DiscretePath

Sample the continuous function f on the closed interval I = [0.0, 1.0].

The sampled path π satisfies the following conditions:

• π starts with f(0.0): V and ends with f(1.0): V
• each point v: V of π is a "sample" of f, in a sense that there is t_v: Double in the closed interval I such that f(t_v) = v. Moreover, the sampling is done in an increasing order, meaning that if v appears before w in π, then t_v < t_w.
• two consecutive v: V and w: V of π are "sufficiently close" samples, in a sense that
  • |t_v - w_v| < maximumDomainGap
  • distance(v, w) < maximumRangeGap

This function is undefined for f which is not continuous (with respect to the metric induced by the norm structure of V; see NormedVectorSpace).

A wrapper for sampleContinuous that operates on a normed vector space over Double.

The constant path containing just one zero vector.

The default semigroup instance that concats paths by rebasing.

Notice that this structure

• is associative
• is only unital if you identify x concatRebase zero with x, where the former has an extra point.
• does not admit inverses. Concatenating a reverse path does not erase the original path.