The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely character...

We aimed to analyze the shape of the glucose, insulin, and C-peptide curves during a 3-h oral glucose tolerance test (OGTT). Another aim was defining an index of shape taking into account the whole OGTT pattern. Five-hundred ninety-two OGTT curves were analyzed, mainly from women with former gestational diabetes, with glycemic concentrations characterized by normal glucose tolerance (n = 411), ...

The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely character...

We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape features in a visually intuitive manner. This method have implications in shape analysis as well as in investigating how the brain perceives and generates curv...

In this paper, we describe an algorithm to measure the shape complexity for discrete approximations of planar curves in 2D images and manifold surfaces for 3D triangle meshes. We base our algorithm on shape curvature, and thus we compute shape information as the entropy of curvature. We present definitions to estimate curvature for both discrete curves and surfaces and then formulate our theory...

Few computer implementations of shape grammars have been written that are applicable to curved shapes. The reason for this is that underlying representations of curves do not lend themselves to providing a unique description of curved shapes. Such a representation is essential for shape algorithms. This paper explains the problems posed in representing curves for shape grammar implementation. T...

The shape features of planar trigonometric Bézier curves with two shape parameters are analyzed. The necessary and sufficient conditions are derived for these curves having one or two inflection points, a loop or a cusp, or be locally or globally convex. All conditions are completely characterized by the relative position of the control polygon’s side vectors. Furthermore we discussed the influ...

Analyzing geometry of sulcal curves on the human cortical surface requires a shape representation invariant to Euclidean motion. We present a novel shape representation that characterizes the shape of a curve in terms of a coordinate system based on the eigensystem of the anisotropic Helmholtz equation. This representation has many desirable properties: stability, uniqueness and invariance to s...

We address the problem of how to perform prescribed shape modification of NURBS curves merely by the modification of the weight of some of their control points. As is known, NURBS curves can be considered as central projections of nonrational B-spline curves. Making use of the property that there is an infinite number of nonrational B-spline curves the central projection of which is a given NUR...

The universal form of univariate Quasi-Bézier basis functions with multiple shape parameters and a series of corresponding QuasiBézier curveswere constructed step-by-step in this paper, using themethod of undetermined coefficients.The series ofQuasi-Bézier curves had geometric and affine invariability, convex hull property, symmetry, interpolation at the endpoints and tangent edges at the endpo...