## [2026/04/11 — version 5.06c]

### Changed
- **triangle**
  - Changed the order of returned points for `reflections` and `projections`:
    (1 → pa, 2 → pb, 3 → pc).
  - Added methods returning directly the vertices of special triangles:
    - `orthic_points()`
    - `medial_points()`
    - `tangential_points()`
- **circle**
  - Modification of the `point` method.  Added an optional point parameter to specify the reference point on the circle.

### Documentation
  - Reorganized the method descriptions in the **point** class, especially for utility   methods and the `rotation` method.
  - Fixed an incorrect example of the `PPP` method in the **point** class.
  - Section 16.4.1 (Parabola construction): corrected `bisector of angle HMF` (instead   of `angle HFT`).
  - Section 7.3 (Use of Trilinear Coordinates): corrected `projection` → `projections`   in the code.
    Thanks to :SwiftWu for these remarks.
  - Added documentation for the `print` method.

## [2026/03/14 — version 5.05c]

### Added
- **triangle**
   - methods `isotomic`, `complement`, `anticomplement`
   - function triangle:ellipse_inscribed({brianchon/center/focus})
   - function triangle:cevian_point(p, q, eps)

- **conics**
   - function EL_five_points(z1,z2,z3,z4,z5)

### Documentation
- **conic**
   - documentation clarification about constructor usage and helper functions


## [2026/03/11 — version 5.04c]

   ### Added

   - **triangle**
     - Added new attributes: `ma`, `mb`, `mc`, `ha`, `hb`, `hc`, `ia`, `ib`, `ic`
       - `ma`, `mb`, `mc`: midpoints of the sides
       - `ha`, `hb`, `hc`: feet of the altitudes
       - `ia`, `ib`, `ic`: feet of the internal angle bisectors

     - Added method: `triangle:reflections(pt)`

   ### Changed

   - **triangle**
   - Renamed method: `projection(pt)` -> `projections(pt)`

   ### Notes
   - **triangle**
      - `projections(pt)` and `reflections(pt)` apply to an arbitrary point.
      - `projection()` and `reflection()` apply to the triangle vertices.


## [2026/03/11 — version 5.04c]

   ### Added

   - **triangle**
     - Added new attributes: `ma`, `mb`, `mc`, `ha`, `hb`, `hc`, `ia`, `ib`, `ic`
       - `ma`, `mb`, `mc`: midpoints of the sides
       - `ha`, `hb`, `hc`: feet of the altitudes
       - `ia`, `ib`, `ic`: feet of the internal angle bisectors

     - Added method: `triangle:reflections(pt)`

   ### Changed

   - **triangle**
   - Renamed method: `projection(pt)` -> `projections(pt)`

   ### Notes
   - **triangle**
      - `projections(pt)` and `reflections(pt)` apply to an arbitrary point.
      - `projection()` and `reflection()` apply to the triangle vertices.


## [2026/03/04 — version 5.03c]

### Changed

- **path**
  - `add_point` now accepts either a `point` object or a string
    representing coordinates (e.g. `"(2,3)"`, `"(1e-5,0)"`).
  - String arguments are automatically parsed using
    `utils.parse_point`.
  - Improves API flexibility while preserving internal
    TikZ-formatted storage.

- **utils**
  - Clarified and documented support for scientific notation
    in `parse_point` (e.g. `1e-5`, `2E3`).
  - Improved documentation of `format_number`,
    `checknumber`, and `to_decimal_string`.
  - Reinforced consistent fixed-decimal formatting
    for TikZ output.

- **tkz-elements.sty**
  - Removed the `tkzelements` environment.

- **point**
  - Unified approximate equality and geometric identity.
  - `__eq` now uses the same Euclidean proximity criterion as `identity`.
  - Removed coordinate-wise comparison in favor of a rotation-invariant
    distance test.
  - Centralized comparison logic for improved numerical consistency.

- **triangle**
  - Added `radical_circle`: the circle orthogonal to the three excentral circles.
  - Added `the_apollonius_center` and `the_apollonius_circle`.
  - `triangle.feuerbach` is now defined as `triangle.euler_circle()`.

### Documentation

- Improved documentation of `\tkzDrawCoordinates`.
- Explained its direct mapping to TikZ `plot coordinates`.
- Clarified that a Lua `path` is a discrete computational object
  rendered as an explicit polygonal chain.
- Emphasized the design principle:

  *Lua computes — TikZ draws.*

- Clarified terminology:
  - **mediator** refers to the **perpendicular bisector** of a segment.


## [2026/02/20 — version 5.02c]

### Added

#### **path**
- Added method `scale` (anisotropic scaling).

#### **fct**
- Added methods `half_tangents` and `tangent`.
- Tangents now return **unit direction points** (instead of `line` objects).
- Fully compatible with `set_scale`.
- Unified implementation based on coordinate generation.

---

### Changed

#### **path**
- In `homothety`, the center argument is now optional.

#### **fct** and **pfct**
- Removed graph-related drawing macros:
  `\tkzDrawPointOnGraph`, `\tkzDrawPointsOnGraph`,
  `\tkzDrawPointOnParamGraph`, and `\tkzDrawPointsOnParamGraph`.

  These macros were incompatible with `set_scale` and conflicted
  with the package design principle: computations must be
  performed in Lua, while drawing is delegated to TikZ or
  `\tkzDrawPoints`.

#### **tkz-elements.sty**
- Cleanup and internal corrections.
- Simplified the Lua–TikZ bridge layer.

## [2026/02/17 — version 5.00c]

### Docs
- Major Documentation Restructuring
- Global Reorganization
     The documentation is now structured into **four coherent parts**:

     1.  **Geometry Core**
     2.  **Algebra and Tools**
     3.  **Lua and Integration**
     4.  **Mathematical and Computational Foundations**

     This restructuring improves conceptual clarity and clearly separates
     geometric theory from implementation details.

- New Sections
     -   Added subsection **"Special Characters and Catcodes"**
     -   Added new section:
     -   **Computational Model and Geometric Engine**

### Added
- **line**
      -   Added method `where_on_line`.
-   New Classes
      -   Added class `fct` (function)
      -   Added class `pfct` (parametric function)
      - Standard tables introduced:
             -   `F` → functions
             -   `PF` → parametric functions
      -   Added class `list_point`

### Changed
-  Unified Geometric Position Model
     - A major harmonization of geometric relation methods has been introduced.
- Standardized Return Values

   All geometric position methods now consistently return:
   -   `"ON"`, `"IN"`, `"OUT"`
   -   or relation-specific classifications (e.g. `"TANGENT"`,
       `"DISJOINT"`, etc.)
   Boolean wrappers remain available for backward compatibility.

- **line** New & Updated Methods
     -   `line:position(pt)`\ → Returns `"ON"` or `"OUT"`.
     -   `line:in_out(pt)`\  → Boolean wrapper of `position`.
     -   `line:path(n)`\  → Parameter `n` is now documented.

- **circle**
    -  `circle:position(obj)` now accepts **generic objects**:
    -   Relation names are now consistently uppercase:
        - `point`      `IN`, `ON`, `OUT`
        - `line`       `DISJOINT`, `TANGENT`, `INTERSECT`
        -  `circle`     Extended circle--circle classification

- **Triangle**
    -  `on_triangle`
    -   New Attributes
         -   `alpha_` , `beta_`,  `gamma_`,  `orientation`,  `cross`

- **angle**  Major development and stabilization.
      -   `value` and `deg` are now **attributes**\ (no longer methods).

- **Path System**
      -   `path:count()` is now documented.
      -   `tkzSetCountFromPath` is now documented.
      -   Improved integration between `list_point` and `path`.

###  New Macros (Graph Support)

- For `fct` and `pfct`:

     -   `\tkzDrawPointOnGraph`
     -   `\tkzDrawPointsOnGraph`
     -    `\tkzDrawPointOnParamGraph`
     -    `\tkzDrawPointsOnParamGraph`

------------------------------------------------------------------------

## [2026/01/25 — version 4.50c]
### Added
- **angle**
  - New class `angle` (experimental):
     provides a dedicated object for oriented and non-oriented angles.
     This class is experimental and not yet fully integrated into all
     parts of the package.
- **list_point**
  - New class `list_point` (experimental):
    container class for ordered collections of points.
    This class is experimental and not yet fully integrated into the
     whole tkz-elements ecosystem.
- **quadrilateral**
   - Added is_convex and corrected area computation in quadrilateral.
- **conic**
   - Added method conic:get(i).
- **point**
   - Added new midpoint helper functions in point:
      - midpoints_chain_(...)
      - midpoints_cycle_(...)
- **matrix**
    -  Added matrix:gauss_jordan and matrix:rank (documentation pending).

### Removed
- Removed alternative and ambiguous definitions:
    - circle:radius(center, radius)
- Deprecated circle constructors in favor of explicit factories:
    - from_radius
    - from_diameter
- Removed obsolete triangle area computation based on circular formulas.

### Fixed
- Fixed a bug in `conic:common_tangent` (`E2 = CO.E2`).
- Fixed incorrect area formula in `circle:area`
  (previously `0.5 * tkz.tau * radius^2`).
- Fixed several bugs in the `circle`, `line`, and `point` classes.
- Fixed a bug in `regular_polygon:side`.
- Fixed `get_points` for ellipses (method no longer applicable).
- Fixed `line_position_(c, r, a, b, EPS)` behavior.
- Fixed issues related to orthogonal constructions in `tkz` (orthopole).
- Improved tkz.parabola.
### Changed
- Replaced `matrix:identity` by `matrix.identity`.
- Rewritten `triangle:get_angle`.
- Changed `orthogonal_circle_through_` implementation.
- Renamed projection-based constructions:
- `proj` → `apothem_foot` in `regular_polygon` and `square`.
- Defined `apothem` as an alias for `inradius`.
- Changed `square:side` into `square.from_side`.
- Changed `square:rotation` into `square.by_rotation`.
- Updated square construction from a line
- `iscyclic` now is `is_cyclic` in quadrilateral.

### Todo
- Clarify and extend common tangent computations for conics.

## [2026/01/22 — version 4.45c]

### Changed
- **tkz-elements.sty**
  - Replaced `luatexluaescapestring` with `luaescapestring`.

- **line**
  -  Simplification of the method `LLL`

### Documentation
- Corrected the example related to the radical center.
- Improved the documentation of the `radical center` and the `radical circle`.
- Added clarifications concerning the `mini` option of `tkz-euclide`, in particular its interaction with
  the `\tkzCompass` macro and the `show` option.
- Removed several sections (`examples`, `theorems`, and `apollonius`) in order to streamline the documentation.
  These materials are now gathered in a separate document entitled *Euclidean Geometry*, available on
  my website: `https://altermundus.fr`.
- Correction of Archimedes Spiral example.

## [2025/12/09 — version 4.44c]

### Added
- **triangle**
  - New methods: `feuerbach_apollonius_k181` and `feuerbach_apollonius`.
  - Kimberling point **#181** added (Apollonius point associated with the Feuerbach configuration).

- **circle**
  - Addition of several special-case handlers inside the `CCC` method.

- **vector**
  - Two new attributes: `dx` and `dy`.
  - New methods: `is_zero`, `is_parallel`, `is_orthogonal`, `dot`, `cross`,
    `angle_to`, `rotate`, `orthogonal`, and `get`.

- **tkz**
  - New constants:
    - `tkz.maxdimen_pt = 16383.99999`
    - `tkz.max_coord_cm = tkz.maxdimen_pt * tkz.pt`  (≈ 575.8 cm)
    - `tkz.max_coord_safe = 0.9 * tkz.max_coord_cm`  (≈ 518 cm)

### Changed
- **tkz-elements.sty**
  - Improved handling of `\tkzGetNodes`: only names of points ending in *p* or *pp* are transformed; all others are preserved.
    The macro now calls the Lua function `tkz.GetNodes`.
  - Update of the `vector` class implementation.
  - Update of `tkz.GetNodes`: coordinate checking has been added; when a coordinate exceeds the safe limit (≈ 518 cm), the
    corresponding node is placed at `(0,0)` and a warning is written to the `.log` file.

### Docs
- Restoration of the *Overview* and *Contents* sections.
- Additions and refinements in the documentation of the `vector` class.
- Correction of the example on **Soddy circles**.


## [2025/11/24 version 4.42c]

### Added
- **angle**
  - New class `angle` (not yet connected to the others).
    The identifier `"A"` is used internally to store objects of type `angle`.

- **circle**
  - Addition of `CCL`.
  - New method `similitude` with optional argument `"internal"` or `"external"`.

- **tkz**
  - New angle-related functions, all accepting an optional EPS argument to adjust precision:
    `tkz.inner_angle`, `tkz.angle_between_vectors`, `tkz.get_angle_normalize`.
  - New comparison helper: `tkz.approx` (optional EPS argument).

- **line**
  - Aliases `perpendicular_bisector` and `bisector` added for `mediator`.
  - New method `harmonic` with optional argument `"internal"`, `"external"`, or `"both"`.

- **triangle**
  - `isodynamic_points` (alias `neuberg_points`).
  - `three_apollonius_circles`.
  - `apollonius_circle`.
  - `apollonius_points`.
  - `apollonius_circles`.

### Changed
- **matrix**
  - Corrections to `print_matrix` and `matrix:print`.
  - Correction of method `htm`.

- **intersection**
  - Rewriting of algorithms with introduction of an EPS parameter to adjust precision.

- **circle**
  - The following functions now accept an optional EPS parameter:
    `on_circle`, `in_out`, `in_disk`, `in_out_disk`,
    `in_disk_strict`, `out_disk_strict`, `in_out_disk_strict`,
    `line_position`, `pole`, `is_tangent`, `is_secant`, `circles_position`,
    `orthogonal_through`, `midcircle`, `common_tangent`.
  - Improved `CLL` for the case of parallel lines.

- **line**
  - Improved `LLL`.

### Docs
- Added Gothic example for CLP.
- Added example with parallel lines for CLL.
- Rewriting of `search_circle.lua`.
- Apollonius section: new CLP examples.
- Lua lesson: using `string.char(37)`.

## [2025/11/13 version 4.40c]

### Added
- **points**:
   - `length(p)`:  `z.A:length(z.B)` equiv. `tkz.length(z.A, z.B)`
-**line**:
   - improvement of `orthogonal_at` and `collinear_at`
- **circle**:
  - `from_radius` equiv. `through` and `from_diameter` equiv. `diameter`
  - modification of `common_tangent`
- **triangle**:
  - `trilinear_to_d`
- **tkz**:
  - `tkz.range`, `tkz.deg`, `tkz.rad` and `tkz.pt`
  - `tkz.is_NaN`, `tkz.is_Inf`, `tkz.notDef`
  - `tkz.fsolve(f, a, b, n [, opts])`
  - `tkz.derivative(f, x0 [, accuracy])`
- **conic**
  - adding `common_tangent`
### Changed
- **conic**:
   -  modification of `path` for an ellipse: new options with "swap" and "ccw" or "cw"
### Docs
   - `\tkzDrawCoordinates[smooth]` instead of `\tkzDrawCoordinatessmooth` in class "conic"
   - adding examples for CCL

## [2025/11/08 version 4.35c]

### Added

- **point**:
   - `shift_collinear_to(B, dist)`,
   `PPP` (circle through three points)
- **line**:
   - `collinear_at_distance(d)`
   - `LLL` (circle tangent to three lines)
- **circle**:
   - `line_position(L)`,
   - `lines_position(L1, L2, mode)`,
   - `is_tangent(L)`, `is_secant(L)`, `is_disjoint(L)`
   - `inversion_neg` (inversion then symmetry)
   - `tangent_parallel`
   - `CLL` or `c_c_ll`
   - add mode in common_tangent by default internal external or both
   - `are_circles_tangents(C)`
   - `CCL` and `CCC` and `CCC_gergonne`
- **path**
   - `get(i)` to extract point of path
- **triangle**
   - modification class triangle: confused test points, collinearity test
   - remove function triangle:c_ll_p
- **tkz**
   - `tkz.approx(x, y)`   comparison of two real numbers
   - `tkz.nodes_from_paths`

 ### Changed
  - All methods relating to contact problems have been improved and supplemented in order to deal with specific cases.
  - I added the following nomenclature for contact issues: `PPP`(new), `LLL`(new), `LPP`, `LLP`, `CPP`, `CCP`, `CLP`,  `CLL`(new), `CCL`(new) and `CCC`(new).
  - `c_lc_p` has two aliases 'c_cl_p' and `CLP`
  - `c_cc_p` has an alias `CCP`
  - colinear is now collinear !
  - tkz-elements-demo_5.lua has been adapted
  - midcircle (amelioration): midcircle between two circles or between a circle and a line.
### Docs
   - typo: correction collinear instead of colinear
   - Added descriptions and examples of new methods, plus a few corrections.


## [2025/10/04 version 4.30c]
### Added
- **circle**:
  - `in_disk` same as `in_out_disk`
  - `on_circle` same as `in_out`
  - `in_disk_strict`
  - `out_disk_strict`
- **line**
  - `side_line` This method assigns a value of -1, 0, or 1 to a given point depending on its position in the plane relative to the line.
  - `on_line` = `in_out_line`
  -   `in_out_segment` = `on_segment`
### Changed
- **circle**
  - `common_tangent` Complete rewriting of the procedure, which now takes into account the position of circles and, above all, adds an option to choose between external tangents and internal tangents when they exist.
  - `c_cc_p` Complete rewriting of the procedure. You can use an "external" or "internal" option to determine whether solution circles exist. The method takes into account the relative position of the circles.
- **line**
  - `c_ll_p(L, p)` now has a line and a point as its argument.

### Docs
- Correction of typography.
- Adjusting documentation for new methods.
- Rewriting of numerous method presentations.

## [2025/09/24 version 4.25c]
### Added
- **path**:
  - `get_point`
  - `iter()`.
- **tkz-elements.sty**:
  - `\tkzGetPointFromPath(#1,#2){#3}`
  - `\tkzPathCount(#1){#2}`
  - `\tkzDrawFromPointToPath`.
- **tkz**: Function `tkz.parabola(a, b, c)` to obtain the quadratic form whose graph passes through the three points `a`, `b`, and `c` (under certain conditions).

### Changed
- **Source structure**: Removed version numbers and dates from each `tkz_elements_xxx.lua` file.
  The official version and release date are now maintained **only** in:
  - `tkz-elements.sty` (for LaTeX users),
  - `README.md`,
  - `CHANGELOG.md`,
  - `doc/tkz-elements.pdf`.
- **occs**: The `coordinates` method now returns numbers instead of strings (removed `checknumber_`).
- **path**: Improved `get_number_path` method.


### Docs
- Renamed several examples: the old names were more explicit.
- After **Overview**, added three navigation tables (attributes, methods, metamethods) for each class. All elements should now be listed, with links to their definitions and, where relevant, to examples.
- Rewrote the section on **path**.
- Added in **Theorems**: Circle–Point Midpoint Theorem.
- Added documentation for the new macros of **tkz-elements.sty**.
- Added in **Examples**: Construction of the midcircle of two disjoint circles.


## [4.21c] — 2025-09-21
### Docs
- Changed the names of the examples.
- The examples now use external Lua files.
- Corrected the documentation.
- Cleaned up the files: unused labels have been removed, as well as **overfull box**.

## [4.20c] — 2025-09-17
### Added
- **triangle**: `thebault/c_c` (Thébault’s problem III), `poncelet_point`, `orthopole(L)`,
  `mixtilinear_incircle`, `three_tangent_circles`, `morley`, `soddy`, `napoleon`.
- **quadrilateral**: support for orthopole via helper function `tkz.orthopole(a, b, c, l)`.

### Changed
- **circle**: improved `common_tangent`, `orthogonal_through`, `orthogonal_from`, `c_cc_p`.
- **line**: improved `distance`.
- **triangle**: rewrites of `symmedian_line`, `altitude`, `bisector`, `bisector_ext`,
  `mediator`, `ex_circle`, `reflection`.

### Fixed
- **circle**: `common_tangent` correctness issues.

### Docs
- New subsection **Best practices** in **Writing Convention, best practices and common mistakes**.
- New examples for `thebault/c_c` in **class triangle** and **theorems** (Thébault’s problem III).
- New examples for `poncelet_point` (triangle and quadrilateral).
- Examples for **orthopole** (triangle + examples section).
- Various corrections.

## [4.15c] — 2025‑06‑15
### Added
- `tkz.trisector` to divide a sector into three equal parts (returns two points).
- Triangle method: `mediator` (perpendicular bisector of the side opposite the chosen vertex).
- Utility: `tkz.is_direct` to test whether ∠ABC is oriented positively.

### Changed
- Triangle methods now accept the vertex **itself** in place of a permutation index (e.g. `bisector`, `altitude`, `ex-circle`), improving clarity and consistency.
- Renamed `tkz_dc` → `tkz.dc`; removed remaining occurrences of the old name.

### Docs
- Updated manual; new example added (**Morley triangle**).

## [4.10c]
### Added
- Modules `utils` and `tkz` (formatting, rounding, comparisons, table ops; helpers like `tkz.solve`, `tkz.midpoint`, `tkz.length`, angle tools, barycenter, etc.).
- `path` class interop with conics and triangles; TikZ macros `\tkzDrawPointsFromPath`, `\tkzGetPointsFromPath`, `\tkzDrawCirclesFromPaths`, `\tkzDrawSegmentsFromPaths`.
- Triangle: `poncelet_point`, `orthopole`.
- Macro aliasing: `\tkzPN` = `\tkzPrintNumber`, `\tkzDrawPath` = `\tkzDrawCoordinates`.
- `\tkzEraseLuaObj` to delete a Lua object.

### Changed
- Circle method `orthogonal_through` rewritten and corrected.

### Docs
- New examples: Archimedean spiral, Poncelet point, Orthopole, Path examples.

## [4.00c]
### Added
- New `path` class; short syntax for constructors (omit `.new`).
- Metapost “mini” macro; options `known` and `near` for intersections; trilinear/barycentric rewrites; line methods `orthogonal_at(pt,k)` and `collinear_at(pt,k)`.

### Changed
- Removed scaling within the Lua section (prefer TikZ‑level scaling).
- Various fixes: triangle `point` method; rectangle `get_lengths`; Gauss pivot improvements.

### Docs
- Major rewrite; new sections (**Short contents, Getting started, Class path, LuaLaTeX for beginners, Global variables and constants, Various functions, Module utils, Metapost**).
