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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)

- Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H Barr, Caltech
- 2001

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)

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)

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 use advanced tensor visualization techniques to study 3D diffusion tensor MRI data of a heart. We use scalar and tensor glyph visualization methods to investigate the data and apply a moving least squares (MLS) fiber tracing method to recover and visualize the helical structure and the orientation of the heart muscle fibers.

Many optimization models of neural networks need constraints to restrict the space of outputs to a subspace which satisfies external criteria. Optimizations using energy methods yield "forces" which act upon the state of the neural network. The penalty method, in which quadratic energy constraints are added to an existing optimization energy, has become… (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)