ABSTRACT
This video describes a new type of 3D curves, which generalizes the family of 2D Euler spirals. They are defined as the curves having both their curvature and their torsion evolve linearly along the curve. The utility of these spirals for curve completion applications is demonstrated. This video accompanies the paper presented in [4].
- G. Barequet and S. Kumar. Repairing CAD models. In IEEE Visualization, 1997. Google ScholarDigital Library
- G. Barequet and M. Sharir. Filling gaps in the boundary of a polyhedron. Computer Aided Geometric Design, 12(2):207--229, 1995. Google ScholarDigital Library
- D. DeCarlo, A. Finkelstein, S. Rusinkiewicz, and A. Santella. Suggestive contours for conveying shape. ACM Trans. Graph., 22(3):848--855, 2003. Google ScholarDigital Library
- G. Harary and A. Tal. 3D Euler spirals for 3D curve completion. In ACM Symposium on Computational Geometry, 2010. Google ScholarDigital Library
- T. Judd, F. Durand, and E. Adelson. Apparent ridges for line drawing. ACM Trans. Graph., 26(3):19:1--7, 2007. Google ScholarDigital Library
- D. Knuth. Mathematical typography. American Mathematical Society, 1(2):337--372, 1979.Google Scholar
- M. Kolomenkin, I. Shimshoni, and A. Tal. Demarcating curves for shape illustration. ACM Trans. Graph., 27(5):157:1--9, 2008. Google ScholarDigital Library
- M. Kolomenkin, I. Shimshoni, and A. Tal. On edge detection on surfaces. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 2767--2774, 2009.Google ScholarCross Ref
- A. Sharf, M. Alexa, and D. Cohen-Or. Context-based surface completion. ACM Trans. Graph., 23(3):878--887, 2004. Google ScholarDigital Library
- S. Yoshizawa, A. Belyaev, and H. P. Seidel. Fast and robust detection of crest lines on meshes. In ACM Symposium on Solid and Physical Modeling, pages 227--232, 2005. Google ScholarDigital Library
Index Terms
- Visualizing 3D Euler spirals
Recommendations
3D Euler spirals for 3D curve completion
SoCG '10: Proceedings of the twenty-sixth annual symposium on Computational geometryShape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curves, which can be utilized for curve completion. It can be considered as the extension to three dimensions of ...
Piecewise 3D Euler spirals
SPM '10: Proceedings of the 14th ACM Symposium on Solid and Physical Modeling3D Euler spirals are visually pleasing, due to their property of having their curvature and their torsion change linearly with arc-length. This paper presents a novel algorithm for fitting piecewise 3D Euler spirals to 3D curves with G2 continuity and ...
Interpolation of two-dimensional curves with Euler spirals
We propose an algorithm for the interpolation of two-dimensional curves using Euler spirals. The method uses a lower order reconstruction to approximate solution derivatives at each sample point. The computed tangents are then used to connect ...
Comments