In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals – functions defined on polyhedral surfaces of arbitrary topology –, we reduce the problem of surface smoothing, or fairing, to low-pass filtering. We describe a very simple surface signal low-pass filter algorithm that applies to surfaces of arbitrary topology. As opposed to other existing optimization-based fairing methods, which are computationally more expensive, this is a linear time and space complexity algorithm. With this algorithm, fairing very large surfaces, such as those obtained from volumetric medical data, becomes affordable. By combining this algorithm with surface subdivision methods we obtain a very effective fair surface design technique. We then extend the analysis, and modify the algorithm accordingly, to accommodate different types of constraints. Some constraints can be imposed without any modification of the algorithm, while others require the solution of a small associated linear system of equations. In particular, vertex location constraints, vertex normal constraints, and surface normal discontinuities across curves embedded in the surface, can be imposed with this technique. CR

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A signal processing approach to fair surface design

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 compare them to existing formulations. Building upon previous work in discrete geometry, these operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators. We show that these estimates are optimal in accuracy under mild smoothness conditions, and demonstrate their numerical quality. We also present applications of these operators, such as mesh smoothing, enhancement, and quality checking, and show results of denoising in higher dimensions, such as for tensor images.

/pdf/discrete-differential-geometry-operators-for-triangulated-2-w8vp3jjpy1.pdf

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

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A Survey of General-Purpose Computation on Graphics Hardware

A Survey of General-Purpose Computation on Graphics Hardware.

To enable flexible, programmable graphics and high-performance computing, NVIDIA has developed the Tesla scalable unified graphics and parallel computing architecture. Its scalable parallel array of processors is massively multithreaded and programmable in C or via graphics APIs.

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NVIDIA Tesla: A Unified Graphics and Computing Architecture

This paper presents a simple-to-use mechanism for the creation of complex smoothly shaped surfaces of any genus or topology. The work described here is the result of research into the fairness of curves and surfaces specified through geometric interpolarity constraints. Constraints consist of positions and, optionally, surface normals and surface curvatures. The outcome of our investigation is a recommendation for the use of nonlinear optimization techniques that minimize a fairness functional based on the variation of curvature. The approach produces very high quality surfaces with predictable, intuitive behavior, while generating, where possible, simple shapes, such as cylinders, spheres, or tori which are commonly used in geometric modeling. From a designer''s point of view, this approach allows the specification of a desired surface in the most natural way. Though computationally intense, the techniques described have now become practical because of the wide availability of very fast work stations. As the processing power available on each desk-top further increases, the techniques described here will become real-time and interactive.

Functional optimization for fair surface design

In this paper we introduce a new surface representing, the displaced subdivision surface. It represents a detailed surface model as a scalar-valued displacement over a smooth domain surface. Our representation defines both the domain surface and the displacement function using a unified subdivision framework, allowing for simple and efficient evaluation of analytic surface properties. We present a simple, automatic scheme for converting detailed geometric models into such a representation. The challenge in this conversion process is to find a simple subdivision surface that still faithfully expresses the detailed model as its offset. We demonstrate that displaced subdivision surfaces offer a number of benefits, including geometry compression, editing, animation, scalability, and adaptive rendering. In particular, the encoding of fine detail as a scalar function makes the representation extremely compact.

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Displaced subdivision surfaces

In this paper we describe the design, programming interface, and implementation of a very efficient user-programmable vertex engine. The vertex engine of NVIDIA's GeForce3 GPU evolved from a highly tuned fixed-function pipeline requiring considerable knowledge to program. Programs operate only on a stream of independent vertices traversing the pipe. Embedded in the broader fixed function pipeline, our approach preserves parallelism sacrificed by previous approaches. The programmer is presented with a straightforward programming model, which is supported by transparent multi-threading and bypassing to preserve parallelism and performance.In the remainder of the paper we discuss the motivation behind our design and contrast it with previous work. We present the programming model, the instruction set selection process, and details of the hardware implementation. Finally, we discuss important API design issues encountered when creating an interface to such a device. We close with thoughts about the future of programmable graphics devices.

/pdf/a-user-programmable-vertex-engine-4k551ifacb.pdf

A user-programmable vertex engine

The present invention provides alignment and ordering of vector elements for SIMD processing. In the alignment of vector elements for SIMD processing, one vector is loaded from a memory unit into a first register and another vector is loaded from the memory unit into a second register. The first vector contains a first byte of an aligned vector to be generated. Then, a starting byte specifying the first byte of an aligned vector is determined. Next, a vector is extracted from the first register and the second register beginning from the first bit in the first byte of the first register continuing through the bits in the second register. Finally, the extracted vector is replicated into a third register such that the third register contains a plurality of elements aligned for SIMD processing. In the ordering of vector elements for SIMD processing, a first vector is loaded from a memory unit into a first register and a second vector is loaded from the memory unit into a second register. Then, a subset of elements are selected from the first register and the second register. The elements from the subset are then replicated into the elements in the third register in a particular order suitable for subsequent SIMD vector processing.

Alignment and ordering of vector elements for single instruction multiple data processing

A mechanism and method for recording stereo video with standard camera system electronics and a uniquely adapted optical assembly is disclosed. The optical assembly comprises left and right optical channels disposed to capture and project separate left and right images onto a single image sensor such that the boundary between the projected images is sharply delineated with no substantial overlap or gap. The viewpoints of the left and right optical channels are separated by a distance, d, such that the captured images are differentiated to produce a stereo image pair. By proper disposition of the left and right optical channels, stereo image pairs exhibiting full stereo overlap without keystone distortion are obtained. One image of the stereo pair is produced for visualization by the left eye and the other image is produced for visualization by the right eye. Alternatively, the images can be interrogated by a computer system for generating three dimensional position data. The image sensor is scanned in a standard fashion such that the left and right images are sampled by the video sampling circuitry of the camera unit at substantially the same time. In one mode, a pair of anamorphic lenses compress the left and right images along the axis of the image sensor scan lines so that each video field represents a stereo pair of images at a substantially unity anamorphic ratio and at an aspect ratio substantially equal to that of the image sensor. In a another mode, a conventional (non-distorting) lens is utilized and each video frame represents a pair of images having an aspect ratio equal to one-half that of the image sensor. A stereo playback mechanism and method is also disclosed.

Henry Packard Moreton

Papers

Functional optimization for fair surface design

Displaced subdivision surfaces

A user-programmable vertex engine

Alignment and ordering of vector elements for single instruction multiple data processing

Optical system for single camera stereo video