A geometric method for computation of geodesic on parametric surfaces

• An efficient geometric algorithm aims to trace geodesic on parametric surfaces.
• Independent of the complex description of the geodesic equations.
• Simpler and faster than the existing geometric method.
• Step size of the algorithm adapts to the geometry of parametric surface.

This paper proposes a geometric algorithm for computation of geodesic on surfaces. The geodesics on surfaces are traced in a simple way which is independent of the complex description of the geodesic equations. Through derivation process, the calculation error of this algorithm is obtained. A step size adjustment strategy which enables the step size adapt to the geometry of surface is introduced. The proposed method is also compared to some other well-known methods in this study. Many geodesics computed using these approaches on various B-spline surfaces or their equivalent tessellated surfaces have been presented. Experiments demonstrate that the proposed algorithm is efficient. Meanwhile, the results show that the step size adjustment strategy works well for most of the cases.