A shape blending algorithm of 2-D curved shapes is presented in this paper. A curvedshape is represented by a closed Non-Uniform Rational B-Spline(NURBS). We determine the inter-mediate shapes by interpolating the int...A shape blending algorithm of 2-D curved shapes is presented in this paper. A curvedshape is represented by a closed Non-Uniform Rational B-Spline(NURBS). We determine the inter-mediate shapes by interpolating the intrinsic definitions of the initial and final control polygons. Thisalgorithm can avoid shrinkage resulted from linear vertex interpolation and produce smcoth intermedi-ate shapes. Aliasing problems can also be easily eliminated.展开更多
This paper presents a new general approach to blend 2D shapes with differenttopologies. All possible topolog-ical evolutions are classified into three types by attaching threedifferent topological cells. This formalis...This paper presents a new general approach to blend 2D shapes with differenttopologies. All possible topolog-ical evolutions are classified into three types by attaching threedifferent topological cells. This formalism is resulted from Morse theory on the behavior of the 3Dsurface around a non-degenerate critical point. Also we incorporate degenerate topologicalevolutions into our framework which produce more attractive morphing effects. The user controls themorph by specifying the types of topological evolutions as well as the feature correspondencesbetween the source and target shapes. Some techniques are also provided to control the vertex pathduring the morphing process. The amount of user input required to produce a morph is directlyproportional to the amount of control the user wishes to impose on the process. The user may allowthe system to automatically generate the morph as well. Our approaches are totally geometric basedand are easy and fast enough in fully interactive time. Many experimental results show theapplicability and flexibility of our approaches.展开更多
文摘A shape blending algorithm of 2-D curved shapes is presented in this paper. A curvedshape is represented by a closed Non-Uniform Rational B-Spline(NURBS). We determine the inter-mediate shapes by interpolating the intrinsic definitions of the initial and final control polygons. Thisalgorithm can avoid shrinkage resulted from linear vertex interpolation and produce smcoth intermedi-ate shapes. Aliasing problems can also be easily eliminated.
文摘This paper presents a new general approach to blend 2D shapes with differenttopologies. All possible topolog-ical evolutions are classified into three types by attaching threedifferent topological cells. This formalism is resulted from Morse theory on the behavior of the 3Dsurface around a non-degenerate critical point. Also we incorporate degenerate topologicalevolutions into our framework which produce more attractive morphing effects. The user controls themorph by specifying the types of topological evolutions as well as the feature correspondencesbetween the source and target shapes. Some techniques are also provided to control the vertex pathduring the morphing process. The amount of user input required to produce a morph is directlyproportional to the amount of control the user wishes to impose on the process. The user may allowthe system to automatically generate the morph as well. Our approaches are totally geometric basedand are easy and fast enough in fully interactive time. Many experimental results show theapplicability and flexibility of our approaches.
