It is well known that the sufficient family of time-optimal paths for both Dubins’ as well as Reeds-Shepp’s car models consist of the concatenation of circular arcs with maximum curvature and straight line segments, all tangentially connected. These time-optimal solutions suffer from some drawbacks. Their discontinuous curvature profile, together with the wear and impairment on the control equi...

Background: Scoliosis is a health problem that causes a side-to-side curvature in the spine. The curvature may have an “S” or “C” shape. To evaluate scoliosis, the Cobb angle has been commonly used. However, digital image processing allows the Cobb angle to be obtained easily and quickly, several researchers have determined that Cobb angle contains high variations (errors) in the measurements. ...

Fin ray structure in ray-finned fishes (Actinopterygii) largely defines fin function. Fin rays convert the muscle activity at the base of the fin to shape changes throughout the external fin web. Despite their critical functional significance, very little is known about the relationship between form and function in this key vertebrate structure. In this study we demonstrate that morphological s...

We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence. We follow [4] in defi...

This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computationa...

The relationship between cardiac output (CardOut) and oxygen consumption (VO2) during exercise has generally been assumed to be linear. To test this assumption, we studied 72 healthy subjects using a graded, 2-min cycle-ergometry exercise test to maximum while measuring gas exchange continuously and CardOut at the end of each stage, the latter using an open-circuit gas technique. Data for VO2 a...

This article describes a natural landmark navigation algorithm for autonomous vehicles operating in relatively unstructured environments. The algorithm employs points of maximum curvature, extracted from laser scan data, as point landmarks in an extended Kalman filter. A curvature scale space algorithm is developed to locate points of maximum curvature. The location of these points is invariant...

There is a need for highly redundant manipulators to work in complex, cluttered environments. We explore kinematics and path planning for highly redundant manipulators by means of a continuous manipulator model, which captures the macroscopic shape of highly redundant manipulators. A path for the continuous manipulator model can be found by nding a smooth path for its end-e ector under a maximu...

There is a need for highly redundant manipulators to work in complex, cluttered environments. We explore kinematics and path planning for highly redundant manipulators by means of a continuous manipulator model, which captures the macroscopic shape of highly redundant manipulators. A path for the continuous manipulator model can be found by nding a smooth path for its end-e ector under a maximu...

We present a meshfree method for the curvature estimation of membrane networks based on the Local Maximum Entropy approach recently presented in [1]. A continuum regularization of the network is carried out by balancing the maximization of the information entropy corresponding to the nodal data, with the minimization of the total width of the shape functions. The accuracy and convergence proper...