This handout was given our during our presentation at SIGGRAPH '96. For more information, you may look at the slides or send email to Michael Herf or Paul Heckbert

### A Guide to Making Your Own

Michael Herf, Paul Heckbert
C.S. Dept., Carnegie Mellon University
SIGGRAPH 1996

This is a quick overview of how to implement our soft shadows algorithm. We'll discuss both workstation (RealityEngine-level) implementations and PC implementations. For a general overview of how the algorithm works, see our Technical Sketch in the SIGGRAPH 96 Visual Proceedings.

To begin, you'll need some scene geometry to render, and a list of polygons you want to generate realistic shadows for. Keep the latter to a small number if you want good performance - most texture mapping hardware and software we've encountered handles large numbers of independent textures very badly.

Next, you'll need a set of lights to illuminate your scene. The physical geometry of the lights really doesn't matter. What is more important is how well you sample them. You should probably have a sampling function which allows incremental improvements in quality. (e.g., you give it a parameter n and it returns the coordinates, colors, and intensities of n or n2 point light samples.) Our implementation uses only parallelogram light sources, and uses a jittered sampling grid across each one. Whatever you do, use stochastic sampling.

### Algorithm Recap/Overview

Preprocessing
• for each light sample point
• compute 4x4 matrix
• for each other polygon
• draw polygon, blackened
• save accumulator into texture memory
Display
• draw scene with texture

### Math: Computing the Transform

This transformation converts any pyramid defined by two points a and b (the point light sample and one vertex of the receiver parallelogram) and two vectors ex and ey to a unit box.

You need a parallelogram to bound each of the receiver polygons. For triangles, make the triangle half of the receiving parallelogram. For general polygons, the simplest bounding parallelogram is a rectangle. Use the above 4x4 matrix to transform every vertex in the scene.

Following that, you'll have to clip against this box: [0, 1] in x, [0, 1] in y, and [1,] in z. Finally, flatten everything in z, and you'll have a hard shadow image in x and y, which you can composite with similar hard shadows.

### RealityEngine/OpenGL Implementation

OpenGL provides an accumulation buffer which allows any linear combination of images. You can use the RE to compute either modulation textures (grayscale images which "modulate" an existing texture), or radiance textures, which accurately depict the diffuse shading from all of your area light sources. The latter is more interesting, and the former more obvious, so I'll be describing how to make radiance textures.

Our implementation decides the size of a texture for a polygon by choosing a power of 2 (clamped at 256) for each width and height, based on the size of the polygon in world space. We set a 2D viewport to encompass these chosen pixels, setting the viewport coordinate system to [0.0, 1.0] for width and height, and determine a global transformation matrix using the following code:

```make_projmatrix(ourmatrix.a);
// OpenGL stuff
glMatrixMode(GL_PROJECTION);
glOrtho(0.0, 1.0, 0.0, 1.0, -0.999, -1000);
glMultMatrixf(ourmatrix.a);
glMatrixMode(GL_MODELVIEW);
```

[The exact parameters for the glOrtho call were found by experimentation.] For each light sample, the target polygon can be subdivided and drawn as a series of triangle strips, each triangle Gouraud-shaded. If you want an ambient component in your texture, you can add this image (without shadows) to your accumulation buffer. Next, all objects should be drawn without z-buffer, without Gouraud shading, just flat black, on top of the shaded background. Add this image to the accumulator after drawing all other objects in the scene. Choose a new light sample, set a new matrix, and keep going until you've exhausted your sample points. After that, you have a radiance texture.

### PC Implementation Tips

Some initial testing indicates that an implementation of this algorithm could be made to run quickly on PC hardware. Memory bandwidth is the limiting factor, but some simplifications to the algorithm can make it speedy.

First, we should only compute modulation textures during the accumulation steps. If you want colored lights as well, do this afterwards using one point per light source. This keeps the depth of the textures to 8 bits, dramatically reducing the amount of memory bandwidth required to do the compositing and drawing.

Second, use adds to do the compositing. With some planning in advance, we don't need an accumulation buffer 2x as big as the depth we draw to (like OpenGL does). Choose the number of lights samples n so that n is a factor of 256-a (for a=ambient intensity). Then, draw each polygon flat-shaded on a black background with color (256-a)/n. These techniques (along with fast software polygon renderers) should make reasonable performance on PCs achievable.

Michael Herf can be contacted at herf+@cmu.edu. Paul Heckbert can be contacted at ph@cs.cmu.edu. What you have just read is a summary of a work in progress, "Simulating Soft Shadows with Graphics Hardware", PH and MH. For more information, see http://www.cs.cmu.edu/~ph.