Automatic parameterization of rational curves and surfaces IV: algebraic space curves
نویسندگان
چکیده
منابع مشابه
Automatic parameterization of rational curves and surfaces III: Algebraic plane curves
We consider algorithms to compute the genus and rational parametric equations, for implicitly defined irreducible rational plane algebraic curves of arbitrary degree. Rational panuneterizations exist for all irreducible algebraic curves of genus O. The genus is compuled by a complete analysis of the singularities of plane algebraic curves, using affine quadratic transformations. The rational pa...
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The investigation of rational varieties with chord length parameterization (shortly RCL varieties) was started by Farin (2006) who observed that rational quadratic circles in standard Bézier form are parametrized by chord length. Motivated by this observation, general RCL curves were studied. Later, the RCL property was extended to rational triangular Bézier surfaces of an arbitrary degree for ...
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Cubicoids (degree 3 surfaces) always have a parameterization in tenos of rational functions, (a polynomial divided by another). On the other hand cubics (degree 3 plane curves) do not always have a rational parameterization. However they always have a parameterization of the type which allows a single square root of rational functions. [n this paper we describe algorithms to obtain rational and...
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We describe algorithms to obtain rational parametric equations, (a polynomial equation divided by another), for degree two curves (conics) and degree two surfaces (conicoids), given the implicit equations. We further consider the rational parameterizations over t':~ fields of rationals, reals and complex numbers. In doing so, solutions are given to important subproblems of finding rational, rea...
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A method for parameterizing nearly arbitrary implicit plane/space curves and surfaces is introduced. The parameterizations are of class Cn−1 if the given curves/surfaces are of class Cn. The computation of points and derivatives is performed numerically. These parameterizations can be used for controlled determination of points on curves and surfaces and for the application of developed techniq...
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ژورنال
عنوان ژورنال: ACM Transactions on Graphics
سال: 1989
ISSN: 0730-0301,1557-7368
DOI: 10.1145/77269.77273