Morphing

A morphing is an encoding of a "matching" between two curves. It is the output of the various Frechet distance computation functions. The package provides some basic geometric types in the cg submodule.

Types

FrechetDist.Morphing — Type
Morphing

Encoding of a moprhing (i.e., matching) between two polygonal cuves.

Functions

FrechetDist.Morphing_monotonize — Function
Morphing_monotonize

Turns a morphing into a monotone morphing, by simply not going back, staying in place if necessary.

FrechetDist.Morphing_verify_valid — Function
Morphing_verify_valid

Does some minimal checks that the morphing is valid. Speciifcally, check the times stemps of the events are valid.

FrechetDist.Morphing_combine — Function
Morphing_combine

Gets two morphings u, v (i.e., two parameterizations) and combine them into a single morphing u(v(.)).

For example, if u: γ → δ and v: δ → ξ, then the returned morphing is u(v(⋅)): γ → ξ.

FrechetDist.Morphing_extract_prm — Function
Morphing_extract_prm

A parameterization is a polygonal curve that starts at (0,0) and
end at (m,n).  The polygonal curve either have positive slope edge,
or vertical or horizontal edges. It can be thought of as a
piecewise linear function from [0,m] to [0,n]. Here m and n are the
lengths of the two given polygons of P and Q, respectively.
FrechetDist.Morphing_as_polygons — Function
Morphing_as_polygons

Turns the morphing matching into a "true" matching, by creating two polygons that their edges are directly matched. The output polygons P and Q will definitely have reapeated points.

FrechetDist.Morphing_extract_vertex_radii — Function
Morphing_extract_vertex_radii

Computes for each polygon vertex, the length of the longest edge
in the matching attached ot it. It is a cheap upper bound on the
local Frechet distance for each vertex (and implicitly the
attached edge).

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