Method for generating curved surface consisting of quartic Bezier triangles patches, from a mesh of planar triangles is disclosed. Mesh of planar triangles is used as input. For each vertices, faces that are joined at the vertex are evaluated to determine the desired surface orientation and a scalar parameter that describes the curvature. This can be expressed as a normal vector with its size representing the scalar parameter. Based on this normal vector, one cubic Bezier control point is generated on each side of triangles surrounding the vertex. Applying this to all vertices in the mesh will form cubic Bezier curve which is the boundary curve shared between the adjacent triangle patches. Once cubic Bezier boundary curves are obtained, quartic Bezier triangles patches can be generated for each triangle in the mesh.