Just In Time VRML Volume Rounding with Polyhedron Bevelling

David C. W. Poon, MSc thesis 1998

Abstract

Polyhedra are widely used as scene components in computer graphics. However, a problem with true polyhedra, as compared to real-world polyhedral objects, is that they have perfectly sharp edges and corners. A solution is to round the edges and corners to produce a softer more natural look. This thesis presents Polyhedron Bevelling, a new fast polygon-based volume rounding method with a simple roundness control. The thesis begins with a user survey of how people perceive roundness, and suggests requirements for an automatic volume rounding method. Two variants of polyhedron bevelling are developed, both based on recursive mesh subdivision techniques. The first method introduces a partitioning scheme to Catmull-Clark/Doo-Sabin subdivision to indirectly control the roundness of the resultant shape. Although the method generates analytically-smooth surfaces, it suffers from several construction limitations and stability problems if the desired roundness is large. The second method makes use of straight skeletons, modifying the actual recursive mesh subdivision to accomplish more directly the task of preserving planar regions. The result is a more stable algorithm. Both methods produce excellent results on a wide range of input meshes both in terms of execution speed and resultant quality. The final contribution of the thesis is the development of a Just-In-Time (JIT) VRML volume rounding extension using the polyhedron bevelling method. With this extension to VRML, rounded scene objects can be described as an initial coarse object representation together with a rounding specification. Polyhedron bevelling is executed just before rendering in real time. The file size required for this JIT approach is typically only 1 - 2% of the size of a standard polygon-mesh representation of the rounded object. The compactness of the design is a great advantage as VRML is designed to work on the Internet, while today's scarce bandwidth severely constrains the feasible scene complexity.

Thesis

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