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This paper describes a method to obtain a closed surface that approximates a general 3D data point set with non-uniform density. Aside from the positions of the initial data points, no other information is used. Particularly, neither the topological relations between the points nor the normal to the surface at the data points are needed. The reconstructed… (More)

The computation of the largest planar region approximating a 3D object is an important problem with wide applications in modeling and rendering. Given a voxelization of the 3D object, we propose an efficient algorithm to solve a discrete version of this problem. The input of the algorithm is the set of grid edges connecting the interior and the exterior of… (More)

Since the publication of the original Marching Cubes algorithm, numerous variations have been proposed for guaranteeing watertight constructions of triangulated approximations of isosurfaces. Most approaches divide the 3D space into cubes that each occupy the space between eight neighboring samples of a regular lattice. The portion of the isosurface inside… (More)

We propose to measure the quality of an affine motion by its steadiness, which we formulate as the inverse of its Average Relative Acceleration (ARA). Steady affine motions, for which ARA&equal;0, include translations, rotations, screws, and the golden spiral. To facilitate the design of pleasing in-betweening motions that interpolate between an initial and… (More)

This paper proposes a technique for the design of luminaire reflector shapes from prescribed optical properties (far-field radiance distribution), geometrical constraints and user's knowledge. This is an important problem in the field of Lighting Engineering, more specifically for Luminaire Design. The reflector's shape to be found is just a part of a set… (More)

This paper describes a multiresolution method for implicit curves and surfaces. The method is based on wavelets, and is able to simplify the topology. The implicit curves and surfaces are deened as the zero-valued algebraic isosurface of a tensor-product uniform cubic Bspline. A wavelet multiresolution method that deals with uniform cubic Bsplines on… (More)