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For a variety of reasons subdivision surfaces have developed into a prominent member of the family of freeform shapes. Based on a standard polygonal mesh a modeller can build various kinds of shapes using an arbitrary topology and special geometrical features like creases. However, the interactive display of subdivision surfaces in current scenegraph… (More)

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… (More)

The problem of collision detection between objects is fundamental in many different communities including CAD, robotics, computer graphics, and computational geometry. This article presents a fast collision detection technique for all types of rigid bodies, demonstrated using polygon soups. We present two algorithms for computing a discrete spherical… (More)

Improving the visual appearance of coarse triangle meshes is usually done with graphics hardware with per-pixel shading techniques. Improving the appearance at silhouettes is inherently hard, as shading has only a small influence there and the geometry must be corrected. With the new geometry shader stage released with DirectX 10, the functionality to… (More)

In this paper we reconsider pairwise collision detection for rigid motions using a k-DOP bounding volume hierarchy. This data structure is particularly attractive because it is equally efficient for rigid motions as for arbitrary point motions (deformations). We propose a new efficient realignment algorithm, which produces tighter results compared to all… (More)

This paper presents a new solver for systems of nonlinear equations. Such systems occur in Geometric Constraint Solving, e.g., when dimensioning parts in CAD-CAM, or when computing the topology of sets defined by nonlinear inequalities. The paper does not consider the problem of decomposing the system and assembling solutions of subsystems. It focuses on… (More)

Polynomial ranges are commonly used for numerically solving polynomial systems with interval Newton solvers. Often ranges are computed using the convex hull property of the tensorial Bernstein basis, which is exponential size in the number <i>n</i> of variables.
In this paper, we consider methods to compute tight bounds for polynomials in <i>n</i>… (More)

For a variety of reasons subdivision surfaces have developed into a prominent member of the family of freeform shapes. Based on a standard polygonal mesh modeller can build various kinds of shapes using an arbitrary topology and special geometrical features like creases. However, the interactive display of subdivision surfaces in current scenegraph systems… (More)

Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability of effectively represent any surface of arbitrary genus. During the last ten years a large body of work has been devoted to the definition… (More)

This article focuses on algorithms for fast computation of the Euclidean distance between a query point and a subdivision surface. The analyzed algorithms include uniform tessellation approaches, an adaptive evalution technique, and an algorithm using Bézier conversions. These methods are combined with a grid hashing structure for space partitioning to… (More)