The Shape Operator of the Bezier Surfaces in Minkowski-3 Space

Abstract

Bezier surfaces are commonly used in Computer-Aided Geometric Design since it enables in geometric modeling of the objects. In this study, the shape operator of the timelike and spacelike surfaces has been analyzed in Minkowski-3 space. Then, the obtained results were applied to a numeric example

The Serret-Frenet Frame of the Rational Bezier Curves in the Euclidean-3 Space by Algorithm Method

“…It seems that the results obtained here are the same as those in the study [10]. As it seems, since taking the weights as , 1 ik   , the rational Bezier curve transforms into polynomial Bezier curves.…”

“…İncesu and et al studied some geometric properties of the Bezier curves and the surfaces [7][8][9]. Kuşak Samancı and et al (2015), for the first time, computed the Serret-Frenet and Bishop frame of the initial and ending points of the Bezier curves in the Euclidean 3-space [10]. After that, Kuşak Samancı (2016) analyzed the Bezier and B-spline curves along with the properties of the textile fibers [11,12].…”

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

“…Ugail et al [ 50 ] analyzed Bézier surfaces in the three-dimensional Minkowski space- , considering both timelike and spacelike cases, and sought to determine the surfaces that are extremals of the Dirichlet functional. Kuşak Samancı and Celik [ 51 ] presented a geometric viewpoint of Bézier surfaces in Minkowski space and determined the shape operator of both timelike and spacelike Bézier surfaces in . In this work, we find the fundamental coefficients, Gauss-curvature, mean-curvature, and shape-operator of the timelike and spacelike shifted-knots Bézier surface.…”

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

“…Georgiev [39] found sufficient conditions for the spacelike Be ´zier surfaces. Kuşak Samancı and Celik [40] analyzed the geometric characteristics such as shape operator, Gauss curvature and mean curvature of the Be ´zier surfaces in Minkowski space. In addition, related studies by Ceylan [41] focus on the geometry of Be ´zier curves in Minkowski space.…”