Shape generation of 3D object of linear lie algebra models based on curvature analysis and integral surfaces

摘要

Linear Lie algebra model of 3D objects are known for their ability to determine a shape uniquely with a complete set of invariants and represent a wide class of smooth surfaces. Since the model represents the surface of a shape as integral curves of linear Lie algebra, it is important to control integral error in order to generate shapes in high precision. This paper proposes a shape generation algorithm based on a curvature analysis. Also, we parallelly compute multiple integral curves to form an intergral surface to shorten the integral process and reduce error accumulation.