Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Real rational curves are not “unit speed”
Computer Aided Geometric Design
Piecewise surface flattening for non-distorted texture mapping
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
The NURBS book
Computing normal vector Bézier patches
Computer Aided Geometric Design - Pierre Bézier
NURBS: From Projective Geometry to Practical Use
NURBS: From Projective Geometry to Practical Use
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Computational Line Geometry
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Short communication: Rational hodographs
Computer Aided Geometric Design
Existence conditions for Coons patches interpolating geodesic boundary curves
Computer Aided Geometric Design
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided Design
Geodesic-like curves on parametric surfaces
Computer Aided Geometric Design
Construction and smoothing of triangular Coons patches with geodesic boundary curves
Computer Aided Geometric Design
A note of boundary geodesic problem on regular surfaces
ECC'11 Proceedings of the 5th European conference on European computing conference
The general orthogonal projection on a regular surface
ECC'11 Proceedings of the 5th European conference on European computing conference
Parametric representation of a surface pencil with a common line of curvature
Computer-Aided Design
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
Computers & Mathematics with Applications
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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In a recent work, Wang et al. [Wang G, Tang K, Tai CH. Parametric representation of a surface pencil with common spatial geodesic. Computer-Aided Design 2004;36(5): 447-59] discuss a constrained design problem appearing in the textile and shoe industry for garment design. Given a model and size, the characteristic curve called girth is usually fixed, and preferably should be a geodesic for manufacturing reasons. The designer must preserve this girth, being allowed to modify other areas according to aesthetic criteria. We present a practical method to construct polynomial surfaces from a polynomial geodesic or a family of geodesics, by prescribing tangent ribbons. Differently from previous procedures, we identify the existing degrees of freedom in terms of control points, and our method yields parametric polynomial surfaces that can be incorporated into commercial CAD programs. The extension to rational geodesics is also outlined.