Sentence examples for representation of the curve from inspiring English sources

where is any intrinsic quantity and does not depend on parameters, is the normal vector, and, as the implicit representation of the curve, is defined as (2).

Introduce the polar coordinates r = |z| and ϑ = argz, and then the parametric representation of the curve just amounts to the following: r = ( R θ ) - δ, ϑ = R θ, Open image in new window.

The parametric representation of the curve is then directly obtained.

The Euclidean curvature as a function of arc-length provides an invariant representation of the curve in the Euclidean plane.

The derivatives required are easily computed from the spline representation of the curve but are also readily available from other smoothing techniques.

This value was used because it gave the best representation of the curve for cardiac event risk and was the best estimate to carry forward over the long-term model.

The latter offered complex textural sweetness, though the idea behind it – a musical representation of the curves in a Bridget Riley painting – dominated the music and ultimately stymied it.

Thus, the given curves unify the representation of the curves for interpolating and approximating the control polygon.

Similar conditions can be derived for higher values of n, simply by differentiating the composition of the parametric representations of the curve and the implicitly defined surface through it with respect to the curve parameter.

Given a parameterization of an algebraic rational curve in a projective space of arbitrary dimension, we introduce and study a new implicit representation of this curve which consists in the locus where the rank of a single matrix drops.

Toward that end, we use non-parametric representations of the curves.