Shadows on Curved Surfaces
One simple way to extend the idea of planar shadows to curved surfaces is to use a generated shadow image as a projective texture. Think of shadows from the light’s point of view. Whatever the light sees is illuminated; what it does not see is in shadow. Say the occluder is rendered in black from the light’s viewpoint into an otherwise white texture. This texture can then be projected onto the surfaces that are to receive the shadow. Effectively, each vertex on the receivers has a (u, v) texture coordinate computed for it and has the texture applied to it. These texture coordinates can be computed explicitly by the application. This differs a bit from the ground shadow texture in the previous section, where objects are projected onto a specific physical plane. Here, the image is made as a view from the light, like a frame of film in a projector
When rendered, the projected shadow texture modifies the receiver surfaces. It can also be combined with other shadow methods, and sometimes is used primarily for helping aid perception of an object’s location.
For example, in a platform-hopping video game, the main character might always be given a drop shadow directly below it, even when the character is in full shadow
More elaborate algorithms can give better results.
For example, Eisemann and Decoret assume a rectangular overhead light and create a stack of shadow images of horizontal slices of the object, which are then turned into mipmaps or similar. The corresponding area of each slice is accessed proportional to its distance from the receiver by using its mipmap, meaning that more distant slices will cast softer shadows.
There are some serious drawbacks of texture projection methods. First, the application must identify which objects are occluders and which are their receivers. The receiver must be maintained by the program to be further from the light than the occluder, otherwise the shadow is “cast backward.” Also, occluding objects cannot shadow themselves. The next two sections present algorithms that generate correct shadows without the need for such intervention or limitations.
Note that a variety of lighting patterns can be obtained by using prebuilt projective textures. A spotlight is simply a square projected texture with a circle inside of it defining the light. A Venetian blinds effect can be created by a projected texture consisting of horizontal lines. This type of texture is called a light attenuation mask, cookie texture, or gobo map. A prebuilt pattern can be combined with a projected texture created on the fly by simply multiplying the two textures together.