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Euler Spiral for Shape Completion
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Suggestive contours for conveying shape
ACM SIGGRAPH 2003 Papers
Context-based surface completion
ACM SIGGRAPH 2004 Papers
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Apparent ridges for line drawing
ACM SIGGRAPH 2007 papers
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Demarcating curves for shape illustration
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G1 interpolation with a single Cornu spiral segment
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Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
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Computers and Graphics
Relief analysis and extraction
ACM SIGGRAPH Asia 2009 papers
Technical section: A controlled clothoid spline
Computers and Graphics
3D Euler spirals for 3D curve completion
Proceedings of the twenty-sixth annual symposium on Computational geometry
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve - properties that have been shown to be important for the appeal of curves. We illustrate its utility in two applications. The first is ''fixing'' curves detected by algorithms for edge detection on surfaces. The second is shape illustration in archaeology, where the user would like to draw curves that are missing due to the incompleteness of the input model.