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Constructing G1 Triangular Interpolation Surface with Normal Control

Given a triangulated mesh with the positions and outer surface normal values at the vertexes, this paper presents a scheme to construct a G1 continuous triangular interpolation surface. Most of local interpolation methods suffer from similar defect that the shape of the constructed surface is flat, the shape of the constructed surfaces by scheme of this paper is not flat, and some surfaces can be reconstructed accurately, such as spheres, columns and cones. Firstly, the scheme estimate if the local parameters related to an edge approximately belong to a simple kind of surfaces which has center point or center axis, similar to a sphere, a column or a cone; if so then reconstruct the sub-patch with the normal extension method; else construct the sub-patch with side-vertex method, where cubic Hermite curve is used, and the lengths of endpoint tangent vectors are determined by shape interpolation method; the patch of a triangular domain is the convex combination of the three sub- patches.