We want to find a measure of how ‘curved’ a curve is. Since this ‘curvature’ should depend only on the ‘shape’ of the curve, it should not be changed when the curve is reparametrized. Further, the measure of curvature should agree with our intuition in simple special cases. Straight lines themselves have zero curvature. Large circles should have smaller curvature than small circles which bend m...

PURPOSE This study evaluated the prevalence of distolingual roots in mandibular molars among Koreans, the root canal system associated with distolingual roots, and the concurrent appearance of a distolingual root in the mandibular first molar and a C-shaped canal in the mandibular second molar. MATERIALS AND METHODS Cone-beam computed tomographic images of 264 patients were screened and exami...

1. Overview 2 1.1. Curve shortening flow 2 1.2. Flow of hypersurfaces 5 1.3. Mean convex surfaces 6 2. The maximum principle 7 3. Unparameterized mean curvature flow 8 3.1. Graphs 8 4. Short-time existence and smoothing 9 5. Long term behavior of mean curvature flow 9 6. Renormalized mean curvature flow 11 7. The level set approach to weak limits 13 8. Weak compactness of submanifolds 16 8.1. E...

in this paper, moment-curvature behavior and ductility of prestressed concrete members based on nonlinear analysis is investigated. influence of various design parameters on ductility of flexural members is determined according to appropriate materials models for stress-strain curves of concrete, prestressing steel and conventional reinforcements. parameters studied include reinforcing index (ω...

Knowing a set of points on a curve, the interpolation problem is to hypothesize the location of the intermediary ones. A large set of interpolation techniques are known. We address the problem of generating a path with minimal maximum curvature, passing through N ordered points and joining the two end-points at predefined directions. This is related to R-geodesics, which have been used to gener...

BACKGROUND Dilation and dissection of aneurysmal ascending aortic tissues occur preferentially at the outer curvature of the vessel. In this study we hypothesize that the density and contractile properties of the vascular smooth muscle cells (VSMCs) of the pig ascending aorta (AA) are heterogeneous and could explain the non-uniform remodeling and weakening of the AA during aneurysm formation. ...

A constrained Delaunay triangle mesh method is presented to recover the surface from the three-dimensional unstructured boundary point cloud. The surfaces of different three-dimensional object models are recovered by this triangle mesh method. The radius of the tested cylinder model can be accurately estimated from the derived maximum principle curvature. The derived minimum principle curvature...