caltech_formfactor's Introduction

On the Formfactor between Two Polygons

Abstract

Form factors are used in radiosity to describe the fraction of diffusely reflected light leaving one surface and arriving at another. They are a fundamental geometric property used for computation. Many special configurations admit closed form solutions. However, the important case of the form factor between two polygons in three space has had no known closed form solution. We give such a solution for the case of general (planar, convex or concave, possibly containing holes) polygons.

Authors

Peter Schröder
Pat Hanrahan

Changes

CMake project & build support
MSVC compatibility fixes
data export for "geometry for two rectangles sharing a common edge" figure

Figure generator

ffData = Import["caltechFF.txt", "Table"];

ListLinePlot[Transpose[ffData], PlotRange -> {{0, 528}, {0, 1.025}},
 ImageSize -> {840 - 24, 512 - 24}, AxesLabel -> {Style["\!\(\*
StyleBox[\"\[Theta]\", \"InlineCode\"]\)", Black,
    FontFamily -> "Cambria", FontSize -> 24],
   Style["F12", Black, FontFamily -> "Cambria", FontSize -> 24]},
 PlotStyle -> Directive[Black, Thick],
 AxesStyle -> Directive[Black, Thick, 16],
 Ticks -> {Table[{i, 180 i/512 \[Degree]}, {i, 512/18, 512, 512/18}],
   Table[N[i], {i, 1/5, 1, 1/5}]}, ImageMargins -> 16]