| In the applications of geometric modeling based on triangular surface, the fluctuation of high degree surfaces'shape and the complexity of storage and data interchange make the research on the approximate degree reduction of triangular surface take attention in recent years. However, triangular surface is not the tensor product surface, general methods for degree reduction of curve and surface are very difficult to be extended directly to triangle surface. The research about the approximate degree reduction of triangular surface is relatively less. So the efficient and applied methods need further studies. Especially, the study of approximate degree reduction of multi-triangular surfaces with GC1 constraint on boundary has never seen before.This paper investigates the approximate multi-degree reduction and joining of exiting parameter curve and surface. Especially, proposing an algorithm of approximate multi-degree reduction of triangular Bézier surfaces by L2 norm with GC1 constraint by adjusting the second line control vertices on boundary. On the basis above, this paper investigates the approximate multi-degree reduction of multi-triangular Bézier surface with constraint. A kind of blending format for the approximate degree reduction of multi-triangular Bézier surface with GC1 constraint is studied. This format makes sure of regulative internal control points after each two triangular Bézier surfaces approximate degree reduction with GC1 constraint on commonality boundary, then structuring blending function and forming a new blending format for the approximate degree reduction surface by blending some groups of control points that is corresponding to every triangular Bézier. This new blending triangular Bézier surface and surrounding surfaces with approximate degree reduction degree still keep GC1 constraint in theory.Finally, give a summary of this paper. The state of art and possible new directions of the approximate multi-degree reduction of parameter surface are stated. |
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