A physically based approach to 2–D shape blending
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This paper presents a new optimization methodology of material blending for heterogeneous object modeling by matching the material-governing features. The proposed method establishes point-to-point correspondence represented by a set of connecting lines between two material directrices. To blend the material features between the directrices, a heuristic optimization method is developed to maximize the sum of the inner products of the unit normals at the end points of the connecting lines and minimize the sum of the lengths of the connecting lines. The geometric features with material information are matched to generate non-self-intersecting and non-twisted connecting surfaces. By subdividing the connecting lines into an equal number of segments, a series of intermediate piecewise curves is generated to represent the material metamorphosis between the governing material-features. A dynamic programming approach developed in our earlier work is presented for comparison purposes, and the computational efficiency of the proposed heuristic method is also compared with earlier techniques in the literature. Computer interface implementation and illustrative examples are also presented in this paper.