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...
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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...
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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...
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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...
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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.
In this paper we introduce a data structure for surface representation, called Handle-Edge, which involves only an intrinsic cell decomposition, and define structural operators, called Morse Operators, which are based...
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ISBN:
(纸本)0819410314
In this paper we introduce a data structure for surface representation, called Handle-Edge, which involves only an intrinsic cell decomposition, and define structural operators, called Morse Operators, which are based on the Handlebody Representation of orientable surfaces with or without boundary. As the description is a topological one it leaves open the dimension of the euclidean space, where the surface is embedded. We apply this representation to the visualization of implicit surfaces embedded in high-dimensional spaces.
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...
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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.
A new algorithm based on curve tracing and decomposition techniques is presented for computing the convex hull of an algebraic curve defined implicitly by f(x,y) = 0;the curve may have multiple components as well as s...
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ISBN:
(纸本)0819410314
A new algorithm based on curve tracing and decomposition techniques is presented for computing the convex hull of an algebraic curve defined implicitly by f(x,y) = 0;the curve may have multiple components as well as singular points. The output is an ordered collection of line segments and sections of the curve represented by a sample point and interval bounds;this representation is suitable for rendering the convex hull by classical curve tracing techniques. Additionally, we present a point classification function for the convex hull based on Sturm sequences. Progress toward extending these results to algebraic surfaces is briefly discussed.
Adaptive chain coding algorithms based on using multiple templates are developed. One algorithm differentially encodes a curve using a directional template whose angle is dynamically scaled to accommodate a variety of...
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ISBN:
(纸本)0819410314
Adaptive chain coding algorithms based on using multiple templates are developed. One algorithm differentially encodes a curve using a directional template whose angle is dynamically scaled to accommodate a variety of curvature properties. A second algorithm differentially encodes using a template with small angular range with another template occasionally used for reorientation if abrupt changes occur in the properties of the underlying curve. By exploiting the piecewise regularity of most curves, our techniques provide substantially more accurate and efficient encodings compared with standard chain coding algorithms.
In this paper we describe the geometric components of our model-based approach to 3D rigid object recognition and positioning from range data that have potential applications in graphics, Geometric Modeling, and Compu...
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ISBN:
(纸本)0819410314
In this paper we describe the geometric components of our model-based approach to 3D rigid object recognition and positioning from range data that have potential applications in graphics, Geometric Modeling, and computer Aided Geometric Design. As in many other object recognition systems, due to occlusion, objects are recognized and located by comparing and geometrically matching small regions of the data set with corresponding regions of known models stored in a database. In our case, a known object is represented in the database as a hierarchical collection of regions, each of them approximated by an algebraic surface. The preliminary recognition and matching is based on comparing euclidean invariant functions of the coefficients of the corresponding polynomials. The final recognition and matching is based on determining how well the data fits a stored model. Although we have not implemented a complete system yet, towards the implementation of an object recognition and position estimation system based on this structure, a number of computational problems associated with algebraic curves and surfaces have been analyzed and solved. These problems, described in this paper, are: (1) how to fit unconstrained algebraic curve and surfaces to data, (2) how to fit bounded algebraic curves and surfaces, (3) how to efficiently compute Euclidean invariants of polynomials, and (4) how to define an intrinsic coordinate system of a polynomial, generalizing the notion of center and principal axes of a nonsingular quadric curve or surface. The intrinsic coordinate system of a polynomial can be used to transform its coefficients to a normal form. The coefficients of a polynomial in normal form constitute a complete set of Euclidean invariants.
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