6533b85bfe1ef96bd12ba7fb
RESEARCH PRODUCT
Blending pieces of Dupin cyclides for 3D modeling and reconstruction : study in the space of spheres
Lucie Druotonsubject
Cyclides de Dupin[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]BlendsDupin cyclidesJoins[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]JointuresSpace of spheresRecollements[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Canal surfacesSurfaces canalEspace de sphèresdescription
The thesis deals with the blending of canal surfaces in geometric modeling using pieces of Dupin Cyclides. We try to solve a problem of reconstructing real parts manufactured and controlled by the CEA of Valduc. Using the space of spheres in which we can manipulate both points, spheres and canal surfaces, we simplify some problems. This space is represented by a 4-dimensional quadric in a 5-dimensional space, equipped with the Lorentz form, it is the Lorentz space. In the space of spheres, problems of blending canal surfaces by pieces of Dupin cyclides are simplified in linear problems. We give algorithms to make such blends using the space of spheres and after we come back to 3 dimensions to draw the result. These blends are always made along characteristics circles of the considered surfaces. By solving the problem of three contact conditions, we highlight another particular curve, on a one parameter familly of cyclides, that we call contact curve along which we could also make this kind of blends
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-04-04 |