Sentence examples for by a control polygon from inspiring English sources

A P-curve is defined by a control polygon; it forms a single C∞ continuous segment with endpoint interpolation.

Computer Aided Geometric Design 15 (9), 879 891] presented a remarkable family of Bézier curves, characterized by a control polygon with constant angle at each vertex and constant ratio between lengths of consecutive edges.

The computed values define a control polygon in each step.

On this basis a new direct method for the design of Bézier curves is described that allows to adapt the control polygon as a whole by moving a point of the associated Bézier curve.

A scheme to specify planar C2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the "ordinary" C2 cubic B-spline curve serves as a reference for the shape of the PH spline.

We present a geometric condition on the control polygon which is equivalent to the injectivity of rational Bézier curve with this control polygon for all possible choices of weights.

B-splines preserve the shape that a spline has the same shape as its control polygon or more precisely.

(iii) B-splines preserve the shape that a spline has the same shape as its control polygon or more precisely.  .

The first is based on the satisfaction of a system of algebraic constraints by the control-polygon legs, and the second uses the fact that numerical quadrature rules that are exact for polynomials of a certain maximum degree generate arc length estimates for PH curves exhibiting a sharp saturation as the number of sample points is increased.

We give an elegant geometric characterization of their control polygons.

The target zone is shown by a yellow polygon.