Casting Fast Shadows for a 3D Cursor

Although rarely at the forefront of our perception, shadows can greatly enhance our ability to perceive depth and other spatial relationships. Unfortunately, except in special cases such as casting a shadow on a simple planar surface, computing and rendering cast shadows is normally too time intensive for use in interaction. The work described here provides a technique for very rapidly rendering a shadow onto any existing scene rendered into a depth buffer. This technique works only for a special case -- casting a shadow from a single convex polygonal object using one light source -- however, this case is useful for interaction since it can provide shadows for a 3D cursor, or a single object being manipulated. An example of a simple cursor with a cast shadow (in this case in the form of a red cube over an irregular surface) is shown below:

To cast a shadow over an existing scene in depth buffer we can make use of the special properties of a single convex polygonal object. In particular, all the surface area upon which a shadow can be cast by such an object will always fall within a convex volume called its "shadow volume". As illustrated below, for this form of volume, any ray (representing, for example, the line of sight through a pixel) is guaranteed to first strike a front facing polygon, then strike a back facing polygon.

To cast a shadow over an existing scene in a depth buffer we need to intersect the surfaces represented in the buffer with the shadow volume. A pixel represents a surface within the shadow volume if it has a depth value between the depth of the front facing polygon and the back facing polygon found along the ray representing the line of sight through that pixel. These pixels should be rendered as in shadow, all others should retain normal rendering. To compute these pixels the steps illustrated below can be used. First the depth buffer is locked so that it is not modified. Next, the shadow is rendered into a separate image or "mask" plane in two steps. First all front facing polygons of the shadow volume are rendered in a foreground "shadow" color.

This renders color onto each pixel which is on a surface behind a front facing polygon. Next, all back facing polygons are rendered in the background color.

This removes shadow from any and all pixels behind a back facing polygon. The end result of these rendering steps is that only pixels representing a surface within the shadow volume remain colored.

These pixels represent the exact extent of the shadow and can be used to render it over the top of the existing scene.

Hudson, Scott, E., "Adding Shadows to a 3D Cursor", ACM Transactions on Graphics, v11, n2, pp. 193-199, April 1992.