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8.1.2.2 Isophotes

Isophotes are curves of constant light intensity on a surface, created by a point light source at infinity with direction l ( $ \vert{\bf l}\vert=1$ ), specified by the user. These curves can be used for the detection of surface irregularities [319,144]. An isophote is a curve for which the quantity
$\displaystyle {\bf N}(u,v)\, \cdot {\bf l}\, =\, \cos \theta\;,$     (8.2)

is constant and equal to $ c$ , for $ 0 \leq c \leq 1$ and $ 0 \leq \theta \leq 90^{\circ}$ where $ {\bf N}(u,v)$ is the unit surface normal vector. When the surface is locally planar (or flat) all normals are parallel and the isophotes do not generally exist. If the surface is $ C^{M}$ continuous then the isophote line will be $ C^{M-1}$ continuous. For rendering isophotes, the values of $ {\bf N}(u,v)\, \cdot {\bf l}$ are computed on a lattice and a number of isophotes are generated by connecting points of equal value found by interpolation between straddling grid points [3]. Color Plate A.1 shows isophotes of the bicubic B-spline surface in Fig. 8.1 with $ {\bf l}=\left(\frac{1}{2}, \frac{1}{2}, \frac{\sqrt{2}}{2}\right)^T$ .

next up previous contents index
Next: 8.1.2.3 Reflection lines Up: 8.1.2 First-order interrogation methods Previous: 8.1.2.1 Shading and ray   Contents   Index
December 2009