nov 2019 16:09 https://theses.gla.ac.uk/id/eprint/76302