Smoothing of polyhedral models
SCG '86 Proceedings of the second annual symposium on Computational geometry
Computer-Aided Design
On algebraic surfaces meeting with geometric continuity
On algebraic surfaces meeting with geometric continuity
G1 interpolation of generally unrestricted cubic Bézier curves
Computer Aided Geometric Design - Special issue: Topics in CAGD
Direct least-squares fitting of algebraic surfaces
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Blending quadric surfaces with quadric and cubic surfaces
SCG '87 Proceedings of the third annual symposium on Computational geometry
Computer Aided Geometric Design
Proceedings on Mathematics of surfaces II
The Exact Solution of Systems of Linear Equations with Polynomial Coefficients
Journal of the ACM (JACM)
Blend surfaces for set theoretic volume modelling systems
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Geometric Modeling with Algebraic Surfaces
Proceedings of the 3rd IMA Conference on the Mathematics of Surfaces
Geometric continuity: a parametrization independent measure of continuity for computer aided geometric design (curves, surfaces, splines)
On local implicit approximation and its applications
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
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We present a simple characterization of the lowest degree, implicitly defined, real algebraic surfaces, which smoothly contain any given number of points and algebraic space curves, of arbitrary degree. The characterization is constructive, yielding efficient algorithms for generating families of such algebraic surfaces. Smooth containment of space curves yields C1-continuous surface fitting, and is a generalization of standard Hermite interpolation applied to fitting curves through point data, equating derivatives at those points. We deal with the containment and matching of “normals” (vectors orthogonal to tangents), possibly varying along the entire span of the space curves. Such Hermite interpolated surfaces prove useful as “blending” or “joining” surfaces for solid models as well as “fleshing” surfaces for curved wireframe models.