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8.1.2.3 Reflection lines

Reflection lines are another first-order interrogation method used in the automotive industry to assess the fairness of a surface. Reflection lines simulate the mirror images of a number of parallel straight fluorescent lights on an automobile surface. In this method, deviations of the surface from a smooth shape can be detected by irregularities of the reflection lines. Originally a reflection line was defined as a reflected image of a linear light source on a surface by Klass [202]. Kaufmann and Klass [190] modified the above definition to reduce the computation as follows. A family of curves $ {\bf q}_i(t)$ , $ i=1\ldots n$ on the surface, which are intersection curves of the surface with a specific family of planes parallel to a unit vector $ {\bf v}$ , are evaluated. For each intersection curve $ {\bf q}_i(t)$ , parameter $ t_i$ that satisfies
$\displaystyle \frac{\dot{\bf q}_i(t)}{\vert\dot{\bf q}_i(t)\vert} \cdot {\bf v}= \cos \phi\;,$     (8.3)

is evaluated. Then points $ {\bf q}_1(t_1)$ , $ {\bf q}_2(t_2), \ldots$ , $ {\bf q}_n(t_n)$ are connected to form the reflection line. The procedure is repeated for different values of $ \phi$ . If iso-parametric lines are used instead of intersection curves of the surface with a family of parallel planes, computational efficiency is further improved as in [3]. Choi and Lee [61] applied the Blinn-Newell type of reflection mapping [118], which uses simple and physically acceptable mapping algorithm, to generate reflection lines on a trimmed NURBS surface. Choi and Lee [61] also provide a thorough recent review of this topic.

Color Plate A.2 depicts reflection lines on the bicubic B-spline surface patch shown in Fig. 8.1, where values of $ \frac{\dot{\bf q}(t)}{\vert\dot{\bf q}(t)\vert} \cdot {\bf v}$ with $ {\bf v}=\left(\frac{1}{2}, \frac{1}{2}, \frac{\sqrt{2}}{2}\right)^T$ are evaluated along iso-parametirc curves and the equal value points found by interpolation between mesh points are connected to form the reflection lines.

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Next: 8.1.2.4 Highlight lines Up: 8.1.2 First-order interrogation methods Previous: 8.1.2.2 Isophotes   Contents   Index
December 2009