Inflection points on 3D curves

摘要

Existing definitions for inflection point on 3D curves lack the direct relation to local shape-characteristics of the 3D curve that the corresponding definition for planar curves has. This paper presents a new generalization of the definition of planar-curve inflection to the case of a 3D curve that is directly related to the local convexity of the 3D curve and to that of orthogonal projections of this 3D curve on planes of interest. Various properties of this new "3D-curve inflection" concept, employing standard Differential-Geometric properties of the 3D curve, are proved, establishing its usefulness for 3D-curve interrogation within current CAD/CAGD curve/surface-design systems.