The Double Insertion, Nonuniform, Stationary subdivision surface (DINUS) generalizes both the nonuniform, bicubic spline surface and the Catmull-Clark subdivision surface. DINUS allows arbitrary knot intervals on the edges, allows incorporation of special features, and provides limit point as well as limit normal rules. It is the first subdivision scheme that gives the user all this flexibility and at the same time all essential limit information, which is important for applications in modeling and adaptive rendering. DINUS is also amenable to analysis techniques for stationary schemes. We implemented DINUS as an Autodesk Maya plugin to show several modeling and rendering examples.

An extended subdivision surface (ESub) is a generalization of Catmull Clark and NURBS surfaces. Depending on the knot intervals and valences of the vertices and faces, Catmull Clark as well as NURBS patches can be generated using the extended subdivision rules. Moreover, an arbitrary choice of the knot intervals and the topology is possible. Special features like sharp edges and corners are consistently supported by setting selected knot intervals to zero or by applying special rules. Compared to the prior nonuniform rational subdivision surfaces (NURSS), the ESubs offer limit-point rules which are indispensable in many applications, for example, for computer-aided design or in adaptive visualization. The refinement and limit-point rules for our nonuniform, nonstationary scheme are obtained via a new method using local Bézier control points. With our new surface, it is possible to start with existing Catmull Clark as well as NURBS models and to continue the modeling process using the extended subdivision options.

Abstract 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.

Abstract Subdivision Surfaces as well as (interactive) ray tracing have become an important issue in computer graphics.But ray tracing of subdivision surfaces has received only little attention. We present a new approach for raytracing of subdivision surfaces. The algorithm uses a projection of the ray onto the surface and works mainly intwo dimensions along this projection. While proceeding from patch to patch, we examine the bounding volume oftheir borders: the lower the distance between ray and subdivision surface, the more refinement steps are adaptivelyapplied to the surface but only along the projection of the ray. The adaptive refinement of a patch is controlled bycurvature, size, its membership to the silhouette, and its potential contribution to the light transport. The algorithmis simple and mainly consists of elementary geometric computations. Hence it is fast and easy to implementwithout the need for elaborate preprocessing. The algorithm is robust in the sense that it deals with all features ofsubdivision surfaces like creases and corners. Categories and Subject Descripters (according to ACM CCS): I.3.7 [Computer Graphics]: Raytracing

Subdivision surfaces have become a standard technique for freeform shape modeling. They are intuitive to use and permit designers to flexibly add detail. But with larger control meshes, efficient adaptive rendering techniques are indispensable for interactive visualization and shape modeling. In this paper, we present a realization of tesselation‐on‐the‐fly for Loop subdivision surfaces as part of a framework for interactive visualization.