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A new parametrization technique and its applications for general Catmull-Clark subdivision surfaces are presented. The new technique extends J. Stam's work by redefining all the eigen basis functions in the parametric representation for general Catmull-Clark subdivision surfaces and giving each of them an explicit form. The entire eigenstructure of the(More)
A new method for constructing a Catmull–Clark subdivision surface (CCSS) that interpolates the vertices of a given mesh with arbitrary topology is presented. The new method handles both open and closed meshes. Normals or derivatives specified at any vertices of the mesh (which can actually be anywhere) can also be interpolated. The construction process is(More)
A voxelization technique and its applications for objects with arbitrary topology are presented. It converts a free-form object from its continuous geometric representation into a set of voxels that best approximates the geometry of the object. Unlike traditional 3D scan-conversion based methods, our voxelization method is performed by recursively(More)
A new adaptive tessellation method for general CatmullClark subdivision surfaces is presented. Development of the new method is based on the observation that optimum adaptive tessellation for rendering purpose is a recursive error evaluation and globalization process. The adaptive tessellation process is done by generating an inscribing polyhedron to(More)
A new method for constructing interpolating Loop subdivision surfaces is presented. The new method is an extension of the progressive interpolation technique for B-splines. Given a triangular mesh M, the idea is to iteratively upgrade the vertices of M to generate a new control mesh $\overline{M}$ such that limit surface of $\overline{M}$ would interpolate(More)
Privacy preservation is a major concern in the application of data mining techniques to counterterrorism and homeland security. Data distortion is a critical component to preserve privacy in security-related data mining applications. We propose a Fast Fourier Transform (FFT) based method for data distortion, and compare it with the Singular Value(More)
An interpolation technique with the capability of local shape control for meshes of arbitrary topology is presented. The interpolation is a progressive process which iteratively updates the given mesh, through a two-phase Doo-Sabin subdivision scheme, until a control mesh whose limit surface interpolates the given mesh is reached. For each iteration of the(More)
In this paper, we present a new adaptive rendering method for general Catmull-Clark subdivision surfaces. The new method is based on direct evaluation of the limit surface to generate an inscribed polyhedron of the limit surface. The method generates fewer polygons in the final rendering process because inscribed approximation usually provides faster(More)