Computational Line Geometry for Design and Manufacturing
Friday, April 27, 2001 - 2:00pm - 3:00pm
Bahram Ravani (University of California)
This presentation develops a computational framework for designing surfaces and sculptured shapes using line geometry. Classical line geometry is reviewed and recent results in developing Bezier and B-spline type line constructs are presented. It is shown that curve type algorithms can be developed for designing surfaces with line geometry. Methods are presented that are based on both the Study representation as well as the Klein model of the line space. A De Casteljau type algorithm and a Lie Group representation are used to provide the computational framework for designing with line geometry. Applications of computational line geometry in Mesh Generation, Robotics, Numerical Control Machining, and Electric Discharge Machining are also presented.