1984
DOI: 10.1016/s0734-189x(84)80048-1
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Implicit representation of parametric curves and surfaces

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Cited by 46 publications
(72 citation statements)
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“…In fact, these are well-known and thoroughly studied problems [3]. In general, exact conversion is possible for certain classes of functions [4], while other classes of functions require approximate techniques [5]. Since the implicit representation makes it hard to express and analyze shapes, and since it is hard and computationally expensive to automate the conversion between the two representations we have chosen to describe shapes parametrically.…”
Section: Shapesmentioning
confidence: 99%
“…In fact, these are well-known and thoroughly studied problems [3]. In general, exact conversion is possible for certain classes of functions [4], while other classes of functions require approximate techniques [5]. Since the implicit representation makes it hard to express and analyze shapes, and since it is hard and computationally expensive to automate the conversion between the two representations we have chosen to describe shapes parametrically.…”
Section: Shapesmentioning
confidence: 99%
“…Therefore, for any parametric curve or surface there exists an implicit polynomial equation defining exactly the same curve or surface. The corresponding algorithm for curves is given in [73] and [74]. In addition, a parametric curve of degree n has an implicit equation of also degree n. Further, the coefficients of this implicit equation are obtained from those of the parametric form by using only multiplication, addition and subtraction, so conversion can be performed through symbolic computation, with no numerical error introduced.…”
Section: Implicitizationmentioning
confidence: 99%
“…In addition, a parametric curve of degree n has an implicit equation of also degree n. Further, the coefficients of this implicit equation are obtained from those of the parametric form by using only multiplication, addition and subtraction, so conversion can be performed through symbolic computation, with no numerical error introduced. Implicitization algorithms also exist for surfaces [51,73,74]. However, a triangular parametric surface patch of degree n has an implicit equation of degree n 2 .…”
Section: Implicitizationmentioning
confidence: 99%
“…Research in implicit surface modeling includes the "blobby model" based on Gaussian function [4,5], and polynomials [6]. Topics such as implicitization [7,8], blending [9,10], interpolation [11], control [12,13], curvature formulation [14], as well as polygonization [15,16] and direct ray tracing [17] have been studied.…”
Section: Introductionmentioning
confidence: 99%