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Although lines in do not have a unique normal vector, Zöckler et al.  illuminate streamlines using the popular reflection model of Phong. They select from all the normal vectors the one coplanar to the light vector L and the tangent vector T. Let N be this normal vector, L the light direction, V the viewing direction, and R the unit reflection vector (the vector in the L-N-plane with the same angle to the surface normal as the incident light). Then the light intensity at a particular point is given by
Since light reflection on stream lines increases the spatial impression of the resulting images, lines shaded with this method provide stronger depth cues (see Figure 1). Furthermore, texture mapping capabilities of modern graphics hardware can be exploited to render these lines efficiently, achieving high frame rates even when large numbers of lines have to be rendered.
A drawback of this method is that the normal vector is not constant but a projection of the light vector into the normal plane of the stream line. This means that the angle between the light vector and the normal vector is minimized, resulting in a more uniform brightness than we are used to perceive in real world. This effect yet can be compensated by exponentiating the diffuse reflection term in Equation (1).
Figure 1: Illuminated Streamlines. The flow around a wing on the left and the electrostatic field of a benzene molecule on the right.
Mon Apr 6 15:08:31 MET DST 1998