Contents Thissectionofthecoursenotesisorganizedasfollows: 1.Introductorymaterialforthissection.Thisincludesabriefoverviewofrelatedandcomplimentarymaterialtophotogrammetricmodeling, suchasstructurefrommotion,stereocorrespondence,shapefrom silhouettes,cameracalibration,laserscanning,andimage-basedrendering. 2.Abibliographyofrelatedpapers. 3.Areprintof: PaulE.Debevec,CamilloJ.Taylor,andJitendraMalik.ModelingandRenderingArchitecturefrom Photographs.InSIGGRAPH96,August1996,pp.11-20. 4.NotesonphotogrammetricrecoveryofarchesandsurfacesofrevolutionwrittenbyGeorgeBorshukov. 5.Copiesoftheslidesusedforthepresentation. Moreinformationcanbefoundin[10],[5],and[13],availableat: http://www.cs.berkeley.edu/debevec/Thesis 1 Introduction Thecreationofthree-dimensionalmodelsofexistingarchitecturalsceneswiththeaidofthecomputerhas beencommonplaceforsometime,andtheresultingmodelshavebeenbothentertainingvirtualenvironments aswellasvaluablevisualizationtools.Large-scaleeffortshavepushedthecampusesofI

We describe and demonstrate an algorithm that takes as input an unorganized set of points fx1�:::�xng IR 3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from two-dimensional slices, and interactive surface sketching.

We give a simple combinatorial algorithm that computes a piecewise-linear approximation of a smooth surface from a finite set of sample points. The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation. We prove the algorithm correct by showing that for densely sampled surfaces, where density depends on "local feature size", the output is topologically valid and convergent (both pointwise and in surface normals) to the original surface. We describe an implementation of the algorithm and show example outputs. 1 Introduction The problem of reconstructing a surface from scattered sample points arises in many applications such as computer graphics, medical imaging, and cartography. In this paper we consider the specific reconstruction problem in which the input is a set of sample points S drawn from a smooth two-dimensional manifold F embedded in three dimensions, and the desired output is a triangular mesh with vertex set equal to S that faithfully represen...

We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.

We present a new set of algorithms for line-art rendering of smooth surfaces. We introduce an efficient, deterministic algorithm for finding silhouettes based on geometric duality, and an algorithm for segmenting the silhouette curves into smooth parts with constant visibility. These methods can be used to find all silhouettes in real time in software. We present an automatic method for generating hatch marks in order to convey surface shape. We demonstrate these algorithms with a drawing style inspired by A Topological Picturebook by G. Francis.

Subdivision is a powerful paradigm for the generation of surfaces of arbitrary topology. Given an initial triangular mesh the goal is to produce a smooth and visually pleasing surface whose shape is controlled by the initial mesh. Of particular interest are interpolating schemes since they match the original data exactly, and play an important role in fast multiresolution and wavelet techniques. Dyn, Gregory, and Levin introduced the Butterfly scheme, which yields C 1 surfaces in the topologically regular setting. Unfortunately it exhibits undesirable artifacts in the case of an irregular topology. We examine these failures and derive an improved scheme, which retains the simplicity of the Butterfly scheme, is interpolating, and results in smoother surfaces.

This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3-D defined by a set of polygons

We describe a multiresolution representation for meshes based on subdivision. Subdivision is a natural extension of the existing patch-based surface representations. At the same time subdivision algorithms can be viewed as operating directly on polygonal meshes, which makes them a useful tool for mesh manipulation. Combination of subdivision and smoothing algorithms of Taubin [26] allows us to construct a set of algorithms for interactive multiresolution editing of complex meshes of arbitrary topology. Simplicity of the essential algorithms for re nement and coarsi cation allows to make them local and adaptive, considerably improving their efficiency. We have built a scalable interactive multiresolution editing system based on such algorithms.

We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). The computation of points on the surface is local, which results in an out-of-core technique that can handle any point set.

Nonphotorealistic rendering (NPR) can help make comprehensible but simple pictures of complicated objects by employing an economy of line. But current nonphotorealistic rendering is primarily a batch process. This paper presents a real-time nonphotorealistic renderer that deliberately trades accuracy and detail for speed. Our renderer uses a method for determining visible lines and surfaces which is a modification of Appel's hidden-line algorithm, with improvements which are based on the topology of singular maps of a surface into the plane. The method we describe for determining visibility has the potential to be used in any NPR system that requires a description of visible lines or surfaces in the scene. The major contribution of this paper is thus to describe a tool which can significantly improve the performance of these systems. We demonstrate the system with several nonphotorealistic rendering styles, all of which operate on complex models at interactive frame rates.