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In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high-fidelity computer graphics objects using imperfectly-measured data… (More)

This paper proposes a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed Finite-Element/Finite-Volume method, and… (More)

The theory of elasticity describes deformable materials such as rubber, cloth, paper, and flexible metals. We employ elasticity theory to construct differential equations that model the behavior of non-rigid curves, surfaces, and solids as a function of time. Elastically deformable models are active: they respond in a natural way to applied forces,… (More)

- Alan H. Barr
- 1981

the basic quadric surfaces and solids, yielding a variety ofusefulforms. Over the past 20 years, a great deal of interest has developed in the use of computer graphics and numerical methods for three-dimensional design. Significant progress in geometric modeling is being made, predominantly for objects best represented by lists of edges, faces, and… (More)

New hierarchical solid modeling operations are developed, which simulate twisting, bending, tapering, or similar transformations of geometric objects. The chief result is that the normal vector of an arbitrarily deformed smooth surface can be calculated directly from the surface normal vector of the undeformed surface and a transformation matrix.… (More)

We present a new algorithm for identifying the distribution of different material types in volumetric datasets such as those produced with magnetic resonance imaging (MRI) or computed tomography (CT). Because we allow for mixtures of materials and treat voxels as regions, our technique reduces errors that other classification techniques can create along… (More)

In this paper, we propose a stable and efficient algorithm for animating mass-spring systems. An integration scheme derived from implicit integration allows us to obtain interactive realistic animation of any mass-spring network. We alleviate the need to solve a linear system through the use of a predictor-corrector approach: We first compute a rapid… (More)

A quadtree algorithm is developed to triangulate deformed, intersecting parametric surfaces. The biggest problem with adaptive sampling is to guarantee that the triangulation is accurate within a given tolerance. A new method guarantees the accuracy of the triangulation, given a "Lipschitz" condition on the surface definition. The method constructs a… (More)

(a) (b) Figure 1: Mars elevation map: (a) raw data, (b) smooth version after anisotropic diffusion. Notice how, with our non-uniform diffusion, the aliasing due to poor quantization is suppressed without altering the general topography of the surface (both pictures are flat-shaded). Abstract In this paper, we present an efficient way to denoise bivariate… (More)

In this paper, we present a robust and mathematically sound ray-intersection algorithm for implicit surfaces. The algorithm is guaranteed to numerically find the nearest intersection of the surface with a ray, and is guaranteed not to miss fine features of the surface. It does not require fine tuning or human choice of interactive parameters. Instead, it… (More)