Developing a General algorithm for Ball Curve with GC2

TL;DR

This paper presents a general algorithm for constructing piecewise Ball Curves with curvature continuity (GC2), requiring tangent vectors and curvatures at points, demonstrated through a vase design.

Contribution

The paper introduces a novel algorithm for GC2 Ball Curves that incorporates curvature and tangent data, enabling smooth curve design.

Findings

Successfully constructed a vase using the GC2 Ball Curve algorithm.

The algorithm ensures curvature continuity in piecewise Ball Curves.

Provides a practical method for curve design with specified curvature and tangents.

Abstract

This paper dwells in developing a general algorithm for constructing a piecewise Ball Curve with curvature continuity (GC2). The proposed algorithm requires GC2 data in which the designer must define unit tangent vectors and signed curvatures at each interpolating points. As a numerical example, a vase is constructed using GC2 piecewise Ball Curve