Implicitizing rational surfaces using moving quadrics constructed from moving planes
نویسندگان
چکیده
منابع مشابه
Implicitizing rational surfaces with base points using the method of moving surfaces
The method of moving planes and moving quadrics can express the implicit equation of a parametric surface as the determinant of a matrix M . The rows of M correspond to moving planes or moving quadrics that follow the parametric surface. Previous papers on the method of moving surfaces have shown that a simple base point has the effect of converting one moving quadric to a moving plane. A much ...
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In this paper we discuss the relationship between the moving planes of a rational parametric surface and the singular points on it. Firstly, the intersection multiplicity of several planar curves is introduced. Then we derive an equivalent definition for the order of a singular point on a rational parametric surface. Based on the new definition of singularity orders, we derive the relationship ...
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Techniques from algebraic geometry and commutative algebra are adopted to establish suucient polynomial conditions for the validity of implicitization by the method of moving quadrics both for rectangular tensor product surfaces of bi-degree (m; n) and for triangular surfaces of total degree n in the absence of base points.
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Many current geometric modeling systems use the rational parametric form to represent surfaces. Although the parametric representation is useful for tracing, rendering and surface tting, many operations like surface intersection desire one of the surfaces to be represented implicitly. Moreover, the implicit representation can be used for testing whether a point lies on the surface boundary and ...
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Article history: Received 17 April 2008 Received in revised form 24 July 2008 Accepted 2 September 2008 Available online 6 September 2008
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2016
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2016.02.001