Prof. L. Shen (University of the Chinese Academy of Sciences, Beijing)
Thursday, June 14, 2018 - 15:00
Weierstraß-Institut
Mohrenstr. 39, 10117 Berlin, Raum: 405/406, 4. Etage
Seminar Numerische Mathematik
Implicitizing rational surfaces is a fundamental computational task in Computer Graphics and Computer Aided Design. Ray tracing, collision detection, and solid modeling all benefit from implicitization procedures for rational surfaces. Recently a popular method is based on analysis of moving planes (syzygies): construct the implicit matrix using moving planes or compute the resultant of μ-basis. The moving planes method relies on the construction of appropriate moving planes. The μ-bases for rational surfaces are difficult to compute. Moreover, μ-bases for a rational surface often have high degrees, so these resultants generally contain many extraneous factors.
Here we develop fast algorithms to implicitize rational tensor product surfaces by computing the resultant of three moving planes corresponding to three syzygies with low degrees. These syzygies are easy to compute, and the resultants of the corresponding moving planes generally contain fewer extraneous factors than the resultants of the moving planes corresponding to μ-bases. We predict and compute all the possible extraneous factors that may appear in these resultants.
submitted by lawrenz (marion.lawrenz@wias-berlin.de, 030 20372566)