I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, New York, 1979.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....SCALED CYCLIDES INTO B EZIER PATCHES Rational Quadric Bezier (RQB) surfaces are parametric surfaces of degree widely used in geometric modeling and shape design. Several books and papers have studied these surfaces and analyzed their properties from mathematical to CAGD points of view [FP79, Far93, Hof89, B 86, AR90] A point on a RQB surface verifies the following expression: C C , C 1 C (22) are surface parameters, is a point of the 3D Euclidian space , are the ....

I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, Chichester, 1979.

....specific operators for the union, intersection and di#erence with a functionally defined transition, which is a smooth transition defined point by point from the Euclidean space E with a single valued function H : R R. Functions H are defined with one dimensional cubic polynomial splines [32] to interpolate the control points. Equation 5 shows the operator used for the union operator. G (f 1 , f 2 ) min (f 1 , f 2 ) H ( f 1 ) 5) This union operator (first proposed by Dekkers et al. [31] is built with a min function which requires continuity to be explicitly controlled ....

....modeling space E . Point p i allows us to compute the point P i (f 1 (p i ) f 2 (p i ) followed by # P i and C i = P i ) The corresponding point k i (i 2) to interpolate, has then the coordinates: k i (# i , C 0 C i ) We have chosen one dimensional cubic polynomial splines [32] to define function m when # P [# 1 , # 2 ] for their adequate smoothness and oscillation properties, and for their inexpensive computation cost. We finally obtain the union Boolean operator with Figure 11: Graph of an interpolation function m(#P ) used to deform the operator and allow the ....

I.D. Faux and M.J. Pratt. Computational Geometry for Design and Manufacture, Ellis Horwood, 1979.

.... Delta Bm;n wm;n : Note that J is now a 3 Theta 4(m 1) n 1) matrix. C. Swung D NURBS Surfaces Many objects of interest, especially manufactured objects, exhibit symmetries. Often it is convenient to model symmetric objects through cross sectional design by specifying profile curves [11]. Woodward [39] introduced the swinging operator by extending the spherical crossproduct with a scaling factor, and applied it to generate surfaces with B spline profile curves. Piegl [25] carried the swinging idea over to NURBS curves. He proposed NURBS swung surfaces, a special type of NURBS ....

I.D. Faux and M.J. Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, Chichester,UK, 1979.

....objects are designed by adjusting control points and weights that are associated with NURBS surface patches. Many objects of interest, especially manufactured objects, exhibit symmetries. Often it is convenient to model symmetric objects through cross sectional design by specifying profile curves [4]. Woodward [5] introduced the swinging operator by extending the spherical cross product with a scaling factor, and applied it to generate surfaces with B spline profile curves (see also [6] Piegl [1] carried the swinging idea over to NURBS curves. He proposed NURBS swung surfaces, a special ....

I.D. Faux and M.J. Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, Chichester,UK, 1979.

....d 2 3, d 0 with the flexibility of degree d, C 2 splines at extraordinary points. 5. Additional Literature Every paper on smooth surfacing defines some, possibly specialized, notion of geometric continuity. Some of the early characterizations can be found in [10] 9] 8] 23] 27] 31] [33] [69] 72] 74] 77] 104,103] 106] 107] 108] 114] 112] 113] 45] 82] 92] 117] 115] 116] 126] 116] 125] and characterizations for curves in [6] 7] 50] 20] 30] A number of publications specifically aim at clarifying the notion of geometric continuity. Kahmann ....

I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, Chichester, 1979.

....[21] Using these methods, numerous collision detection approaches have been presented varying in complexity, time, and efficiency. A comparative study of the well known interference algorithms can be found in [15] Surface intersection problems were addressed using four main categories of methods [9], namely algebraic, lattice evaluation, marching methods, and recursive subdivision methods. Some of the early work using a computational method to check for the interference of edges and surfaces of two defined solids was presented by [6] Other methods of collision detection include the use of ....

Faux, I. and Pratt, M.J., 1979, Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester.

....are dense and noisy. x1. Introduction In many science and engineering problems there is a need to fit a curve or curves to an irregularly spaced set of points. Curve fitting has been studied extensively in Approximation Theory and Geometric Modeling, and there are numerous books on the subject [1,5,6,12,23]. Existing techniques typically find a single curve segment that approximates or interpolates the given points. Many techniques assume that the points are ordered and fit a curve to them by minimizing an error criterion [3,7,8,14,16,22,27,29,31,34] If the points are ordered, piecewise polynomial ....

Faux, I. D. and M. J. Pratt, Computational Geometry for Design and Manufacture, Ellis Horwood, Chichester, 1979.

....responds smoothly and monotonically with respect to intensity or exhibits a particular asymtotic behavior. We establish density values for all possible measured values by interpolating with respect to log(G) which for most CCD cameras is approximately linear. We use cubic spline interpolation [5]. Once the function G(ae 0 iffiae) has been established then optical densities are determined by measuring the response with and without the object of interest and then to subtract the corresponding densities. In practice this implies the storage of the bright field image because the ....

I D Faux and M J Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, Chichester, UK, 1979.

....B spline with positive weights, and is therefore compatible with internal representations used by most solid modeling systems. In prior work, an explicit parametric form for a conic arc that blends two segments and passes through a third point has been studied by Liming [12] and Faux and Pratt [4], but the cases of parallel and nonparallel segments must be handled separately. A rational quadratic B ezier formula for the nonparallel case is presented in [3] In [16] Piegl proposes infinite control points which can be used to handle parallel end tangents [15] In [3] Farin derives a ....

I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, Chichester, 1979.

.... curves (with Learning to track the motion of visual contours 3 appropriate variations, in each case, where multiple knots are used to vary curve continuity) The vector B(s) consists of blending coefficients defined by B(s) B 1 (s) BNc (s) where Bm (s) is a B spline basis function [18, 7] appropriate to the order of the curve and its set of knots. 2.2 Tracking as estimation over time The tracking problem is to estimate the motion of some curve in examples in this paper it will be the outline of a hand or of lips. The underlying curve the physical truth is assumed to ....

I.D. Faux and M.J. Pratt. Computational Geometry for Design and Manufacture. Ellis-Horwood, 1979.

....are good. At this point, each gradient is a 2 D line; we know its elevation only where is crosses contour lines. 5 The next step is to interpolate elevations along the whole gradient, from the known elevations at the contours. The 1 D interpolation method is a Catmull Rom (aka Oberhauser) spline, (Faux Pratt 1981), which has a continuous second derivative. The splines must be smoothed to create the final surface; the thin plate approximation is applied once again. 4 Experiments We tested our new approximation algorithms on various sets of USGSDLG contour data. To evaluate the fits, we calculated ....

Faux, I. & Pratt, M. (1981), Computational geometry for design and manufacture, Mathematics and its applications, Halsted Press.

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I.D. Faux and M.J. Pratt, Computational Geometry for Design and Manufacture, Ellis Horwood, 1978.

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I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, New York, 1979.

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Faux,I.D. and Pratt,M.J. (1985) Computational Geometry for Design and Manufacture, Ellis Horwood Limited, Chichester, UK.

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I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacturing.

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I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacturing. John Wiley &Sons, 1979.

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I.D.FauxandM.J.Pratt. Computational Geometry for Design and Manufacture. Ellis Horwood, Chichester, 1979.

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I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacturing. John Wiley &Sons, 1979.

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I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacturing.

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I. D. Faux and M. J. Pratt. Computational Geometry for Design and Manufacturing. John Wiley & Sons, 1979.

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I.D. Faux and M.J. Pratt. Computational Geometry for Design and Manufacture, Ellis Horwood, 1979. 3

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I.D. Faux and M.J. Pratt. Computational Geometry for Design and Manufacture, Ellis Horwood, 1979. 3

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Faux I.D. and Pratt M. J. Computational Geometry for design and manufacture . Ellis Horwood, Chichester UK, 1979.

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Faux, I. D. and Pratt, M. J., 1981, Computational Geometry for Design and Manufacture, John Wiley

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Faux, I. D. and Pratt, M. J. (1979), Computational Geometry for Design and Manufacture, Ellis Horwood Publishers, Ltd., New York, NY.

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