The idea of using the stencil buffer to generate shadows has been around for over a decade, but only recently has 3D graphics hardware advanced to the point where using the stencil algorithm on a large scale has become practical. Not long ago, there existed some unsolved problems pertaining to stencil shadows that prevented the algorithm from working correctly under various conditions. Advances have now been made, however, so that stencil shadows can be robustly implemented to handle arbitrarily positioned point lights and infinite directional lights having any desired spatial relationship with the camera. This article presents the intricacies of the entire stencil shadow algorithm and covers every mathematical detail of its efficient implementation.
Algorithm Overview
The basic concept of the stencil shadow algorithm is to use the stencil buffer as a masking mechanism to prevent pixels in shadow from being drawn during the rendering pass for a particular light source. This is accomplished by rendering an invisible shadow volume for each shadow-casting object in a scene using stencil operations that leave nonzero values in the stencil buffer wherever light is blocked. Once the stencil buffer has been filled with the appropriate mask, a lighting pass only illuminates pixels where the value in the stencil buffer is zero.
As shown in Figure 1, an object’s shadow volume encloses the region of space for which light is blocked by the object. This volume is constructed by finding the edges in the object’s triangle mesh representing the boundary between lit triangles and unlit triangles and extruding those edges away from the light source. Such a collection of edges is called the object’s silhouette with respect to the light source. The shadow volume is rendered into the stencil buffer using operations that modify the stencil value at each pixel depending on whether the depth test passes or fails. Of course, this requires that the depth buffer has already been initialized to the correct values by a previous rendering pass. Thus, the scene is first rendered using a shader that applies surface attributes that do not depend on any light source, such as ambient illumination, emission, and environment mapping.
Figure 1. An object’s shadow volume encloses the region of space for which light is blocked by the object. |
The original stencil algorithm renders the shadow volume in two stages. In the first stage, the front faces of the shadow volume (with respect to the camera) are rendered using a stencil operation that increments the value in the stencil buffer whenever the depth test passes. In the second stage, the back faces of the shadow volume are rendered using a stencil operation that decrements the value in the stencil buffer whenever the depth test passes. As illustrated in Figure 2, this technique leaves nonzero values in the stencil buffer wherever the shadow volume intersects any surface in the scene, including the surface of the object casting the shadow.
Figure 2. Numbers at the ends of rays emanating from the camera position C represent the values left in the stencil buffer for a variety of cases. The stencil value is incremented when front faces of the shadow volume pass the depth test, and the stencil value is decremented when back faces of the shadow volume pass the depth test. The stencil value does not change when the depth test fails. |
There are two major problems with the method just described. The first is that no matter what finite distance we extrude an object’s silhouette away from a light source, it is still possible that it is not far enough to cast a shadow on every object in the scene that should intersect the shadow volume. The example shown in Figure 3 demonstrates how this problem arises when a light source is very close to a shadow-casting object. Fortunately, this problem can be elegantly solved by using a special projection matrix and extruding shadow volumes all the way to infinity.
Figure 3. No matter what finite distance an object’s silhouette is extruded away from a light source, moving the light close enough to the object can result in a shadow volume that cannot reach other objects in the scene. |
The second problem shows up when the camera lies inside the shadow volume or the shadow volume is clipped by the near plane. Either of these occurrences can leave incorrect values in the stencil buffer causing the wrong surfaces to be illuminated. The solution to this problem is to add caps to the shadow volume geometry, making it a closed surface, and using different stencil operations. The two caps added to the shadow volume are derived from the object’s triangle mesh as follows. A front cap is constructed using the unmodified vertices of triangles facing toward the light source. A back cap is constructed by projecting the vertices of triangles facing away from the light source to infinity. For the resulting closed shadow volume, we render back faces (with respect to the camera) using a stencil operation that increments the stencil value whenever the depth test fails, and we render front faces using a stencil operation that decrements the stencil value whenever the depth test fails. As shown in Figure 4, this technique leaves nonzero values in the stencil buffer for any surface intersecting the shadow volume for arbitrary camera positions. Rendering shadow volumes in this manner is more expensive than using the original technique, but we can determine when it’s safe to use the less-costly depth-pass method without having to worry about capping our shadow volumes.
Figure 4. Using a capped shadow volume and depth-fail stencil operations allows the camera to be inside the shadow volume. The stencil value is incremented when back faces of the shadow volume fail the depth test, and the stencil value is decremented when front faces of the shadow volume fail the depth test. The stencil value does not change when the depth test passes. |
The details of everything just described are discussed throughout the remainder of this article. In summary, the rendering algorithm for a single frame runs through the following steps.
A Clear the frame buffer and perform an ambient rendering pass. Render the visible scene using any surface shading attribute that does not depend on any particular light source.
B Choose a light source and determine what objects may cast shadows into the visible region of the world. If this is not the first light to be rendered, clear the stencil buffer.
C For each object, calculate the silhouette representing the boundary between triangles facing toward the light source and triangles facing away from the light source. Construct a shadow volume by extruding the silhouette away from the light source.
D Render the shadow volume using specific stencil operations that leave nonzero values in the stencil buffer where surfaces are in shadow.
E Perform a lighting pass using the stencil test to mask areas that are not illuminated by the light source.
F Repeat steps B through E for every light source that may illuminate the visible region of the world.
For a scene illuminated by n lights, this algorithm requires at least n+1 rendering passes. More than n+1 passes may be necessary if surface shading calculations for a single light source cannot be accomplished in a single pass. To efficiently render a large scene containing many lights, one must be careful during each pass to render only objects that could potentially be illuminated by a particular light source. An additional optimization using the scissor rectangle can also save a significant amount of rasterization work -- this optimization is discussed in the last section of this article.