Bézier Triangle-Based Interpolatory √3 -Subdivision

In order to construct high quality subdivision surfaces efficiently, an interpolating √3 -subdivision method based on Bézier triangle is proposed. We subdivide a triangle mesh in three main steps: construct a cubic Bézier triangle interpolating the vertices and vertex normals of every triangle on the control mesh; compute the center point and center normal vector for every Bézier triangle; re-triangulate the newly computed center points and old vertices. A method to subdivide boundary triangles or singular triangles with thin shapes is also proposed. Since every new face vertex and new vertex normal is only computed based on the vertices and vertex normal of a local triangle, this method is very easy to implement and it is also possible to accelerate the subdivision by parallel computing. Numerical examples show that the proposed method can produce smooth and fair-looking subdivision surfaces. Moreover, the shape of the limit surfaces can be edited effectively by adjusting the normal direction of the initial vertices.