A Viewpoint-Dependent Approach to Ray Trace Free-Form Surfaces

• Published in: Computer graphics forum Vol. 23; no. 2; pp. 143 - 155
• Main Authors: Formella, A., Müller, K.
• Format: Journal Article
• Language: English
• Published: 9600 Garsington Road , Oxford , OX4 2DQ , UK Blackwell Publishing Ltd 01.06.2004
• Subjects: Algorithms; Bézier curves; Computer graphics; free-form surfaces; I.3.5 [Computer Graphics]: Free-form surfaces; I.3.7 [Computer Graphics]: Ray tracing; ray tracing; Studies; view-dependent representation
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/j.1467-8659.2004.00748.x

For convincing realistic scenes objects with free‐form surfaces are essential. Especially for photorealistic rendering pure polygonal models are often not sufficient. We present a new kind of algorithm to render free‐form surfaces in a rendering system based on ray tracing. We describe a triangular patch as usual by its three points and normal vectors, but base the intersection calculation as well on the viewpoint of the camera (or, in general, on the ray itself). Hence, the shape of the object depends to some extent on the sampling rays. However, the resulting differences of, for instance, the shape of the silhouette to the shape of the corresponding shadow is usually not perceived by the observer of the rendered image. Because we perform a direct computation without a tessellation process, the resulting surface, its shadows, and its reflections appear smooth independent of the distance to the camera. Furthermore, the memory consumption depends only linearly on the number of input triangles. Special features like creases, T‐vertices, and darts are also well supported. The computed uv‐coordinates provide a direct means for texture mapping whose visual appearance improves significantly compared to triangle meshes of the same resolution.