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The Curve Of Least Energy
, 1983
"... Here we search fi)r the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computeraided design, curves have been sought which maximize "smoothness". The curve discus ..."
Abstract

Cited by 72 (2 self)
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Here we search fi)r the curve which has the smallest integral of the square of curvature, while passing through two given points with given orientation. This is the true shape of a spline used in lofting. In computeraided design, curves have been sought which maximize "smoothness". The curve discussed here is the one arising in this way from a commonly used measure of smoothness. The human visual system may use such a curve when it constructs a subjective contour.
3D Euler spirals for 3D curve completion
 In ACM Symposium on Computational Geometry
, 2010
"... Shape 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 the 2D Euler spiral. We prove several propertie ..."
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Cited by 5 (2 self)
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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 curves, 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 these curves – properties that have been shown to be important for the appeal of curves. We illustrate their 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. Categories and Subject Descriptors I.3 [Computer Graphics]: Computational Geometry and Object Modeling—Curve, surface, solid, and object representations
unknown title
, 1994
"... Parameterization invariance and shape equations of elastic axisymmetric vesicles ..."
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Parameterization invariance and shape equations of elastic axisymmetric vesicles
A Level Set Method to Extract the Skelton of an Object
"... Abstract — Shape skeletonization (i.e., symmetry axes extraction) is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper we propose a variational method to extract axes of symmetry of an object. The proposed met ..."
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Abstract — Shape skeletonization (i.e., symmetry axes extraction) is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper we propose a variational method to extract axes of symmetry of an object. The proposed method is based on a levelset formulation that takes into consideration the singularities of an object. Firstly, the object is segmented using ChanVese method, the segmented object is then reinitialized to a distance function. Then we define energy functional, the minimum of this functional will occur at singularities of the distance function. The minimum of the functional is computed with the calculus of variation and the gradient descent method that provide an evolution equation solved with the wellknown level set method.