Denote a point in the plane by z=(z,y) and a polynomial of nth degree in z by f(z) /spl Sigma//sub i,j//spl ges/o/sub 1/i+j/spl les/n(a/sub ij/x/sup i/y/sup j/). Denote by Z(f) the set of points for which f(z)=0. Z(f)...
详细信息
Denote a point in the plane by z=(z,y) and a polynomial of nth degree in z by f(z) /spl Sigma//sub i,j//spl ges/o/sub 1/i+j/spl les/n(a/sub ij/x/sup i/y/sup j/). Denote by Z(f) the set of points for which f(z)=0. Z(f) is the 2D curve represented by f(z). In this paper, we present a new approach to fitting 2D curves to data in the plane (or 3D surfaces to range data) which has significant advantages over presently known methods. It requires considerably less computation and the resulting curve can be forced to lie close to the data set at prescribed points provided that there is an nth degree polynomial that can reasonably approximate the data. Linear programming is used to do the fitting. The approach can incorporate a variety of distance measures and global geometric constraints.
This paper addresses the problem of reconstructing two-dimensional curves and three-dimensional surfaces from scattered, sparse measurements. We extend the rational Gaussian (RaG) functions introduced by Goshtasby (19...
详细信息
This paper addresses the problem of reconstructing two-dimensional curves and three-dimensional surfaces from scattered, sparse measurements. We extend the rational Gaussian (RaG) functions introduced by Goshtasby (1993) to general rational radial basis functions and develop a method to compute the smoothness parameters for the shape model by considering the adjacency relation of the control points. Experimental results demonstrate substantial improvements over the original RaG-based method when the input data is sparse and the distribution of the control points is highly nonuniform.
This paper presents procedures for the explicit parametric representation and global description of surfaces of simply connected 3-D objects. The novel techniques overcome severe limitations of earlier methods (restri...
详细信息
This paper presents procedures for the explicit parametric representation and global description of surfaces of simply connected 3-D objects. The novel techniques overcome severe limitations of earlier methods (restriction to star-shaped objects (D. H. Ballard and Ch. M. Brown, computervision, Prentice-Hall, Englewood Cliffs, NJ, 1981), constraints on positioning and shape of cross-sections (F. Solina and R. Bajcsy, IEEE Trans. Pattern Anal. Mach. Intell. 12(2), 1990, 131-147;L. H. Staib and J. S. Duncan, in Visualization in Biomedical Computing 1992 (R. A. Robb, Ed.), Vol. Proc. SPIE 108, pp. 90-104, 1992), and nonhomogeneous distribution of parameter space). We parametrize the surface by defining a continuous, one-to-one mapping from the surface of the original object to the surface of a unit sphere. The parametrization is formulated as a constrained optimization problem. Practicable starting values are obtained by an initial mapping based on a heat conduction model. The parametrization enables us to expand the object surface into a series of spherical harmonic functions, extending to 3-D the concept of elliptical Fourier descriptors for 2-D closed curves (E. Persoon and K. S. Fu, IEEE Trans. Syst. Man Cybernetics 7(3), 1977, 388-397;F. P. Kuhl and Ch. R. Giardina, Comput. graphics Image Process. 18(3), 1982, 236-258). Invariant, object-centered descriptors are obtained by rotating the parameter net and the object into standard positions. The new methods are illustrated with 3-D test objects. Potential applications are recognition, classification, and comparison of convoluted surfaces or parts of surfaces of 3-D shapes. (C) 1995 Academic Press, Inc,
While there have been great strides in the development of systems to recognize 3D objects in images using viewpoint independent features, we have yet to develop algorithms for recognizing complex curved objects from l...
详细信息
This conference proceedings contain 33 papers. The main subjects are: Wavelets and approximation theory, mathematical techniques, curves and surfaces, surface reconstruction techniques, geometric modeling, and surface...
详细信息
ISBN:
(纸本)0819410314
This conference proceedings contain 33 papers. The main subjects are: Wavelets and approximation theory, mathematical techniques, curves and surfaces, surface reconstruction techniques, geometric modeling, and surface triangulation.
In computergraphics and geometric modeling one generally faces the problem to integrate a variety of curve and surface types in to a single program. Object-oriented design offers the opportunity to use the inherent h...
详细信息
ISBN:
(纸本)0819410314
In computergraphics and geometric modeling one generally faces the problem to integrate a variety of curve and surface types in to a single program. Object-oriented design offers the opportunity to use the inherent hierarchical structure of curves and surfaces to solve this problem. This paper presents an object-oriented framework together with its C++ implementation that starts from an abstract class of general differentiable curves and surfaces and in turn refines this design to curves and surfaces that are explicitly given in either parametric or implicit form. Most of the standard curve and surface types are derived from these classes. Examples that visualize the differential geometry of curves and surfaces illustrate the approach.
This article describes a method that uses deformable curves and deformable surfaces to generate a C1 continuous parametric surface from unorganized data points. The triangular patch was used as the surface element for...
详细信息
ISBN:
(纸本)0819410314
This article describes a method that uses deformable curves and deformable surfaces to generate a C1 continuous parametric surface from unorganized data points. The triangular patch was used as the surface element for generating an n-sided surface. A new method for generating the topology is also presented. The concept of elastically deformable shapes attracted toward data points by spring-like forces is used to seek the optimal shape which minimizes an associated energy functional.
In this paper we discuss two problems. One problem is: how to approximate the rolling ball blend by a series of bicubic patches? The other problem is: what to do if the rolling ball blend surface is self intersecting?
ISBN:
(纸本)0819410314
In this paper we discuss two problems. One problem is: how to approximate the rolling ball blend by a series of bicubic patches? The other problem is: what to do if the rolling ball blend surface is self intersecting?
computer aided design and manufacturing processes frequently map planar triangulations onto surfaces. Due to their properties relevant to finite element analysis, Delaunay triangulations have become popular for triang...
详细信息
ISBN:
(纸本)0819410314
computer aided design and manufacturing processes frequently map planar triangulations onto surfaces. Due to their properties relevant to finite element analysis, Delaunay triangulations have become popular for triangulating arbitrary planar domains that are subsequently mapped onto surfaces. Although surface triangulations cannot enjoy all the properties of planar triangulations, utilization of as many of the properties of Delaunay triangulations as possible in algorithms for triangulating surfaces can have advantages as well as disadvantages. This paper focuses on the advantages and disadvantages of using Delaunay criteria in triangulating surfaces.
computer aided design of freeformed surfaces is strongly biased towards input and optimization of surfaces. Input modules are based on digitizing drawings or placing and manipulating spline control vertices. Design, e...
详细信息
ISBN:
(纸本)0819410314
computer aided design of freeformed surfaces is strongly biased towards input and optimization of surfaces. Input modules are based on digitizing drawings or placing and manipulating spline control vertices. Design, especially during the idea generation (or conceptual) design phase, is poorly supported. We present a system based on direct manipulation of shaded images of the surfaces. The designer sketches profiles on a tablet. The profiles are positioned in object space with a spaceball (6D joystick). A network of crossing curves is built interactively. The system constructs patches over this network in realtime. The designer can correct a profile by sketching. The affected surfaces are updated immediately. Patches are defined by the curves and estimated cross-boundary derivatives. They connect with G1 continuity. Our prototype surface modeler avoids the need for exact dimensions and precise coordinates, as seen in traditional systems. Instead, it supports fast, intuitive generation and evaluation of surfaces. We discuss a comparison with other systems regarding the time needed to model shapes, and some opinions of professional industrial designers.
暂无评论