Two moving coordinate frames for sweeping along a 3D trajectory
Computer Aided Geometric Design
SIAM Journal on Computing
A computational approach to edge detection
Readings in computer vision: issues, problems, principles, and paradigms
Solid shape
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
The NURBS book
Illumination for computer generated pictures
Communications of the ACM
Multiresolution feature extraction for unstructured meshes
Proceedings of the conference on Visualization '01
Implicit modeling of swept surfaces and volumes
VIS '94 Proceedings of the conference on Visualization '94
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
Computer Aided Geometric Design
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
Generalized sweep templates for implicit modeling
GRAPHITE '05 Proceedings of the 3rd international conference on Computer graphics and interactive techniques in Australasia and South East Asia
| Hi-index | 0.00 |
This work describes a framework for the modeling of sweep solids on freeform surfaces, considering various geometric and functional constrains. The sweeping procedure begins with the definition of a trajectory on the surface. Besides smoothness and minimal length, other requirements may apply. Therefore, it is convenient to formulate the optimal trajectory tracing as a geodesic curve computation on the surface. The trajectory defined on the surface is offsetted inside in order to make the sweep solid tangent to the surface. The offset curve shape is iteratively optimized while preserving minimal distance from the surface. Then, a frame field is defined over the offset curve and the cross-section contour is swept according to this field. The major obstacle is how to construct the frame field such that the resulting sweep solid will be smooth and free of self-intersections. In order to resolve these issues a new minimal distortion frame is introduced. The key idea is to weaken the orthogonality constraint between the cross-section plane and the trajectory curve to avoid self-intersections of the resulting sweep solid. The proposed approach was employed for semi-automatic computer aided design of ventilation tubes for customized hearing aid devices. This approach was tested in a real production environment, where it was proved robust and efficient. Although the modeling pipeline described in the paper is optimized for the specific design task, the proposed techniques are general and can be utilized in many related applications where sweeping surface modeling and manipulation are involved.