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Discontinuity Meshing

# Shadows and Discontinuity Meshing

A discontinuity mesh describes illumination discontinuities in
a scene illuminated by an area light source.
More precisely: In a 3D scene consisting of a planar polygonal
light source and a number of polyhedral objects (which have planar
faces), define the **direct primary irradiance** as

0 1 /
B (x) = ---- | N(x) L(omega,x) d omega
pi /
V(x)

where *x* is a point on a face of the scene, *V(x)* is
the set of directions in which the light source is visible from
*x*, *N(x)* is the outward face normal at *x*,
*L(omega,x)* is a vector in direction *omega* with
magnitude equal to the light intensity in that direction, and *d
omega* is an infinitesimal solid angle.
Shadow boundaries correspond to discontinuities in *B^0(x)* and
in its first and second derivatives. These shadow boundaries form
lines and conic curves on the surfaces of the scene.
Examples are shown below, where pink lines are second derivative
discontinuities (called D2 EV), yellow conic curves are also
second derivative discontinuities (called D2 EEE), and blue lines
are first derivative discontinuites (called D1).

Intensities are quantized in the images, resulting in obvious
isolux contours. Pixel values have been jittered slightly to smooth
the isolux contours. This is best viewed with 24-bit colour.

Please refer to the paper
for a description of our discontinuity meshing algorithm, as well as
references to much of the other work in discontinuity meshing. See
also

### A Room

### A Cube

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