Detecting and decomposing self-overlapping curves
Computational Geometry: Theory and Applications
SKETCH: an interface for sketching 3D scenes
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Teddy: a sketching interface for 3D freeform design
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Smooth meshes for sketch-based freeform modeling
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
Conceptual design and analysis by sketching
Artificial Intelligence for Engineering Design, Analysis and Manufacturing
Lofting curve networks using subdivision surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SmoothSketch: 3D free-form shapes from complex sketches
ACM SIGGRAPH 2006 Papers
Sketch interface for 3D modeling of flowers
SIGGRAPH '04 ACM SIGGRAPH 2004 Sketches
Self-overlapping curves revisited
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Direct rendering of Boolean combinations of self-trimmed surfaces
Computer-Aided Design
Tweening boundary curves of non-simple immersions of a disk
Proceedings of the Eighth Indian Conference on Computer Vision, Graphics and Image Processing
Technical note: Self-overlapping curves: Analysis and applications
Computer-Aided Design
Consistent volumetric discretizations inside self-intersecting surfaces
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Hi-index | 0.00 |
The process of generating a 3D model from a set of 2D planar curves is complex due to the existence of many solutions. In this paper we consider a self-intersecting planar closed loop curve, and determine the 3D layered surface P with the curve as its boundary. Specifically, we are interested in a particular class of closed loop curves in 2D with multiple self-crossings which bound a surface homeomorphic to a topological disk. Given such a self-crossing closed loop curve in 2D, we find the deformation of the topological disk whose boundary is the given loop. Further, we find the surface in 3D whose orthographic projection is the computed deformed disk, thus assigning 3D coordinates for the points in the self-crossing loop and its interior space. We also make theoretical observations as to when, given a topological disk in 2D, the computed 3D surface will self-intersect.