Practice: Mesh and Display Issues

Read CW [10] Chapter 8 and pages 136-152 in Chapter 6.

Properties of a Good Mesh

Order and Continuity

Problems and benefits with sampling over patches.

Problems and benefits with sampling at vertices.

Common mesh artifacts.

Density

Shape

Aspect ratio

Grading (Mesh size varies smoothly)

Conformance (Vertices line up across boundaries)

We are discussing a priori meshing (meshing that happens before the solution takes place) but all of these points apply to adaptive meshing as well.

Creation of the Initial Mesh

In real radiosity systems, the input data comes from a variety of sources. This data is usually not ideal, and may be far from it. The input geometry should be pre-processed in order to get it ready for meshing. This involves several steps:

Merge coplanar, adjacent surfaces.

Remove unnecessary vertices

Worry about degenerate geometry.

Worry about numeric problems.

After preprocessing, the initial mesh can be created. For now, the initial mesh is also the final mesh, so it must be created fine enough to capture all interesting detail. Eventually, the initial mesh will be subdivided by the radiosity system. Depending upon how this is done, the initial mesh should be created as large as possible, so that the number of mesh elements is as small as possible.

Grid Superposition

Superimposes a grid over the surface. Has problems at edges (Used by Baum etal. [4]).

Template Mapping

Mesh in parameter space.

Multiblocking

Chop geometry into simpler pieces and create the mesh on those. This includes D⁰ discontinuity mesh and Campbell's BSP tree meshing.

More Info

Ronchamp: A Case Study [18]

Making Radiosity Usable: Automatic Preprocessing and Meshing Techniques for the Generation of Accurate Radiosity Solutions [4]

Discontinuity Meshing [23]

BSP trees for discontinuities [6]