Matrix analysis
IBM Journal of Research and Development
Smooth interpolation of orientations with angular velocity constraints using quaternions
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Jacobi's method for skew-symmetric matrices
SIAM Journal on Matrix Analysis and Applications
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
Characterizations of the set of rational parametric curves with rational offsets
Proceedings of the international conference on Curves and surfaces in geometric design
Hamilton and Jacobi Meet Again: Quaternions and the Eigenvalue Problem
SIAM Journal on Matrix Analysis and Applications
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Real-time CNC interpolators for Pythagorean-hodograph curves
Computer Aided Geometric Design
The elastic bending energy of Pythagorean-hodograph curves
Computer Aided Geometric Design
Rational blending surfaces between quadrics
Computer Aided Geometric Design
Spherical Pythagorean-hodograph curves
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Contour machining of free-form surfaces with real-time PH curve CNC interpolators
Computer Aided Geometric Design
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Performance analysis of CNC interpolators for time-dependent feedrates along PH curves
Computer Aided Geometric Design
Optimal slicing of free-form surfaces
Computer Aided Geometric Design
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
Computer Aided Geometric Design
Characterization and construction of helical polynomial space curves
Journal of Computational and Applied Mathematics
Euclidean and Minkowski Pythagorean hodograph curves over planar cubics
Computer Aided Geometric Design
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Rational space curves are not “unit speed”
Computer Aided Geometric Design
Preface: Pythagorean-hodograph curves and related topics
Computer Aided Geometric Design
Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
Computer Aided Geometric Design
Nonexistence of rational rotation-minimizing frames on cubic curves
Computer Aided Geometric Design
Journal of Symbolic Computation
Advances in Computational Mathematics
Rational Pythagorean-hodograph space curves
Computer Aided Geometric Design
Low degree euclidean and minkowski pythagorean hodograph curves
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Spatial pythagorean hodograph quintics and the approximation of pipe surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3
Journal of Computational and Applied Mathematics
On the approximation order of a space data-dependent PH quintic Hermite interpolation scheme
Computer Aided Geometric Design
Hi-index | 0.00 |
The structural invariance of the four-polynomial characterization for three-dimensional Pythagorean hodographs introduced by Dietz et al. (1993), under arbitrary spatial rotations, is demonstrated. The proof relies on a factored-quaternion representation for Pythagorean hodographs in three-dimensional Euclidean space--a particular instance of the "PH representation map" proposed by Choi et al. (2002)--and the unit quaternion description of spatial rotations. This approach furnishes a remarkably simple derivation for the polynomials u'(t), v'(t), p'(t), q'(t) that specify the canonical form of a rotated Pythagorean hodograph, in terms of the original polynomials u(t), v(t), p(t), q(t) and the angle θ and axis n of the spatial rotation. The preservation of the canonical form of PH space curves under arbitrary spatial rotations is essential to their incorporation into computer-aided design and manufacturing applications, such as the contour machining of free-form surfaces using a ball-end mill and real-time PH curve CNC interpolators.