COMPARISON BETWEEN CURVATURE AND NORMAL CURVATURE ON SMOOTH LOGICALLY CARTESIAN SURFACE MESHES USING MATLAB

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within the surface as measured along curves on the surface. One of the fundamental concepts investigated is the Gaussian curvature, Surfaces naturally arise as graphs of functions of a pair of variables, and sometimes appear in parametric form or as loci associated to space curves. The aim of this paper is to compare between Curvature and Normal Curvature on Smooth Logically Cartesian Surface Meshes using Matlab And we found In case 1 , case 2 and case 3 figures show the main results between two sheets curvature and one sheet curvature when we adjust the parameter in 3 Axis vectors as follows in case 1 shown that the parameters as two faces curvature , In case 2 shown that the parameter of case 2 as a positive face of curvature (upper curvature ) or one sheet curvature and case 3 processed the parameters in negative way of curvature (lower curvature ) or one sheet curvature . As for the normal curve shown the sample data in positive direction of plan that means is approximately near to one sheet positive direction.