A Shadow-Volume Algorithm for Opaque and Transparent Nonmanifold Casters

Since precise shadows can be generated in real-time, graphics applications often use the shadow volume algorithm. This algorithm was limited to manifold casters, but recently has been extended to general non-manifold casters with oriented triangles. We provide a further extension to general non-manifold meshes and an additional extension to shadows of transparent casters. To achieve these, we first introduce a generalization of an object’s silhouette to non-manifold meshes. By using this generalization, we can compute the number of caster surfaces between the light and receiver, and furthermore, we can compute the light intensity arrived at the receiver fragments after the light has traveled through multiple colored transparent receiver surfaces. By using these extensions, shadows can be generated from transparent casters that have constant color and opacity. Introduction. In real-time graphics applications such as games, shadows of various objects add important visual realism and provide additional information on the spatial relationships between objects in the scene. For example, a shadow drawn at the foot of a game character makes the user believe that the foot is resting on the ground. When the game character is jumping, the user can estimate the height of the character from the location of the shadow. Similarly, in CAD or data visualization applications, shadows help the user to understand the three-dimensional layout of various objects. Rendering shadows is still a problem without a unified approach. Therefore, © A K Peters, Ltd. 1 1086-7651/06 $0.50 per page i i “jgt” — 2008/7/20 — 19:20 — page 2 — #2 i i i i i i 2 journal of graphics tools Figure 1. Shadows from a colored transparent caster. different algorithms have been developed for various applications. Among such applications, games require real-time rendering of shadows, for which two commonly used methods are available: the shadow map and the shadow volume algorithms. The shadow map algorithms are fast and robust, but have aliasing artifacts since the resolution of the shadow map is limited. In contrast, shadow volume algorithms, introduced in [Crow 77], do not have aliasing artifacts, but have been limited to manifold meshes or non-manifold meshes made of one-sided polygons. We propose a method that extends the application of the shadow volume to general non-manifold mesh that can even become transparent as shown in Fig. 1. Suppose that we have a screen-space mask that represents whether pixels are inside the shadow or not. Then, shadows are trivially obtained by rendering each pixel with or without specular and diffuse lighting depending on the mask. Therefore, computing this mask is the main idea in the shadow volume method. We briefly introduce this idea in the following paragraphs. We first assume a point light source. The mask is obtained by rendering the boundary of the umbra. The boundary of the umbra consists of the caster surface and special set of polygons obtained by extruding the silhouette edges of the caster along the light direction. To facilitate future discussions, we will use the term shadow polygon to refer to the polygon that bound the shadow volume. In fig. 2, where the umbra of a triangle V0V1V2 is shown, shadow polygons are the triangle V0V1V2, and all the polygons obtained by extruding edges. Furthermore, we distinguish two types of shadow polygons: the extrusion polygons that form the sides of the volume, i i “jgt” — 2008/7/20 — 19:20 — page 3 — #3 i i i i i i B.Kim, K.Kim, G.Turk: A Shadow Volume Algorithm for Opaque and Transparent Non-Manifold Casters 3