Global Curve Analysis via a Dimensionality Lifting Scheme

Freeform rational parametric curves and surfaces have been playing a major role in computer aided design for several decades. The ability to analyze local (differential) properties of parametric curves is well established and extensively exploited. In this work, we explore a different lifting approach to global analysis of freeform geometry, mostly curves, in IR2 and IR3. In this lifting scheme, we promote the problem into a higher dimension, where we find that in the higher dimension, the solution is simplified.

[1]  Jörg Peters,et al.  Computing moments of objects enclosed by piecewise polynomial surfaces , 1998, TOGS.

[2]  Gershon Elber,et al.  Mold Accessibility via Gauss Map Analysis , 2005, J. Comput. Inf. Sci. Eng..

[3]  Gershon Elber,et al.  Trimming local and global self-intersections in offset curves/surfaces using distance maps , 2006, Comput. Aided Des..

[4]  Dinesh Manocha,et al.  Efficient and exact manipulation of algebraic points and curves , 2000, Comput. Aided Des..

[5]  Gershon Elber.  Distance Separation Measures Between Parametric Curves and Surfaces Toward Intersection and Collision Detection Applications , 2005 .

[6]  Tony C. Woo,et al.  Visibility maps and spherical algorithms , 1994, Comput. Aided Des..

[7]  Fopke Klok.  Two moving coordinate frames for sweeping along a 3D trajectory , 1986, Comput. Aided Geom. Des..

[8]  Gershon Elber,et al.  Hidden curve removal for free form surfaces , 1990, SIGGRAPH.

[9]  Gershon Elber.  Multiresolution Curve Editing With Linear Constraints , 2001 .

[10]  Basile Sauvage,et al.  Area preserving deformation of multiresolution curves , 2005, Comput. Aided Geom. Des..

[11]  R. K. Shyamasundar,et al.  Introduction to algorithms , 1996 .

[12]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[13]  Ralph R. Martin,et al.  Two-dimensional visibility charts for continuous curves , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[14]  Gershon Elber,et al.  Symbolic and Numeric Computation in Curve Interrogation , 1995, Comput. Graph. Forum.

[15]  안희갑.  Separating an Object from its Cast. , 1997 .

[16]  Alla Sheffer,et al.  Volume-preserving free-form solids , 1995, IEEE Trans. Vis. Comput. Graph..

[17]  H. Piaggio.  Differential Geometry of Curves and Surfaces , 1952, Nature.

[18]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[19]  Gershon Elber.  Trimming Local and Global Self-intersections in Offset Curves Using Distance Maps , 2003, IMA Conference on the Mathematics of Surfaces.

[20]  Arthur Appel,et al.  The notion of quantitative invisibility and the machine rendering of solids , 1967, ACM National Conference.