| In this paper, we consider path planning for a car-like vehicle. We deene a new problem adding to the classical one a continuous-curvature constraint and a bound on the curvature derivative, so as to reeect the fact that a car-like vehicle can only reorient its front wheels with a nite velocity. As optimal solutions can contain an innnity of pieces, we propose a solution to compute Sub-optima...

Elastic objects under confinement are common in mechanics and biology. Examples include mitochondria and chromosomes, for which conformation and function are strongly determined by confining forces. When elastic objects grow in a confined space, minimization of elastic energy creates a complex spatial configuration and force network. To simulate a two-dimensional ring growing within a rigid cir...

‎let $m^n$ be an $n(ngeq 3)$-dimensional complete connected and‎ ‎oriented spacelike hypersurface in a de sitter space or an anti-de‎ ‎sitter space‎, ‎$s$ and $k$ be the squared norm of the second‎ ‎fundamental form and gauss-kronecker curvature of $m^n$‎. ‎if $s$ or‎ ‎$k$ is constant‎, ‎nonzero and $m^n$ has two distinct principal‎ ‎curvatures one of which is simple‎, ‎we obtain some‎ ‎charact...

In this paper, we present a novel approach for three-dimensional face recognition by extracting the curvature maps from range images. There are four types of curvature maps: Gaussian, Mean, Maximum and Minimum curvature maps. These curvature maps are used as a feature for 3D face recognition purpose. The dimension of these feature vectors is reduced using Singular Value Decomposition (SVD) tech...

Saccade curvature is becoming a popular measure for detecting the presence of competing saccadic motor programs. Several different methods of quantifying saccade curvature have been employed. In the present study, we compared these metrics with each other and with novel measures based on curve fitting. Initial deviation metrics were only moderately associated with the more widely used metric of...

We describe an algorithm for solving an important geometric problem arising in computer-aided manufacturing. When machining a pocket in a solid piece of material such as steel using a rough tool in a milling machine, sharp convex corners of the pocket cannot be done properly, but have to be left for finer tools that are more expensive to use. We want to determine a tool path that maximizes the ...

Unbranched tendrils arising from the fifth node of light grown Alaska pea plants were found to reach maturity at the age of 10 days. Such tendrils, when stroked, coiled rapidly. They remained maximally irritable for at least 3 days.Coiling was separable into 2 components, curvature (measured in degrees) and elongation. Coiling reached a maximum from one-half to 3 hours after tactile stimulation...

In a space of planar curves with prescribed end points and prescribed length, suppose that a weighted L∞-norm of the curvature is to be minimized. If no other constraints are given, then this variational problem is very similar to a problem that was solved by E. Schmidt with geometric considerations. Using tools from the calculus of variations, we obtain a different approach that permits a gene...