Pythagorean-Hodograph B-Spline Curves
Gudrun Albrecht, Carolina Vittoria Beccari, Jean-Charles Canonne,, Lucia Romani

TL;DR
This paper introduces a new class of planar Pythagorean-Hodograph B-Spline curves that generalize existing PH curves, offering exact arc-length and offset computations, with applications in CAD, robotics, and computer graphics.
Contribution
The paper defines Pythagorean-Hodograph B-Spline curves, extending PH curves to B-Spline form, and provides formulas, properties, and practical examples for their use.
Findings
Arc-length of these curves is a B-Spline function.
Offsets of these curves are NURBS curves.
They have advantages in CAD and motion control applications.
Abstract
We introduce the new class of planar Pythagorean-Hodograph (PH) B-Spline curves. They can be seen as a generalization of the well-known class of planar Pythagorean-Hodograph (PH) B\'ezier curves, presented by R. Farouki and T. Sakkalis in 1990, including the latter ones as special cases. Pythagorean-Hodograph B-Spline curves are non-uniform parametric B-Spline curves whose arc-length is a B-Spline function as well. An important consequence of this special property is that the offsets of Pythagorean-Hodograph B-Spline curves are non-uniform rational B-Spline (NURBS) curves. Thus, although Pythagorean-Hodograph B-Spline curves have fewer degrees of freedom than general B-Spline curves of the same degree, they offer unique advantages for computer-aided design and manufacturing, robotics, motion control, path planning, computer graphics, animation, and related fields. After providing a…
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Computer Graphics and Visualization Techniques · 3D Shape Modeling and Analysis
