Geometric continuity of ruled surfaces

doi:10.1016/S0167-8396(97)00032-0

Computer Aided Geometric Design

Volume 15, Issue 3, March 1998, Pages 289-310

https://doi.org/10.1016/S0167-8396(97)00032-0 Get rights and content

Abstract

This paper develops a theory for higher order continuity of ruled surfaces constructed from ruled surface patches. Continuity is defined by the equivalence of a minimal set of geometric properties for the ruled surfaces and their evolutes using the dual arc element as the parameter of the surface. The method used is a completely new approach to higher-order continuity of ruled surfaces. Also, contact continuity is compared to continuity of the Frenet trihedrons and the curvatures. These continuity conditions can be used in design procedures for ruled surface segments in CAGD.

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Geometric continuity of ruled surfaces

Abstract

Journal of Approximation Theory

Computer Aided Geometric Design

Computer Aided Geometric Design

Mechanism and Machine Theory

Mechanisms and Machine Theory

Smooth curves and surfaces

On the definition of geometric continuity

Computer-Aided Design

Geometric Concepts for Geometric Design

Theoretical Kinematics

Vector and Tensor Analysis

The Screw Calculus and its Application in Mechanics

Piecewise polynomial spaces and geometric continuity of curves

Numerische Mathematik

Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide

Higher path-curvature analysis in plane kinematics

ASME Journal of Engineering for Industry

Differential Geometry

Liniengeometrie

Fundamentals of Computer Aided Geometric Design

Curvature theory in space kinematics