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10.1.3 Spotlight Effects using Projective Textures

The projective texture technique described earlier can be used to generate a number of interesting illumination effects. One of the possible effects is spotlight illumination. The OpenGL lighting model already includes a spotlight illumination model, providing control over the cutoff angle (spread of the cone), the exponent (concentration across the cone), direction of the spotlight, and attenuation as a function of distance. The OpenGL model typically suffers from undersampling of the light. Since the lighting model is only evaluated at the vertices and the results are linearly interpolated, if the geometry being illuminated is not sufficiently tessellated incorrect illumination contributions are computed. This typically manifests itself by a dull appearance across the illuminated area or irregular or poorly defined edges at the perimeter of the illuminated area. Since the projective method samples the illumination at each pixel the undersampling problem is eliminated.

Similar to the Phong highlight method, a suitable texture map must be generated. The texture is an intensity map of a cross-section of the spotlight's beam. The same type of exponent parameter used in the OpenGL model can be incorporated or a different model entirely can be used. If 3D textures are available the attenuation due to distance can be approximated using a 3D texture in which the intensity of the cross-section is attenuated along the $r$-dimension. When geometry is rendered with the spotlight projection, the $r$ coordinate of the fragment is proportional to the distance from the light source.

In order to determine the transformation needed for the texture coordinates, it is easiest to think about the case of the eye and the light source being at the same point. In this instance the texture coordinates should correspond to the eye coordinates of the geometry being drawn. The simplest method to compute the coordinates (other than explicitly computing them and sending them to the pipeline from the application) is to use an GL_ EYE_LINEAR texture generation function with an GL_ EYE_PLANE equation. The planes simply correspond to the vertex coordinate planes (e.g., the $s$ coordinate is the distance of the vertex coordinate from the $y$-$z$ plane, etc.). Since eye coordinates are in the range [-1.0, 1.0] and the texture coordinates need to be in the range [0.0, 1.0], a scale and translate of 0.5 is applied to $s$ and $t$ using the texture matrix. A perspective spotlight projection transformation can be computed using gluPerspective() and combined into the texture transformation matrix. The transformation for the general case when the eye and light source are not in the same position can be computed by incorporating into the texture matrix the inverse of the transformations used to move the light source away from the eye position.

With the texture map available, the method for rendering the scene with the spotlight illumination is as follows:

  1. Initialize the depth buffer.
  2. Clear the color buffer to a constant value which represents the scene ambient illumination.
  3. Draw the scene with depth buffering enabled and color buffer writes disabled.
  4. Load and enable the spotlight texture, set the texture environment to GL_ MODULATE.
  5. Enable the texgen functions, load the texture matrix.
  6. Enable blending and set the blend function to GL_ ONE, GL_ ONE.
  7. Disable depth buffer updates and set the depth function to GL_ EQUAL.
  8. Draw the scene with the vertex colors set to 1.0.
  9. Disable the spotlight texture, texgen and texture transformation.
  10. Set the blend function to GL_ DST_COLOR.
  11. Draw the scene with normal illumination.

There are three passes in the algorithm. At the end of the first pass the ambient illumination has been established in the color buffer and the depth buffer contains the resolved depth values for the scene. In the second pass the illumination from the spotlight is accumulated in the color buffer. By using the GL_ EQUAL depth function, only visible surfaces contribute to the accumulated illumination. In the final pass the scene is drawn with the colors modulated by the illumination accumulated in the first two passes to arrive at the final illumination values.

The algorithm does not restrict the use of texture on objects, since the spotlight texture is only used in the second pass and only the scene geometry is needed in this pass. The second pass can be repeated multiple times with different spotlight textures and projections to accumulate the contributions of multiple light sources.

There are a couple of considerations that also should be mentioned. Texture projection along the negative line-of-sight of the texture (back projection) can contribute undesired illumination. This can be eliminated by positioning a clip plane at the near plane of the line-of-site. Also, OpenGL encourages but does not guarantee pixel exactness when various modes are enabled or disabled. This can manifest itself in undesirable ways during multipass algorithms. For example, enabling texture coordinate generation may cause fragments with different depth values to be generated compared to the case when texture coordinate generation is not enabled. This problem can be overcome by re-establishing the depth buffer values between the second and third pass. This is done by redrawing the scene with color buffer updates disabled and the depth buffering configured the same as for the first pass. Also, use a texture wrap mode of GL_ CLAMP to keep the spotlight pattern from repeating. When using a linear texture filter, use a black texel border to avoid clamping artifacts or, if available, use the GL_ CLAMP_TO_EDGE wrap mode.

It is also possible to render the entire scene in a single pass. If none of the objects in the scene are textured, the complete image could be rendered once, if the ambient illumination can be summed with spotlight illumination while the objects are rendered. Some vendors have added an additive texture environment function as an extension which makes this operation feasible. A cruder method that works in OpenGL 1.1 involves illuminating the scene using normal OpenGL lighting, using the spotlight texture to modulate the scene brightness.

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