Preface: Pythagorean-hodograph curves and related topics
Computer Aided Geometric Design
An Interpolation Method That Minimizes an Energy Integral of Fractional Order
Computer Mathematics
Journal of Symbolic Computation
Salkowski curves revisited: A family of curves with constant curvature and non-constant torsion
Computer Aided Geometric Design
Non-existence of rational arc length parameterizations for curves in Rn
Journal of Computational and Applied Mathematics
Quintic space curves with rational rotation-minimizing frames
Computer Aided Geometric Design
Circular spline fitting using an evolution process
Journal of Computational and Applied Mathematics
Complex rational Bézier curves
Computer Aided Geometric Design
A symbolic-numerical envelope algorithm using quadratic MOS patches
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
On control polygons of quartic Pythagorean--hodograph curves
Computer Aided Geometric Design
On convolutions of algebraic curves
Journal of Symbolic Computation
Construction of rational surface patches bounded by lines of curvature
Computer Aided Geometric Design
Hermite interpolation by hypocycloids and epicycloids with rational offsets
Computer Aided Geometric Design
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
Journal of Symbolic Computation
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Advances in Computational Mathematics
Geometric Hermite interpolation by monotone helical quintics
Computer Aided Geometric Design
Curve interpolation based on the canonical arc length parametrization
Computer-Aided Design
Graphical Models
Rational Pythagorean-hodograph space curves
Computer Aided Geometric Design
Computer Aided Geometric Design
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
Journal of Computational and Applied Mathematics
Cubic helical splines with Frenet-frame continuity
Computer Aided Geometric Design
Computer Aided Geometric Design
3D Euler spirals for 3D curve completion
Computational Geometry: Theory and Applications
Construction of rational curves with rational rotation-minimizing frames via möbius transformations
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Geometric design using space curves with rational rotation-minimizing frames
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Reparameterization of curves and surfaces with respect to their convolution
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Low degree euclidean and minkowski pythagorean hodograph curves
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Surfaces with rational chord length parameterization
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Support function of pythagorean hodograph cubics and G1 hermite interpolation
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
G2 hermite interpolation with curves represented by multi-valued trigonometric support functions
Proceedings of the 7th international conference on Curves and Surfaces
Design of C2 spatial pythagorean-hodograph quintic spline curves by control polygons
Proceedings of the 7th international conference on Curves and Surfaces
On a special class of polynomial surfaces with pythagorean normal vector fields
Proceedings of the 7th international conference on Curves and Surfaces
Algebraic curves of low convolution degree
Proceedings of the 7th international conference on Curves and Surfaces
Curves and surfaces with rational chord length parameterization
Computer Aided Geometric Design
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
Original Articles: Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
Mathematics and Computers in Simulation
Simple determination via complex arithmetic of geometric characteristics of Bézier conics
Computer Aided Geometric Design
An isoperimetric type problem for primitive Pythagorean hodograph curves
Computer Aided Geometric Design
An approach to geometric interpolation by Pythagorean-hodograph curves
Advances in Computational Mathematics
Parameterizing rational offset canal surfaces via rational contour curves
Computer-Aided Design
Planar C1 Hermite interpolation with uniform and non-uniform TC-biarcs
Computer Aided Geometric Design
Reducibility of offsets to algebraic curves
Computer Aided Geometric Design
On the approximation order of a space data-dependent PH quintic Hermite interpolation scheme
Computer Aided Geometric Design
C1 rational interpolation of spherical motions with rational rotation-minimizing directed frames
Computer Aided Geometric Design
An interpolation scheme for designing rational rotation-minimizing camera motions
Advances in Computational Mathematics
C1 Hermite interpolation with PH curves by boundary data modification
Journal of Computational and Applied Mathematics
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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By virtue of their special algebraic structures, Pythagorean-hodograph (PH) curves offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. This book offers a comprehensive and self-contained treatment of the mathematical theory of PH curves, including algorithms for their construction and examples of their practical applications. Special features include an emphasis on the interplay of ideas from algebra and geometry and their historical origins, detailed algorithm descriptions, and many figures and worked examples. The book may appeal, in whole or in part, to mathematicians, computer scientists, and engineers.