An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Conditions of Nondegeneracy of Three-Dimensional Cells. A Formula of a Volume of Cells
SIAM Journal on Scientific Computing
Conditions for the invertibility of the isoparametric mapping for hexahedral finite elements
Finite Elements in Analysis and Design
Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics)
A Computational Differential Geometry Approach to Grid Generation (Scientific Computation)
A Computational Differential Geometry Approach to Grid Generation (Scientific Computation)
Geometric Modeling
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Trivariate polynomial maps are often used to model volumetric objects in three-space. It is necessary, therefore, to efficiently compute points, vectors, and other geometric properties of such objects. These properties are formulated it terms of the metric and the curvature tensors associated with the map. The simplest trivariate map is the trilinear. The map and its Jacobian are represented in tensor product Bézier form and a pyramid algorithm is utilized to compute points and vectors associated with the map. In addition, sufficient conditiona for the positivity of the Jacobian are given and an algorithm for solving the inversion problem is derived.