Sederberg, T., and Chen, F. Implicitization using moving curves and surfaces. Proceedings of SIGGRAPH (1995), 301--308. 8  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the perturbing variable) However, this term also contains an extraneous factor which turns out to be the projection of the seam curves and can be used to compute a rational parameterisation of these curves. Recent works have tried to lower the size of the matrix from which the resultant is formed [89]. 6.4. View consistency Constraints derived from assumptions about models and projections can be translated into an algebraic form. These algebraic constraints are typically nonlinear equations and inequalities (we assume that we deal with ideal images in which image coordinates are exactly ....

T.W. Sederberg and F. Chen. Implicitization using moving curves and surfaces. Computer Graphics Proceedings, Annual Conference Series, 29:301-308, 1995. Proceedings of Siggraph'95.

....equation of the surface. Residual resultants can also be used here to get the implicit equation of a parameterized surface, even in the case of base points, as it is shown in L. Bus e s work [15] Other methods using socalled moving surfaces have been studied in order to get the implicit equation [83, 27, 28]. These techniques can also be used to compute equations of o set curves (resp. surfaces) and equidistant curves (resp. surfaces) 51] ....

T. Sederberg and F. Chen, Implicitization using moving curves and surfaces, Proceedings of SIGGRAPH, (1995), pp. 120-160.

....by computing the determinant of a maximal minor of the Bezoutian matrix of p0 Gamma xp3 ; p1 Gamma yp3 ; p2 Gamma zp3 (see [3] but here we are interested in nding exactly the implicit equation. The third method to solve the implicitization problem is the method introduced by Tom Sederberg in [24] and called the moving quadric method. This method is based on the study of the syzygies of the ideal I dened by the polynomials p0 ; p1 ; p2 ; p3 and gives the implicit equation as a determinant of a certain matrix. The formulation of the implicit equation in a determinantal form can be very ....

Sederberg, T., and Chen, F. Implicitization using moving curves and surfaces. Proceedings of SIGGRAPH (1995), 301308. 8

.... very complicated and distinct [3] Ideally we would like to compute the implicit equation from a matrix that has the style of the Sylvester resultant (simple repetitive entries and sparse) and the order of the Dixon resultant (2mn) This goal can be achieved by applying the method of moving planes [7]. A moving plane is a family of parameterized planes. For each xed value of the parameters, the moving plane is the implicit equation of a plane. We shall show that the implicit equation of a generic rational tensor product surface of bi degree (m; n) can be generated from a set of 2m or 2n speci ....

....2 1) linearly independent moving planes. The original method of moving planes then constructs the implicit equation of the parametric surface (1) by taking the determinant of the coecient matrix of the ( 1 1) 2 1) linearly independent moving planes that follow the parametric surface [7]. Speci cally, we can choose 1 = 2m 1, 2 = n 1. Then from Equation (4) we obtain a homogeneous linear system of 6mn equations with 8mn unknowns. This system has at least 2mn linearly independent solutions: p 1 2m 1 X i=0 n 1 X j=0 (A (1) i;j x B (1) i;j y C (1) i;j z D (1) ....

T. W. Sederberg and F. L. Chen. Implicitization Using Moving Curves and Surfaces. Proceedings of SIGGRAPH95, 301-308, 1995.

....the perturbing variable) However, this term also contains an extraneous factor which turns out to be the projection of the seam curves and can be used to compute a rational parameterisation of these curves. Recent works have tried to lower the size of the matrix from which the resultant is formed [89]. 6.4. View consistency Constraints derived from assumptions about models and projections can be translated into an algebraic form. These algebraic constraints are typically nonlinear equations and inequalities (we assume that we deal with ideal images in which image coordinates are exactly ....

T.W. Sederberg and F. Chen. Implicitization using moving curves and surfaces. Computer Graphics Proceedings, Annual Conference Series, 29:301--308, 1995. Proceedings of Siggraph'95.

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Sederberg, T., and Chen, F. Implicitization using moving curves and surfaces. Proceedings of SIGGRAPH (1995), 301--308. 8

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Thomas W. Sederberg and Falai Chen. Implicitization using moving curves and surfaces. Computer Graphics, 29(Annual Conference Series):301--308, 1995.

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Thomas W. Sederberg and Falai Chen. Implicitization using moving curves and surfaces. In Robert Cook, editor, SIGGRAPH 95 Conference Proceedings, Annual Conference Series, pages 301--308. ACM SIGGRAPH, Addison Wesley, August 1995.

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T. W. Sederberg, F. Chen. Implicitization Using Moving Curves and Surfaces, Proceedings of SIGGRAPH, 1995, 301-308.

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Sederberg, T. W., Chen, F. (1995), Implicitization Using Moving Curves and Surfaces, Proceedings of SIGGRAPH, 301-308.

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T. W. Sederberg, F. Chen. Implicitization Using Moving Curves and Surfaces, Proceedings of SIGGRAPH, 301-308, 1995.

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