Apparatus and method for geometric morphing

A method of transforming a source shape corresponding to a source object to a target shape corresponding to a target object comprising the steps in combination:

• storing in a memory a first set of data points corresponding to said source shape and a second set of data points corresponding to said target shape;
• generating a four dimensional simplical complex corresponding to said source shape and said target shape;
• and
• extracting one or more mixed shapes from one or more cross-sections of said four dimensional simplical complex, each of said mixed shapes depending on said source shape and said target shape;
• constructing one or more skins, each of said skins corresponding to one or more of said mixed shapes;
• and
• displaying one or more of said skins on an output device.

Apparatus for graphically transforming a source shape to a target shape comprising, in combination:

• a storage device for storing a first data point set corresponding to said source shape and a second data point set corresponding to said target shape;
• a memory for storing a series of computer instructions and data structures;
• a microprocessor for executing said series of computer instructions, said microprocessor generating a first Delaunay complex and a first skin corresponding to said first data point set, said microprocessor generating a second Delaunay complex and a second skin corresponding to said second data point set, said microprocessor generating a plurality of alpha complexes corresponding to the transformation of said source shape to said target shape, and said microprocessor generating a plurality of skins corresponding to said plurality of alpha complexes;
• an output device for graphically depicting said first skin, said second skin, and one or more of said plurality of skins.

Apparatus for graphically transforming a first geometric object to a second geometric object comprising, in combination:

• measuring means for generating a first point set corresponding to said first object and generating a second point set corresponding to said second object;
• storage means for storing said first data point set and said second data point set;
• generating means for:
• (a) generating a first combinatorial representation of said first data point set;
• (b) generating a second combinatorial representation of said second data point set;
• (c) defining a motion between said first point set and said second point set and between said first combinatorial representation and said second combinatorial representation;
• and
• transforming said first combinatorial representation into said second combinatorial representation in response to said motion.