The work reported here is an integral part of a system developed for the automated reconstruction of arbitrary-shaped physical objects using vision systems, three dimensional computergraphics, and B-Spline surface ap...
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ISBN:
(纸本)0791807487
The work reported here is an integral part of a system developed for the automated reconstruction of arbitrary-shaped physical objects using vision systems, three dimensional computergraphics, and B-Spline surface approximation techniques. Digitized planar contour points are automatically fitted in the image and world space to define a minimum number of B-Spline control points using least-squares approximation techniques. The final set of points represent the B-Spline control net of the entire surface of the object. The resulting curves and surfaces can be further interactively modified until a satisfactory fit is obtained. Three parametrization techniques, viz., uniform, chord length, and affine invariant angle method are implemented and adjusted to their local minima using the Newton-Raphson iteration method. The effect of each method on the accuracy of the reconstructed surface is discussed. The techniques were tested using a clay model of a human face. The uniform parametrization performed better with the highest speed of convergence and best least-squares error characteristics. On the other hand, it was less effective in detecting sharp corners as compared to the other two methods. The results also show that there is a minimum number of control points for every surface beyond which there is no error improvement. This is useful in several industrial applications when checking surface accuracy of manufactured parts using Coordinate Measuring Machines (CMM).
The work reported here is an integral part of a system developed for the automated reconstruction of arbitrary-shaped physical objects using vision systems, three dimensional computergraphics, and B-Spline surface ap...
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Since its genesis more than thirty-five years ago, the field of computervision has been known by various names, including pattern recognitions, image analysis, and image understanding. The central problem of computer...
ISBN:
(数字)9780821877074
Since its genesis more than thirty-five years ago, the field of computervision has been known by various names, including pattern recognitions, image analysis, and image understanding. The central problem of computervision is obtaining descriptive information by computer analysis of images of a scene. Together with the related fields of image processing and computergraphics, it has become an established discipline at the interface between computer science and electrical engineering. This volume contains fourteen papers presented at the AMS Special Session on Geometry Related to computervision, held in Hoboken, New Jersey in October 1989. This book makes the results presented at the Special Session, which previously had been available only in the computer science literature, more widely available within the mathematical sciences community. Geometry plays a major role in computervision, since scene descriptions always involve geometrical properties of, and relations among, the objects or surfaces in the scene. The papers in this book provide a good sampling of geometric problems connected with computervision. They deal with digital lines and curves, polygons, shape decompositions, digital connectedness and surfaces, digital metrics, and generalizations to higher-dimensional and graph-structured “spaces.” Aimed at computer scientists specializing in image processing, computervision, and pattern recognition—as well as mathematicians interested in applications to computer science—this book will provide readers with a view of how geometry is currently being applied to problems in computervision.
The proceedings contain 39 papers. The topic discussed include: CAD/CAM in the French automobile industry;symmetric algorithms for curves and surfaces;estimation of motion parameters from sparse range data using surfa...
The proceedings contain 39 papers. The topic discussed include: CAD/CAM in the French automobile industry;symmetric algorithms for curves and surfaces;estimation of motion parameters from sparse range data using surface interpolation;delaunay's tetrahedronalization: an efficient algorithm for 3-D triangulation;radial basis function approach to interpolation of large reflecting surfaces;partitioning and mapping B-spline surface fitting algorithm into fixed-size VLSI arrays;and decomposition and representation of planar curves using curvature-tuned smoothing.
In this paper, we show that B -spline curves and surfaces can be viewed as digital filters. Viewing B -spline problems as digital filters allows one to predict some properties of the generated curves and surfaces. We ...
In this paper, we show that B -spline curves and surfaces can be viewed as digital filters. Viewing B -spline problems as digital filters allows one to predict some properties of the generated curves and surfaces. We find that even-order B -splines and odd-order B -splines behave differently when used in curve and surface interpolation. Even-order B -splines generate smoother curves and surfaces than do odd-order B -splines.
Rational curves and splines are one of the building blocks of computergraphics and geometricmodeling. Although a rational curve is more flexible than its polynomial counterpart,many properties of polynomial curves ar...
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ISBN:
(纸本)0819402982
Rational curves and splines are one of the building blocks of computergraphics and geometric
modeling. Although a rational curve is more flexible than its polynomial counterpart,
many properties of polynomial curves are not applicable to it. For this reason it is very useful
to know if a curve presented as a rational space curve has a polynomial parametrization.
In this paper, we present an algorithm to decide if a polynomial parametrization exists,
and to compute the parametrization.
In algebraic geometry it is known that a rational algebraic curve is polynomially parametrizable
if it has one place at infinity. This criterion has been used in earlier methods to test
polynomial parametrizability of space curves. These methods project the curve into the
plane and test parametrizability there. But this gives only a sufficient condition for the
original curve. In this paper we give a simple condition which is both necessary and sufficient
for polynomial parametrizability. The calculation of the polynomial parametrization
is simple, and involves only a rational reparametrization of the curve.
Q uadric surfaces such as cylinders and spheres play a fundamental role in CAGD.This paper describes a new method for creating triangular surface patches on a quadricsurface. The surface patches are defined using a re...
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ISBN:
(纸本)0819402982
Q uadric surfaces such as cylinders and spheres play a fundamental role in CAGD.
This paper describes a new method for creating triangular surface patches on a quadric
surface. The surface patches are defined using a restricted type of quadratic Bezier
control polyhedron. The control polyhedron and the resulting quadric surface patch
satisfy all of the standard properties of parametric Bezier surfaces, including interpolation
of the corners of the control polyhedron and the convex hull property. A new
technique for creating a C1 mesh of these quadric surface patches is also introduced.
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