Rendering multi-perspective images with trilinear projection

Abstract

Non-linear projections of 3D graphical scenes can be used to compute reflections and refractions in curved surfaces, draw artistic images in the style of Escher or Picasso, and produce visualizations of complex data. Previously, most non-linear projections were rendered by ray tracing. This paper presents trilinear projection, a technique for rendering non-linear projections in a manner that achieves significant performance benefits by taking advantage of current rendering hardware and software.Trilinear projections are geometrically similar to Phong-shaded triangular patches, and like Phong patches they can be joined to represent more complicated shapes. The paper details how a single trilinear projection projects a scene point, how projections of scene triangles can be built up by considering the connectivity of projected points, and how multiple trilinear projections can be combined. Finally, it outlines a method for using trilinear projection to approximate reflections and refractions on curved surfaces.