Geometric analysis of non-degenerate shifted-knots Bézier surfaces in Minkowski space

Abstract

In this paper, we investigate the properties of timelike and spacelike shifted-knots Bézier surfaces in Minkowski space-E 1 3. These surfaces are commonly used in mathematical models for surface formation in computer science for computer-aided geometric design and computer graphics, as well as in other fields of mathematics. Our objective is to analyze the characteristics of timelike and spacelike shifted-knots Bézier surfaces in Minkowski space-E 1 3. To achieve this, we compute the fundamental coefficients of shifted-knots Bézier surfaces, including the Gauss-curvature, mean-curvature, and shape-operator of the surface. Furthermore, we present numerical examples of timelike and spacelike bi-quadratic (m = n = 2) and bi-cubic (m = n = 3) shifted-knots Bézier surfaces in Minkowski space-E 1 3 to demonstrate the applicability of the technique in Minkowski space.

Exploring q-Bernstein-Bézier surfaces in Minkowski space: Analysis, modeling, and applications

“…The Bézier-surfaces formed by the product of two Bézier-curves have the same properties as well. Bézier surfaces have found numerous applications [ 3 , 4 ] across various disciplines, particularly in optimization theory, where they are utilized to find minimal Bézier surfaces, serving as extremals constrained by energy functionals in both Euclidean- and Minkowski space- [ 5 – 12 ]. These surfaces show promise as candidates for optimization studies.…”