Principal Investigator Nicholas Patrikalakis
Project Website http://deslab.mit.edu/DesignLab/itango/front.html
Surface intersections are needed in a variety of CAD/CAM applications like solid modeling, contouring, manufacturing simulation and NC machining.
In this web page we briefly describe a state-of-the-art solution scheme for the surface intersection problem. We also give some important links as to how exactly are we plan to do the above.
Consider two rational polynomial parametric (RPP) surfaces P and Q. We are interested in finding out their intersection. In general the intersection of two surfaces can have many components. Each component of the intersection in the model space has a counterpart in the parametric space of each of the surfaces.
Application in CAD/CAM/CAE:(*) Validated bounds for self intersection is very useful in NC machining, where the tool path often follows an offset of the surface to be machined.
(*) Validated error bounds for surface intersection are essential in interval boundary representation for consistent solid models (gap formation is resolved). o Presentation on Interval Boundary Representation.
(*) Tracing true intersection curve is essential to obtain correct contours, which can further be used for navigation (topography), and obtaining the contour bands for surface properties.
(*) Manufacturing simulation is another application where accurate evaluation of intersection is needed. o Applications of correctly traced SSI.
Current Research Work:(*) One important aspect which we are presently studying is a mechanism for strict error control for a validated interval solution scheme applied to surface intersection problem.
(*) Strict bounds for the starting point is another concern, with special effort going into the multiple root evaluation.
(*) Topology resolution to robustly identify all the intersection curve segments is yet another topic of study.