Curvesimilarities

Added

**Utility (`curvesimilarities.util`)**

- Polyline sampling function `sample_polyline()`.
- Polyline refining function `refine_polyline()`.
- Parameter space function `parameter_space()`.
- Function `curvespace_path()` which converts parameter space path to curve space point pairs.

Changed

**Integral Fréchet distance (`curvesimilarities.integfrechet`)**

- Squared Euclidean distance is used instead of Euclidean distance.

Removed

**Average Fréchet distance (`curvesimilarities.averagefrechet`)**

- Average Fréchet distance `afd()` and its optimal warping path `afd_owp()`.

Added

**Fréchet distance (`curvesimilarities.frechet`)**

- `fd()` now accepts `rel_tol` and `abs_tol` arguments for its parametric search tolerance.

Changed

- Every curve similarity function now returns the similarity in `float` type.

Fixed

**Fréchet distance (`curvesimilarities.frechet`)**

- Convergence failure of `fd()` during its parametric search.

Fixed

**Fréchet distance (`curvesimilarities.frechet`)**

- Degenerate case during computing the XY-monotone axis of level set for `ifd()` and its variants.

Fixed

**Integral Fréchet distance (`curvesimilarities.integfrechet`)**

- Bug during computing `ifd_owp()` and its variants.

Fixed

**Integral Fréchet distance (`curvesimilarities.integfrechet`)**

- Another degenerate case in line-line integration is now dealt with.

Added

**Average Fréchet distance (`curvesimilarities.averagefrechet`)**

- Average Fréchet distance `afd()` and its optimal warping path `afd_owp()`.
- Quadratic average Fréchet distance `qafd()` and its optimal warping path `qafd_owp()`.

**Dynamic time warping (`curvesimilarities.dtw`)**

- Squared dynamic time warping distance `sdtw()` and its optimal warping path `sdtw_owp()`.

Changed

**Dynamic time warping (`curvesimilarities.dtw`)**

- `dtw_owp()` now returns both the distance and the optimal warping path.

Removed

**Dynamic time warping (`curvesimilarities.dtw`)**

- `dtw_acm()` is removed.

Fixed

- Curves degenerated into a point are now dealt with.