Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
IBM Journal of Research and Development
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Curves with rational Frenet-Serret motion
Computer Aided Geometric Design
Hermite interpolation with Tschirnhausen cubic spirals
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Convex Optimization
On Geometric Interpolation by Polynomial Curves
SIAM Journal on Numerical Analysis
Geometric interpolation by planar cubic polynomial curves
Computer Aided Geometric Design
Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Computer Aided Geometric Design
Original Articles: Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
Mathematics and Computers in Simulation
C1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs
Journal of Computational and Applied Mathematics
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The problem of geometric interpolation by Pythagorean-hodograph (PH) curves of general degree n is studied independently of the dimension d驴驴驴2. In contrast to classical approaches, where special structures that depend on the dimension are considered (complex numbers, quaternions, etc.), the basic algebraic definition of a PH property together with geometric interpolation conditions is used. The analysis of the resulting system of nonlinear equations exploits techniques such as the cylindrical algebraic decomposition and relies heavily on a computer algebra system. The nonlinear equations are written entirely in terms of geometric data parameters and are independent of the dimension. The analysis of the boundary regions, construction of solutions for particular data and homotopy theory are used to establish the existence and (in some cases) the number of admissible solutions. The general approach is applied to the cubic Hermite and Lagrange type of interpolation. Some known results are extended and numerical examples provided.