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UNCLASSIFIED CAGD techniques for differentiable manifolds
"... This paper is part of the following report: ..."
Geometries for CAGD
"... plete. A much more complete picture is achieved in connection with the references in those chapters we are referring to. The addressed geometric concepts cannot be discussed in sucient detail within the present frame. For a careful and detailed study of most of the material in this chapter we refer ..."
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plete. A much more complete picture is achieved in connection with the references in those chapters we are referring to. The addressed geometric concepts cannot be discussed in sucient detail within the present frame. For a careful and detailed study of most of the material in this chapter we refer to the monograph by Pottmann and Wallner [89], which focusses on line geometry and its applications in geometric computing. However, it also provides the necessary classical background of related areas such as projective geometry, differential geometry and algebraic geometry. 1. Curves and Surfaces in Projectlye Geometry Differential geometry in projective spaces requires some modifications over Euclidean differential geometry. In ndimensional real projective space P, a point X is represented by a onedimensional subspace of] n+l . Any basis vector x = (x0, , x) in this subspace delivers the homogeneous coordinates (x0,...,x). The latter are just defined up to a scalar multiple, and thus
Machine Vision Tools for CAGD
 Int. J. Pattern Recognition and Artificial Intelligence
, 1996
"... . In this paper, the problem of constructing geometric models from data provided by 3D imaging sensors is addressed. Such techniques allow for rapid modeling of sculptured freeform shapes and generation of geometric models for existing parts. In order for a complete data set to be obtained, multip ..."
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. In this paper, the problem of constructing geometric models from data provided by 3D imaging sensors is addressed. Such techniques allow for rapid modeling of sculptured freeform shapes and generation of geometric models for existing parts. In order for a complete data set to be obtained
Geometric Constraints for CAGD
 In Proceedings of the 3rd International Conference on Mathematical Methods for CAGD, Ulvic
, 1995
"... . To enrich the shape vocabulary of mechanical CAD systems, we develop techniques that allow defining freeform curves from geometric constraints. An important aspect of this aproach is the ability to obtain all possible instances of curve segments satisfying the constraints of a dimensioned sketch. ..."
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Cited by 10 (3 self)
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. To enrich the shape vocabulary of mechanical CAD systems, we develop techniques that allow defining freeform curves from geometric constraints. An important aspect of this aproach is the ability to obtain all possible instances of curve segments satisfying the constraints of a dimensioned sketch
Subdivision schemes in CAGD
 Advances in Numerical Analysis
, 1992
"... Computer Aided Geometric Design (CAGD) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their e cient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical quanti ..."
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Cited by 7 (2 self)
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Computer Aided Geometric Design (CAGD) is a branch of applied mathematics concerned with algorithms for the design of smooth curves and surfaces and for their e cient mathematical representation. The representation is used for the computation of the curves and surfaces, as well as geometrical
PRODUCT CAGD ENTITIES
"... Abstract. We focus on the implicitization of parametric CAGD entities which are supposed to be of tensor product type. The presented approach is featured by its ability to treat polynomial or rational splines having a great number of control points. For Bsplines, we describe a method of exactly obt ..."
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Abstract. We focus on the implicitization of parametric CAGD entities which are supposed to be of tensor product type. The presented approach is featured by its ability to treat polynomial or rational splines having a great number of control points. For Bsplines, we describe a method of exactly
Implicit Curves and Surfaces in CAGD
, 1992
"... We review the role of implicit algebraic cnrves and surfaces in computeraided geometric design, and disrw,.'I its possible evolution. implicit curves and surfaces OfTllf certain strengths t.hat complement the strength of parametrir curVE'S llllcl surfacffi. An,f' [ reviewing nasic f ..."
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We review the role of implicit algebraic cnrves and surfaces in computeraided geometric design, and disrw,.'I its possible evolution. implicit curves and surfaces OfTllf certain strengths t.hat complement the strength of parametrir curVE'S llllcl surfacffi. An,f' [ reviewing nasic fads from Rigebraic geometry, we explore the prohlemll of convert.ing het.wt>en implicit and parallletric forms. While ronvt'rsioll from paralllf't,ric 1.0 implicit form is always possible in principle, a number of practical problems have forced the field to explore alternatives. We review flome of these alternatives, based on two fundamental ideas. First, we can defer the symbolic computation necessary for the conversion, and map all geometry algorithms to an "unevaluated " implicit form that is a certain determinant. This approach negotiates between symbolic ami numeric",1 computation, placing greater stress all the numerical side. Second, we can sidestep all symholic computations by not even formulating an implicit form, but rather using a more general system of nonlinear equations. Doing so simplifies a number of otherwi~e difficult geometric operations, but requires developing a separate algorithmic infrastructure. This second approach generalizes both implicit and parametric forms.
CAGD and Scientific Visualization vorgelegt von
"... In this work we investigate the correlation between the two disciplines CAGD and Scientific Visualization. Both are correlated to Computer Graphics but became disciplines of their own and therefore developed rather independently of each other. It is the task of this work to analyze the interapplicab ..."
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In this work we investigate the correlation between the two disciplines CAGD and Scientific Visualization. Both are correlated to Computer Graphics but became disciplines of their own and therefore developed rather independently of each other. It is the task of this work to analyze
Results 1  10
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