Tom Duchamp

Surface reconstruction from unorganized points

This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. Previous surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. The reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. Phases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces.

Mesh optimization

We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0, produce a mesh M, of the same topological type as M0 , that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles). CR

Multiresolution analysis of arbitrary meshes

In computer graphics and geometric modeling, shapes are often represented by triangular meshes. With the advent of laser scanning systems, meshes of extreme complexity are rapidly becoming commonplace. Such meshes are notoriously expensive to store, transmit, render, and are awkward to edit. Multiresolution analysis offers a simple, unified, and theoretically sound approach to dealing with these problems. Lounsbery et al. have recently developed a technique for creating multiresolution representations for a restricted class of meshes with subdivision connectivity. Unfortunately, meshes encountered in practice typically do not meet this requirement. In this paper we present a method for overcoming the subdivision connectivity restriction, meaning that completely arbitrary meshes can now be converted to multiresolution form. The method is based on the approximation of an arbitrary initial mesh M by a mesh MJ that has subdivision connectivity and is guaranteed to be within a specified tolerance. The key ingredient of our algorithm is the construction of a parametrization of M over a simple domain. We expect this parametrization to be of use in other contexts, such as texture mapping or the approximation of complex meshes by NURBS patches. CR

Piecewise smooth surface reconstruction

We present a general method for automatic reconstruction of accurate, concise, piecewise smooth surface models from scattered range data. The method can be used in a variety of applications such as reverse engineering—the automatic generation of CAD models from physical objects. Novel aspects of the method are its ability to model surfaces of arbitrary topological type and to recover sharp features such as creases and corners. The method has proven to be effective, as demonstrated by a number of examples using both simulated and real data. A key ingredient in the method, and a principal contribution of this paper, is the introduction of a new class of piecewise smooth surface representations based on subdivision. These surfaces have a number of properties that make them ideal for use in surface reconstruction: they are simple to implement, they can model sharp features concisely, and they can be fit to scattered range data using an unconstrained optimization procedure.

Surface light fields for 3D photography

A surface light field is a function that assigns a color to each ray originating on a surface. Surface light fields are well suited to constructing virtual images of shiny objects under complex lighting conditions. This paper presents a framework for construction, compression, interactive rendering, and rudimentary editing of surface light fields of real objects. Generalization of vector quantization and principal component analysis are used to construct a compressed representation of an objects surface light field from photographs and range scans. A new rendering algorithm achieves interactive rendering of images from the compressed representation, incorporating view-dependent geometric level-of-detail control. The surface light field representation can also be directly edited to yield plausible surface light fields for small changes in surface geometry and reflectance properties.

Interactive skeleton-driven dynamic deformations

This paper presents a framework for the skeleton-driven animation of elastically deformable characters. A character is embedded in a coarse volumetric control lattice, which provides the structure needed to apply the finite element method. To incorporate skeletal controls, we introduce line constraints along the bones of simple skeletons. The bones are made to coincide with edges of the control lattice, which enables us to apply the constraints efficiently using algebraic methods. To accelerate computation, we associate regions of the volumetric mesh with particular bones and perform locally linearized simulations, which are blended at each time step. We define a hierarchical basis on the control lattice, so for detailed interactions the simulation can adapt the level of detail. We demonstrate the ability to animate complex models using simple skeletons and coarse volumetric meshes in a manner that simulates secondary motions at interactive rates.

Interactive multiresolution surface viewing

Multiresolution analysis has been proposed as a basic tool supporting compression, progressive transmission, and level-of-detail control of complex meshes in a unified and theoretically sound way. We extend previous work on multiresolution analysis of meshes in two ways. First, we show how to perform multiresolution analysis of colored meshes by separately analyzing shape and color. Second, we describe efficient algorithms and data structures that allow us to incrementally construct lower resolution approximations to colored meshes from the geometry and color wavelet coefficients at interactive rates. We have integrated these algorithms in a prototype mesh viewer that supports progressive transmission, dynamic display at a constant frame rate independent of machine characteristics and load, and interactive choice of tradeoff between the amount of detail in geometry and color. The viewer operates as a helper application to Netscape, and can therefore be used to rapidly browse and display complex geometric models stored on the World Wide Web. CR

View-base Rendering: Visualizing Real Objects from Scanned Range and Color Data

Modeling arbitrary real objects is difficult and rendering textured models typically does not result in realistic images. We describe a new method for displaying scanned real objects, called view-based rendering. The method takes as input a collection of colored range images covering the object and creates a collection of partial object models. These partial models are rendered separately using traditional graphics hardware and blended together using various weights and soft z-buffering. We demonstrate interactive viewing of real, non-trivial objects that would be difficult to model using traditional methods.

A multiresolution framework for dynamic deformations

We present a novel framework for the dynamic simulation of elastic deformable solids. Our approach combines classical finite element methodology with a multiresolution subdivision framework in order to produce fast, easy to use, and realistic animations. We represent deformations using a hierarchical basis constructed using volumetric subdivision. The subdivision framework provides topological flexibility and the hierarchical basis allows the simulation to add detail where it is needed. Since volumetric parameterization is difficult for complex models, we support the embedding of objects in domains that are easier to parameterize.

Robust meshes from multiple range maps

This paper presents a method for modeling the surface of an object from a sequence of range maps. Our method is based on a volumetric approach that produces a compact surface without boundary. It provides robustness through the use of interval analysis techniques and computational efficiency through hierarchical processing using octrees.