curvaturewise

Curvaturewise is an adverb used to describe analysis, description, or criteria that are organized with reference to curvature. It is not a standard mathematical term, but is sometimes used in informal or semi-formal discussion to distinguish curvature-based considerations from those based on other geometric quantities.

In differential geometry, computer graphics, and related fields, curvaturewise reasoning may guide tasks such as smoothing, segmentation, and feature detection by focusing on curvature properties rather than solely on length or area. It can also appear in discussions of curve and surface design where curvature distribution is a primary criterion.

Examples include a curvaturewise analysis of a planar curve parameterized by arc length, examining the curvature function κ(s) along s to locate high-curvature regions. For surfaces, a curvaturewise approach may use principal curvatures κ1 and κ2, Gaussian curvature K, or mean curvature H to identify ridges, valleys, or areas of high bending.

Origin and usage: curvaturewise appears as a nonce or informal term formed from curvature and -wise. It is not standardized in mathematical vocabulary; formal writing typically uses “curvature-based” or “with respect to curvature” instead.