Sentence examples for analytical shapes from inspiring English sources

Such curves provide a valuable alternative to the rational Bézier model, because they can deal with both free form curves and remarkable analytical shapes, including the circle, cycloid and helix.

In this work we construct three novel families of approximating subdivision schemes that generate piecewise exponential polynomials and we show how to convert these into interpolating schemes of great interest in curve design for their ability to reproduce important analytical shapes and to provide highly smooth limit curves with a controllable tension.

Then, in addition to the straight lines, it was used to establish analytical shapes such as circles and ellipses in the 2D images.

In addition to the control points, other advantages of using this model is that it can offer a common mathematical form for standard analytical shapes and also provide the flexibility to design a large variety of parametric shapes.

Such small differences may be caused by statistical fluctuations and small approximations in attenuation correction used in reconstructions of simulated tomographic data (voxelized attenuation maps were used in reconstructions, while in GATE analytical shapes are used).

The basic principle employed to detect such analytical shapes is similar to the one used to determine straight lines, and is based on the directional structuring between the parameter definition in the Hough space and the border points in the image space.

An analytical shape sensitivity analysis method with respect to positions and shapes of components is developed.

An optimization framework, which couples an analytical shape parameterization to the flow/adjoint solver and to algorithms for constrained optimization, is tested on airfoil design cases involving transonic as well as supersonic flows.

An n-dimensional binary image I being a subset of (mathbb {R}^{n}), an analytical shape may be defined by a parametric equation: (mathcal {C}^{mathbf {a_{0}}} = left {mathbf {x} in mathbb {R}^{n}; phi (mathbf {x},mathbf {a_{0}}) = 0right }), where x is the spatial variable, and (mathbf {a_{0}} in mathbb {R}^{m}) is a constant parameter.

For beams with a linear relationship between the cross-sectional moment of inertia and area optimal shapes of analytical form are derived.

By using analytical mode shapes as the interpolating functions for both displacements and stresses on the reference edges of a plate, a wave element is formulated for use in the boundary element method to study Lamb wave propagation and interaction in plates, to achieve both accuracy and computational efficiency.