Recent progress in acquiring shape from range data permits the acquisition of seamless million-polygon meshes from physical models. In this paper, we present an algorithm and system for converting dense irregular polygon meshes of arbitrary topology into tensor product B-spline surface patches with accompanying displacement maps. This choice of representation yields a coarse but efficient model suitable for animation and a fine but more expensive model suitable for rendering. The first step in our process consists of interactively painting patch boundaries over a rendering of the mesh. In many applications, interactive placement of patch boundaries is considered part of the creative process and is not amenable to automation. The next step is gridded resampling of eachboundedsection of the mesh. Our resampling algorithm lays a grid of springs acrossthe polygonmesh, then iterates between relaxing this grid and subdividing it. This grid provides a parameterization for the mesh section, w...

We describe a multiresolution curve representation, based on wavelets, that conveniently supports a variety of operations: smoothing a curve; editing the overall form of a curve while preserving its details; and approximating a curve within any given error tolerance for scan conversion. We present methods to support continuous levels of smoothing as well as direct manipulation of an arbitrary portion of the curve; the control points, as well as the discrete nature of the underlying hierarchical representation, can be hidden from the user. The multiresolution representation requires no extra storage beyond that of the original control points, and the algorithms using the representation are both simple and fast.

Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition—the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product B-spline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single B-spline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of B-spline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the B-spline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy user-specified error tolerances, and demonstrate our method on both synthetic and real data.

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. We provide such a representation of a surface, based on the Laplacian of the mesh, by encoding each vertex relative to its neighborhood. The Laplacian of the mesh is enhanced to be invariant to locally linearized rigid transformations and scaling. Based on this Laplacian representation, we develop useful editing operations: interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric details between two surfaces, and transplanting of a partial surface mesh onto another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of our approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

This paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C²-continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse-tofine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high-fidelity reconstruction is possible from a selected set of sparse and irregular samples.

: This paper proposes a method called meshless parameterization, for parameterizing and triangulating "single patch" unorganized point sets. The points are mapped into a planar parameter domain by solving a sparse linear system. By making a standard triangulation of the parameter points, we obtain a corresponding triangulation of the original data set.

A new tracing algorithm is described that supports haptic rendering of NURBS surfaces without the use of any intermediate representation. By using this tracing algorithm in conjunction with algorithms for surface proximity testing and surface transitions, a complete haptic rendering system for sculptured models has been developed. The system links an advanced CAD modeling system with a Sarcos force-reflecting exo-skeleton arm. A method for measuring the quality of the tracking component of the haptic rendering separately from the haptic device and force computation is also described.

Scalar fields arise in every scientific application. Existing scalar visualization techniques require that the user infer the global scalar structure from what is frequently an insufficient display of information. We present a visualization technique which numerically detects the structure at all scales, removing from the user the responsibility of extracting information implicit in the data, and presenting the structure explicitly for analysis. We further demonstrate how scalar topology detection proves useful for correct visualization and image processing applications such as image co-registration, isocontouring, and mesh compression. Keywords: Scientific Visualization, Scalar Fields, Curves and Surfaces, Vector Topology 1 Introduction Visualizationof scalar fields is common across all scientific disciplines, includinggeographic data such as altitude and temperature, medical applications with CT and MRI values, and pressure and vorticity magnitude in computational fluid dynamics. ...

By its dual representation, a developable surface can be viewed as a curve of dual projective 3-space. After introducing an appropriate metric in the dual space and restricting ourselves to special surface classes, we derive linear approximation algorithms for developable NURBS surfaces, including multiscale approximations. Special attention is paid to controlling the curve of regression. Keywords: computer aided geometric design, surface approximation, developable surface, dual representation, NURBS 1 Introduction A developable surface is a surface which can be unfolded (developed) into a plane without stretching or tearing. Mathematically speaking, there is a mapping of the surface into the Euclidean plane which is isometric, at least locally. Because of this property, developable surfaces possess a variety of applications in manufacturing with materials that are not amenable to stretching. These include the formation of aircraft skins, ship hulls, ducts and automobile parts such as...

We present an algorithm to approximate a set of unorganized points with a simple curve without self-intersections. The moving least-squares method has a good ability to reduce a point cloud to a thin curve-like shape which is a near-best approximation of the point set. In this paper, an improved moving least-squares technique is suggested using Euclidean minimum spanning tree, region expansion and refining iteration. After thinning a given point cloud using the improved moving least-squares technique we can easily reconstruct a smooth curve. As an application, a pipe surface reconstruction algorithm is presented.