In this paper, we present an efficient approach for parameterizing a genus-zero triangular mesh onto the sphere with an optimal radius in an as-rigid-as-possible (ARAP) manner, which is an extension of planar ARAP parametrization approach to spherical domain. We analyze the smooth and discrete ARAP energy and formulate our spherical parametrization energy from the discrete ARAP energy. The solution is non-trivial as the energy involves a large system of non-linear equations with additional spherical constraints. To this end, we propose a two-step iterative algorithm. In the first step, we adopt a local/global iterative scheme to calculate the parametrization coordinates. In the second step, we optimize a best approximate sphere on which parametrization triangles can be embedded in a rigidity-preserving manner. Our algorithm is simple, robust, and efficient. Experimental results show that our approach provides almost isometric spherical parametrizations with lowest rigidity distortion over state-of-the-art approaches. 
As-rigid-as-possible spherical parametrization