Visualization of the Curvature Monotonicity Region of 3D Cubic Polynomial Bézier Curves

Abstract

In this research, we propose a method for visualizing the curvature monotonicity region for a specific control point of a 3D cubic polynomial Bezier curve using a GPU. A control point is assumed to move in the plane with a constant depth from the viewpoint to the control point, and the curvature monotonicity region is visualized in the plane. Therefore, as the viewpoint position changes, the appearance of the curvature monotonicity region also changes. The proposed method makes it possible to change the shape of a 3D cubic polynomial Bezier curve while checking the region of a control point where the curvature is monotonically varying.