Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
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
Real-time CNC interpolators for Pythagorean-hodograph curves
Computer Aided Geometric Design
The elastic bending energy of Pythagorean-hodograph curves
Computer Aided Geometric Design
Construction and shape analysis of PH Hermite interpolants
Computer Aided Geometric Design
Performance analysis of CNC interpolators for time-dependent feedrates along PH curves
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
Characterization and construction of helical polynomial space curves
Journal of Computational and Applied Mathematics
Weierstrass-type approximation theorems with Pythagorean hodograph curves
Computer Aided Geometric Design
On quadratic two-parameter families of spheres and their envelopes
Computer Aided Geometric Design
PN surfaces and their convolutions with rational surfaces
Computer Aided Geometric Design
On control polygons of quartic Pythagorean--hodograph curves
Computer Aided Geometric Design
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
Planar C1 Hermite interpolation with uniform and non-uniform TC-biarcs
Computer Aided Geometric Design
C1 Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
A scheme to specify planar C^2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the ''ordinary''C^2 cubic B-spline curve serves as a reference for the shape of the PH spline. The method facilitates intuitive and efficient constructions of open and closed PH spline curves, that typically agree closely with the corresponding cubic B-spline curves. The C^2 PH quintic spline curve associated with a given control polygon and knot sequence is defined to be the ''good'' interpolant to the nodal points of the C^2 cubic spline curve with the same B-spline control points, knot sequence, and end conditions-it may be computed to machine precision by just a few Newton-Raphson iterations from a close starting approximation. The relation between the PH spline and its control polygon is invariant under similarity transformations. Multiple knots may be inserted to reduce the order of continuity to C^1 or C^0 at specified points, and by means of double knots the PH splines offer a linear precision and local shape modification capability. Although the non-linear nature of PH splines precludes proofs for certain features of cubic B-splines, such as convex-hull confinement and the variation-diminishing property, this is of little practical significance in view of the close agreement of the two curves in most cases (in fact, the PH spline typically exhibits a somewhat better curvature distribution).