An algebraic approach to curves and surfaces on the sphere and on other quadrics

DOI10.1016/0167-8396(93)90037-4zbMath0781.65009OpenAlexW2089358519MaRDI QIDQ687452

Roland Dietz, Josef Hoschek, Bert Jüttler

Publication date: 25 October 1993

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-8396(93)90037-4

zbMATH Keywords

computer aided design Bézier patch hyperbolic projection pythagorean triples quadric patches tensor product patch triangular surface patches

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17) Projective analytic geometry (51N15)

Related Items (58)

Smooth surface interpolation using patches with rational offsets ⋮ Hermite interpolation by piecewise polynomial surfaces with polynomial area element ⋮ Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations ⋮ Almost universal parametrizations for cubic surfaces ⋮ Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves ⋮ In memoriam Josef Hoschek ⋮ The shape of spherical quartics ⋮ Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces ⋮ Almost rotation-minimizing rational parametrization of canal surfaces ⋮ Symbolic computation of the orthogonal projection of rational curves onto rational parameterized surfaces ⋮ Rational parametrization of quadrics and their offsets ⋮ A Laguerre geometric approach to rational offsets ⋮ Determination and classification of triangular quadric patches ⋮ Minimal rational parametrizations of canal surfaces ⋮ Construction of Smooth Isogeometric Function Spaces on Singularly Parameterized Domains ⋮ Rational blending surfaces between quadrics ⋮ Interpolation on quadric surfaces with rational quadratic spline curves ⋮ Surfaces containing two circles through each point ⋮ Optimal interpolation with spatial rational Pythagorean hodograph curves ⋮ Partial fraction decomposition for rational Pythagorean hodograph curves ⋮ Construction of rational surface patches bounded by lines of curvature ⋮ Rational Pythagorean-hodograph space curves ⋮ Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space ⋮ Interpolation on the hypersphere with Thiele type rational interpolants ⋮ Characterization and construction of helical polynomial space curves. ⋮ High order parametric polynomial approximation of quadrics in $\mathbb{R}^d$ ⋮ Geometry of the ringed surfaces in $\mathbb{R}^4$ that generate spatial Pythagorean hodographs ⋮ Rational curves and surfaces with rational offsets ⋮ Surfaces containing two isotropic circles through each point ⋮ About the construction of rational curves and surfaces on quadrics ⋮ Some remarks on quadrics ⋮ Visualization of dental information within CT volumes ⋮ Rational fixed radius rolling ball blends between natural quadrics ⋮ Pythagorean-hodograph preserving mappings ⋮ Rational rotation-minimizing frames on polynomial space curves of arbitrary degree ⋮ $C^{2}$ spherical Bézier splines ⋮ Rational Offset Surfaces and their Modeling Applications ⋮ Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves ⋮ ConstructingG¹continuous curve on a free-form surface with normal projection ⋮ Geometric elements and classification of quadrics in rational Bézier form ⋮ A geometric product formulation for spatial pythagorean hodograph curves with applications to Hermite interpolation ⋮ Rational space curves are not ``unit speed ⋮ $C^d$ Hermite interpolations with spatial Pythagorean hodograph B-splines ⋮ Weierstrass-type approximation theorems with Pythagorean hodograph curves ⋮ Modified Rodrigues parameters: an efficient representation of orientation in 3D vision and graphics ⋮ A characterization of helical polynomial curves of any degree ⋮ Bézier tilings of the sphere and their applications in benchmarking multipatch isogeometric methods ⋮ Rational interpolation on a hypersphere ⋮ Higher dimensional PH curves ⋮ Rational two-parameter families of spheres and rational offset surfaces ⋮ A variational approach to spline curves on surfaces ⋮ Unnamed Item ⋮ Euler-Rodrigues frames on spatial Pythagorean-hodograph curves. ⋮ Rational framing motions and spatial rational Pythagorean hodograph curves ⋮ $C^2$ Hermite interpolation by Pythagorean Hodograph space curves ⋮ B-spline Pythagorean hodograph curves in Clifford algebras ⋮ Offsets, conchoids and pedal surfaces ⋮ Universal parametrization and interpolation on cubic surfaces

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