Bezier

Performance Optimizations
- Change `wiggle_interval` to return `success` bool instead of raising an exception. This allows the implicitization approach to use it without having to use exceptions for flow-control. (Fixes [22][5].)
- Switching Fortran speedups from `f2py` to Cython (this is because `f2py` artificially limits the feature set of Fortran, i.e. user defined types)
- Moving some more code to Fortran (e.g. `bbox_line_intersect()` [`3dcf640`][11])

New Features
- Making Fortran features available outside of Python (see [Native Libraries][1])
- C headers for each Fortran module (via [`bezier.get_include()`][2])
- Cython `.pxd` declarations for all Fortran modules
- `libbezier` static library (via [`bezier.get_lib()`][3])
- Implementing [`bezier_roots()`][13] polynomial root solver for polynomials written in Bernstein basis. ([`0dd6369`][12])

Miscellany
- Getting `bezier` [published][10] in the Journal of Open Source Science (JOSS). See [review][9]. ([`e6c4536`][7] and [`975ac6b`][8])
- Updating error message for `locate()` methods and adding a note that `locate()` / `evaluate*()` are (essentially) inverses. H/T to pdknsk [36][4]
- Using Fortran-contiguous arrays in `_check_non_simple()`. ([`b06c78e`][6])
- Moving most of `Curve.subdivide()` and `Surface.subdivide()` logic into helpers. This is part of an effort to make all helpers take low-level data types rather than `Curve`s, `Surface`s, etc. ([`34515bd`][14] and [`1fc80e5`][15])
- Split `speedup.f90` into submodules `curve.f90`, `surface.f90`, etc. ([`75349b7`][16], [`dfd6bba`][17], [`7096a9d`][18], [`c326c00`][19])
- Adding `BEZIER_JOURNAL` option to `setup.py`. This stores a record of compiler commands invoked during installation. See [Native Libraries][1] for more details. ([`3d832e7`][20] and [`c64a97a`][21])

[1]: http://bezier.readthedocs.io/en/0.5.0/native-libraries.html
[2]: http://bezier.readthedocs.io/en/0.5.0/reference/bezier.html#bezier.get_include
[3]: http://bezier.readthedocs.io/en/0.5.0/reference/bezier.html#bezier.get_lib
[4]: https://github.com/dhermes/bezier/pull/36
[5]: https://github.com/dhermes/bezier/pull/22
[6]: https://github.com/dhermes/bezier/commit/b06c78e50d53bf673bcf0b71fa84b36c8df564d8
[7]: https://github.com/dhermes/bezier/commit/e6c45360f0c8412ae90d967463a14c49490d70ee
[8]: https://github.com/dhermes/bezier/commit/975ac6b1a4313db4dcdc17396d6d34561005939e
[9]: https://github.com/openjournals/joss-reviews/issues/267
[10]: http://joss.theoj.org/papers/10.21105/joss.00267
[11]: https://github.com/dhermes/bezier/commit/3dcf64090bb5874320dcde86eaf449e94278dd08
[12]: https://github.com/dhermes/bezier/commit/0dd6369b0f77e4c0cf8113f2d25812addc90482a
[13]: http://bezier.readthedocs.io/en/0.5.0/algorithm-helpers.html#bezier._implicitization.bezier_roots
[14]: https://github.com/dhermes/bezier/commit/34515bd6246f57fbb311b4089520a24e8237294a
[15]: https://github.com/dhermes/bezier/commit/1fc80e54ad1b45cb628af06e5a2100eeb9282865
[16]: https://github.com/dhermes/bezier/commit/75349b745063a9bbc623808b3f7bbf6b7641c008
[17]: https://github.com/dhermes/bezier/commit/dfd6bba303ac0a8492fac1f309086b685e52ab59
[18]: https://github.com/dhermes/bezier/commit/7096a9d646930378476e650c77d0652a48bf148a
[19]: https://github.com/dhermes/bezier/commit/c326c00a5c0ee74f9aa53c2b104ac6d4eb5c6794
[20]: https://github.com/dhermes/bezier/commit/3d832e78af2a951a642ff5860b9593abfa674ec3
[21]: https://github.com/dhermes/bezier/commit/c64a97aa5599220b927094a41de04b0c75bbec33

Performance Optimizations
- [Adding][29] Fortran [speedups][30] for many crucial computation helpers including
- intersecting line segments
- (vectorized) Horner's method for evaluating a B&xe9;zier curve at multiple parameters at once
- (vectorized) Horner's method for evaluating a B&xe9;zier surface
- computing "linearization error" (how close a curve is to a line)
- specializing a B&xe9;zier curve to a sub-interval
- using Newton's method to refine a curve-curve intersection
- [Adding][10] `_verify` switch to [`Surface.locate()`][11] and [`Curve.intersect()`][14] to selectively disable overly defensive value checking. (Making sure to use this switch during "internal" computation.)
- Making sure NumPy arrays are Fortran-contiguous as often as possible (e.g. snippets and source, via `np.asfortranarray()`). This is to avoid (and emphasize) a non-trivial overhead when passing a C-contiguous array to a Fortran function. ([`03a7242`][15], [`6064e4c`][16], [`f1804f4`][17])
- Using Horner's method in `Curve.evaluate_multi()` and `Surface.evaluate_barycentric()`, rather than inferior (sometimes non-vectorized) approaches ([`dee8181`][18], [`2611e64`][19])
- Made surface-surface intersection more resilient / lenient for corner intersections. For "nearby" intersections, parameter values can be rounded to `0` or `1`. ([`4a8458c`][25])

New Features
- [Adding][23] optional `strategy` argument (one of geometric or algebraic) to [`Surface.intersect()`][24]
- Added "algebraic" [`IntersectionStrategy`][20] via curve [implicitization][27] ([reference][28])
- Adding [`Curve.reduce_()`][21] which acts as a partial inverse to [`Curve.elevate()`][31]. It is only a complete inverse when a curve is degree-elevated, otherwise it returns the "best" reduced form (in the least squares sense).

Interface Changes
- (**Breaking change**) [Removing][5] `show` keyword from [`Curve.plot()`][2], [`Surface.plot()`][3] and [`CurvedPolygon.plot()`][4]
- [Adding][32] `color` keyword to [`Curve.plot()`][2]
- [Adding][26] `alpha` keyword to [`Curve.plot()`][2]
- (**Breaking change**) [Splitting][6] the [`Surface.evaluate_multi()`][7] method into [`Surface.evaluate_barycentric_multi()`][8] and [`Surface.evaluate_cartesian_multi()`][9]
- [Adding][22] `__dict__` helpers on `Curve`, `CurvedPolygon` and `Surface`. These are `property`s intended only for REPL use, since classes with `__slots__` no longer have a `__dict__` attribute.

Miscellany
- Adding [`IntersectionClassification`][1] to docs ([ref][5])
- [Moving][12] most plotting into a dedicated module. More importantly, importing plotting helpers at **run-time** rather at **import time**. So if computational code never plots, it won't eat the import cost of `matplotlib`. [Removing][13] `matplotlib` as a dependency.

[1]: http://bezier.readthedocs.io/en/0.4.0/algorithm-helpers.html#bezier._surface_helpers.IntersectionClassification
[2]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.curve.html#bezier.curve.Curve.plot
[3]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.surface.html#bezier.surface.Surface.plot
[4]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.curved_polygon.html#bezier.curved_polygon.CurvedPolygon.plot
[5]: https://github.com/dhermes/bezier/commit/828f4238971b12a9d494ce38387cec855d063c91
[6]: https://github.com/dhermes/bezier/commit/cea88285b8c9002a57efd88e69b5bd2ef46e7ca7
[7]: http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_multi
[8]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_barycentric_multi
[9]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_cartesian_multi
[10]: https://github.com/dhermes/bezier/commit/dcf40f4c9ed2167e96fc8f4675aeedcc2d811a0b
[11]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.surface.html#bezier.surface.Surface.locate
[12]: https://github.com/dhermes/bezier/commit/dc4d33cfcf7f9ac6e794b856dc6d76635d362922
[13]: https://github.com/dhermes/bezier/commit/064e2c5efe7fa6498d74a33798a363e2c8e0b83e
[14]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.curve.html#bezier.curve.Curve.intersect
[15]: https://github.com/dhermes/bezier/commit/03a72428c6f9d3bd3a1fac9b7f9afa615ce12d46
[16]: https://github.com/dhermes/bezier/commit/6064e4c314d8d717873d46e6ef35c0bbc9772728
[17]: https://github.com/dhermes/bezier/commit/f1804f442f190d0bc36782e940ee0b8a68c5ecd6
[18]: https://github.com/dhermes/bezier/commit/dee81813e34d5f69c52f48aa90f7c11eb4ddc3ec
[19]: https://github.com/dhermes/bezier/commit/2611e64a735e46317cce08a41270d61024705fd9
[20]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.curve.html#bezier.curve.IntersectionStrategy
[21]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.curve.html#bezier.curve.Curve.reduce_
[22]: https://github.com/dhermes/bezier/commit/f0fca088ac6f70c39f9f5af457c29e3c82f094b5
[23]: https://github.com/dhermes/bezier/commit/e72ca20f0f4ee0f6399b56805b30fe67a02aa04f
[24]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.surface.html#bezier.surface.Surface.intersect
[25]: https://github.com/dhermes/bezier/commit/4a8458c823d8acc185818f856889cff6f46300d3
[26]: https://github.com/dhermes/bezier/commit/dcbeefc25b7f5f9a1fa725dac04e81a43039f680
[27]: https://github.com/dhermes/bezier/commits/0.4.0/src/bezier/_implicitization.py
[28]: https://en.wikipedia.org/wiki/Resultant
[29]: https://github.com/dhermes/bezier/commits/0.4.0/src/bezier/speedup.f90
[30]: https://github.com/dhermes/bezier/blob/0.4.0/src/bezier/speedup.f90
[31]: http://bezier.readthedocs.io/en/0.4.0/reference/bezier.curve.html#bezier.curve.Curve.elevate
[32]: https://github.com/dhermes/bezier/commit/ce838a2aaef2281f06603d1c76324a3aa8289cf9

Performance Optimizations
- Adding `__slots__` for all classes
- Removing all usage of `property` calls from internal callers (to avoid function call overhead)
- Avoiding un-necessary data copying, e.g. `nodes[[0], :]` creates a copy but

python
nodes[0, :].reshape((1, 2))


does not ([more details](https://docs.scipy.org/doc/numpy-1.6.0/reference/arrays.indexing.html#advanced-indexing))
- Adding `_verify` switches to selectively disable overly defensive value checking. Added to [`CurvedPolygon`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.curved_polygon.html#bezier.curved_polygon.CurvedPolygon) constructor, [`Surface.evaluate_barycentric()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_barycentric), [`Surface.evaluate_cartesian()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_cartesian), [`Surface.evaluate_multi()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_multi) and [`Surface.intersect()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.intersect). Internal callers with already verified data now skip verification steps
- [Bailing out early](https://github.com/dhermes/bezier/commit/db816eb5a748bb997adcc2d7d9008638e22a824c) if surface bounding boxes are disjoint in [`Surface.intersect()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.intersect)

Breaking Changes
- Requiring `degree` in [`Curve`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.curve.html#bezier.curve.Curve) and [`Surface`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface) constructors, but adding [`Curve.from_nodes()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.curve.html#bezier.curve.Curve.from_nodes) and [`Surface.from_nodes()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.from_nodes) factories to accept nodes only (computing the degree in the constructor every time is a waste of flops, especially if the caller knows the degree)
- [Removing](https://github.com/dhermes/bezier/commit/3393b9010c26b55a9c29afc2702426bb179b85a1) public [`Curve.copy()`](http://bezier.readthedocs.io/en/0.2.1/reference/bezier.curve.html#bezier.curve.Curve.copy) and [`Surface.copy()`](http://bezier.readthedocs.io/en/0.2.1/reference/bezier.surface.html#bezier.surface.Surface.copy)
- [Removing](https://github.com/dhermes/bezier/commit/3393b9010c26b55a9c29afc2702426bb179b85a1) custom equality checks for [`Curve`](http://bezier.readthedocs.io/en/0.2.1/reference/bezier.curve.html#bezier.curve.Curve.__eq__) and [`Surface`](http://bezier.readthedocs.io/en/0.2.1/reference/bezier.surface.html#bezier.surface.Surface.__eq__) objects. The previous implementation did not factor in all relevant values
- Returning `1xD` arrays [instead of flattened](https://github.com/dhermes/bezier/commit/b5e5b327594c6143956ed98703f596ff82b7501a) `D`-dimensional 1D arrays from [`Curve.evaluate()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.curve.html#bezier.curve.Curve.evaluate), [`Surface.evaluate_barycentric()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_barycentric), [`Surface.evaluate_cartesian()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.evaluate_cartesian), and related helpers
- Renaming [`Intersection.left/right`](http://bezier.readthedocs.io/en/0.2.1/algorithm-helpers.html#bezier._intersection_helpers.Intersection.left) as [`first/second`](http://bezier.readthedocs.io/en/0.3.0/algorithm-helpers.html#bezier._intersection_helpers.Intersection.first) (They were poorly named originally, since "left" and "right" were in reference to where they were used **in code**, not geometry. This class is not part of the public interface, but it is documented.)

Bug Fixes
- Handling cases where one corner of a surface touches another but their interiors don't intersect (in [`Surface.intersect()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.intersect)). Adding `ignored_corner` classification to handle these curve-curve intersecions that don't contribute to a surface-surface intersection
- Throwing exception in [`Curve.locate()`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.curve.html#bezier.curve.Curve.locate) when the subdivided intervals are very far apart (13)
- Improving [`Surface.is_valid`](http://bezier.readthedocs.io/en/0.3.0/reference/bezier.surface.html#bezier.surface.Surface.is_valid) by considering the signs of the Jacobian determinant at corner nodes (12)

Miscellany
- Adding possible strategy to avoid linear convergence in [`newton_refine()`](http://bezier.readthedocs.io/en/0.3.0/algorithm-helpers.html#bezier._intersection_helpers.newton_refine)
- Adding AppVeyor configuration to make sure there are no Windows issues, testing exclusively with `conda` install
- Updating generated images with `matplotlib` 2.0

- Added [`Curve.locate()`](http://bezier.readthedocs.io/en/0.2.1/reference/bezier.curve.html#bezier.curve.Curve.locate) and [`_curve_helpers.newton_refine()`](http://bezier.readthedocs.io/en/0.2.1/algorithm-helpers.html#bezier._curve_helpers.newton_refine) helper
- Adding optional `color` to [`Surface.plot()`](http://bezier.readthedocs.io/en/0.2.1/reference/bezier.surface.html#bezier.surface.Surface.plot)
- Adding [`Surface.elevate()`](http://bezier.readthedocs.io/en/0.2.1/reference/bezier.surface.html#bezier.surface.Surface.elevate) for degree elevation
- Fixing nodes defining the [self-intersecting curve](http://bezier.readthedocs.io/en/0.2.1/curve-curve-intersection.html#detecting-self-intersections) in `curve-curve-intersection` (no code in `bezier` was broken / fixed, just "bad" docs)
- Allow wiggle outside of `[0, 1]` when intersecting linearizations in `from_linearized()`
- Collapsing almost-same parameter values in `intersect_one_round()` (via `from_linearized()`). Previously checked for bitwise equality and relied on checking values at the boundary of a subdivided interval
- Adding non-public `bezier._plot_helpers` module

- **Primary feature**: [`Surface.intersect()`](http://bezier.readthedocs.io/en/0.2.0/reference/bezier.surface.html#bezier.surface.Surface.intersect) added
- To support intersection, needed [`CurvedPolygon`](http://bezier.readthedocs.io/en/0.2.0/reference/bezier.curved_polygon.html#bezier.curved_polygon.CurvedPolygon), i.e. an object defined only by its curved sides (whereas a `Surface` may have interior control points)
- [`Curve.specialize`](http://bezier.readthedocs.io/en/0.2.0/reference/bezier.curve.html#bezier.curve.Curve.specialize) for chopping a `Curve` at arbitrary parameter values (this is also used in surface-surface intersection)
- Added images to most documented functions and methods to illustrate the concept at hand. For example
[`classify_intersection`](http://bezier.readthedocs.io/en/0.2.0/algorithm-helpers.html#bezier._surface_helpers.classify_intersection) has **seven** images to enumerate all of the possible cases covered in the algorithm.
- Added [`Surface.locate()`](http://bezier.readthedocs.io/en/0.2.0/reference/bezier.surface.html#bezier.surface.Surface.locate), made possible by [`newton_refine`](http://bezier.readthedocs.io/en/0.2.0/algorithm-helpers.html#bezier._surface_helpers.newton_refine)
- Added [Algorithm Helpers](http://bezier.readthedocs.io/en/0.2.0/algorithm-helpers.html) doc to try to explain some of the core algorithms at work (not all are documented yet). Some of this content was previously documented in the `bezier.curve` module, but was moved. Since, documentation has been added for `get_curvature`, `newton_refine` (for surfaces), `classify_intersection` (to determine how two curves interact while intersecting) and for some helper classes.
- Added `Surface.base_x`, `Surface.base_y` and `Surface.width` [properties](http://bezier.readthedocs.io/en/0.2.0/reference/bezier.surface.html#bezier.surface.Surface.width) to allow tracking a sub-surface during the subdivision process (this is an analogue to the `Curve.start` and `Curve.end` [properties](http://bezier.readthedocs.io/en/0.2.0/reference/bezier.curve.html#bezier.curve.Curve.start))
- Added `Curve.edge_index`, `Curve.next_edge` and `Curve.previous_edge` [properties](http://bezier.readthedocs.io/en/0.2.0/reference/bezier.curve.html#bezier.curve.Curve.edge_index) to allow tracking when curves are actually the sides of a `Surface`

Changes:
- Adding [`Curve.elevate()`](http://bezier.readthedocs.io/en/0.1.1/reference/bezier.curve.html#bezier.curve.Curve.elevate) for degree elevation
- Upgrading curve-curve intersection algorithm to ignore parallel line segments that don't meet (rather than throwing `NotImplementedError`)
- Making [`segment_intersection()`](http://bezier.readthedocs.io/en/0.1.1/reference/bezier.curve.html#bezier._intersection_helpers.segment_intersection) return a `success` bool instead of raising `NotImplementedError` on failure
- Updating docs for [`newton_refine()`](http://bezier.readthedocs.io/en/0.1.1/reference/bezier.curve.html#bezier._intersection_helpers.newton_refine) with two examples and making [`parallel_different()`](http://bezier.readthedocs.io/en/0.1.1/reference/bezier.curve.html#bezier._intersection_helpers.parallel_different) a publicly documented function (as a partner to `segment_intersection()`)
- Adding some more examples / failures to `curve-curve-intersection` [doc](http://bezier.readthedocs.io/en/0.1.1/curve-curve-intersection.html)