View-Independent Reconstruction

Read CW[10] Chapter 9.

Combining HR and Discontinuity Meshing

This method is described more completely in [24]

1.

Discontinuity Locations

2.

Initial Linking

3.

Global Pass (introduce discontinuities as needed)

4.

Local Pass

The discontinuity locations are stored (as segments) on each surface. All D⁰ discontinuities in the environment as well as all D¹ and D² discontinuities from the light source are computed. During refinement, these discontinuities are used to determine how to subdivide. The discontinuity that best splits a surface is used, although preference is given to D⁰ discontinuities. The mesh itself is stored as a BSP tree. If no more discontinuities exist, the mesh is subdivided by splitting the patch in half as best as possible.

For the local pass, a mesh is created that incorporates all discontinuities, even those that hadn't been needed during the global pass. The mesh is represented as a Delaunay triangulation of the discontinuity segments (and possibly any additionally segments added by the BSP subdivision, although that is not mentioned.) For each vertex in the mesh, the radiance is computed exactly. here are four approaches to this.

• Look up the value in the mesh.
• Recompute unoccluded form factors from source to vertex.
• Recompute unoccluded form factors and visibility to vertex.
• Recompute only for links to light sources.

General Approach

1.

Create a global solution.

2.

Analyze the global solution (optional).

3.

Create(refine) a display mesh.

4.

Compute values for the display mesh.

Items 3 and 4 may need to be repeated until satisfactory.

Analyzing the global solution means determining where additional or different information is needed in order to create a solution that give the greatest perceptual accuracy using the least number of polygons. Another approach would be just to create a very fine display mesh, and then use one of the many mesh simplification algorithms to create a more optimal mesh.

Ideally, the display mesh would include the (important) discontinuities. Lischinski computed them explicitly. This may be fine for simple polygonal environments with a few simple lights, but in practice is not practical. A better, although not necessarily doable, approach would be to have the mesh adapt to fit the characteristics of the radiance function. If sophisticated enough, this could resolve discontinuities as well.

The local pass involves reconstructing the radiance at a single point. There are many approaches to doing this. The fact that we are gathering to mesh vertices rather than to pixels helps a lot, as any small errors we make will get spread out smoothly over the mesh. The standard time versus quality tradeoffs appear here. Ideally we would recompute complete vertex to source form factors, but usually the visibility component makes this too expensive.