We present a novel method for real-time rendering of subdivision surfaces whose goal is to make subdivision faces as easy to render as triangles, points, or lines. Our approach uses standard GPU tessellation hardware and processes each face of a base mesh independently, thus allowing an entire model to be rendered in a single pass. The key idea of our method is to subdivide the u, v domain of each face ahead of time, generating a quadtree structure, and then submit one tessellated primitive per input face. By traversing the quadtree for each post-tessellation vertex, we are able to accurately and efficiently evaluate the limit surface. Our method yields a more uniform tessellation of the surface, and faster rendering, as fewer primitives are submitted. We evaluate our method on a variety of assets, and realize performance that can be three times faster than state-of-the-art approaches. In addition, our streaming formulation makes it easier to integrate subdivision surfaces into applications and shader code written for polygonal models. We illustrate integration of our technique into a full-featured video game engine.

Current GPUs perform a significant amount of redundant shading when surfaces are tessellated into small triangles. We address this inefficiency by augmenting the GPU pipeline to gather and merge rasterized fragments from adjacent triangles in a mesh. This approach has minimal impact on output image quality, is amenable to implementation in fixed-function hardware, and, when rendering pixel-sized triangles, requires only a small amount of buffering to reduce overall pipeline shading work by a factor of eight. We find that a fragment-shading pipeline with this optimization is competitive with the REYES pipeline approach of shading at micropolygon vertices and, in cases of complex occlusion, can perform up to two times less shading work.

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 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.

Abstract Four functionals for the computation of minimum cost curves are compared. Minimization of these functionals result in the widely studied Minimum Energy Curve (MEC), the recently introduced Minimum Variation Curve (MVC), and their scale‐invariant counterparts, (SI‐MEC, SI‐MVC). We compare the stability and fairness of these curves using a variety of simple interpolation problems. Previously, we have shown MVC to possess superior fairness. In this paper we show that while MVC have fairness and stability superior to MEC they are still not stable in all configurations. We introduce the SI‐MVC as a stable alternative to the MVC. Like the MVC, circular and helical arcs are optimal shapes for the SI‐MVC. Additionally, the application of scale invariance to functional design allows us to investigate locally optimal curves whose shapes are dictated solely by their topology, free of any external interpolation or arc length constraints.

This paper presents a simple-to-use mechanism for the creation of complex smoothly shaped surfaces of any genus or topological type.The surfaces are specified through interpolated geometric constraints consisting of positions and, optionally, surface normals and surface curvatures.From a designer's point of view, this is a very natural way to specify a desired shape, whether free-form or technical.Nonlinear optimization techniques are then used to minimize a fairness functional based on the variation of curvature.This functional 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.While easy to use, this optimization-based approach is computationally quite demanding.With more efficient optimization algorithms and with the ever increasing processing power available on every desk-top, the techniques described here will provide the basis for a new class of practical interactive geometric modeling tools.

The support of free-form surfaces by modem solid modeling systems has necessitated the development of hardware and algorithms for the interactive display of surface patches. This paper describes an algorithm for the display of multiple surface patches at frame rates capable of providing smooth motion. The algorithm runs on the Silicon Graphics IRIS 4D GT workstation. Real-time motion is achieved by exploiting a microcodable pipeline of floating point processors and existing support for the display of Gouraud shaded Z-buffered polygons. The paper presents tradeoffs in the development of a high performance rendering algorithm. We discuss issues related to hardware support, surface representation, adaptive display, and the minimization of display artifacts such as faceting and cracking. More detailed discussion addresses the choice of Bezier surface patches and subdivision criteria.

A library of routines has been developed for the design of arbitrarily curved three-dimensional surfaces. The routines provide for the description and editing of surfaces. Surfaces are defined by families of parametric curves which are blended, using linear interpolation, approximating splines or interpolating splines. Each component curve is in turn defined by a set of ordered control points which are blended using any of these techniques. This approach affords greater flexibility than more classical methods such as bi-variate patches. The editing facilities include the basic spatial transforms as well as a full complement of attribute setting functions.