← etc / geometor • etc

modules¶

geometor.etc¶

Tools for processing and modeling the Encyclopedia of Triangle Centers (ETC).

Key Components¶

Triangles: Exact canonical symbolic reference triangles (geometor.etc.triangles).
Symbolic Cache: Exact symbolic center evaluator and disk cache (geometor.etc.symbolic_cache).
Ops: Exact Euclidean construction primitives and canonical Principles of Geometry operators (geometor.etc.ops).
Ingest: Tools (ingest_folder()) to split and organize the raw HTML source.
Parser: Tools (parse_center()) to extract center data from HTML.
Glossary: Tools (extract_glossary_terms()) to handle glossary terms, persons, and citations.
Construct: Coordinate/incidence resolver, Model builder, and per-center model.py generator (geometor.etc.construct).
Render: Explorer-styled SVG renderer with exact symbolic HUD metadata (geometor.etc.render).
Transform: Tools (generate_rst_files()) to generate per-center ReStructuredText folders and graphics.

Submodules¶

Attributes¶

`CANONICAL_CENTER_CONCORDANCE`
`CANONICAL_TRIANGLES`

Classes¶

`CenterConcordance`	Concordance entry linking canonical function names, Kimberling IDs, and classical citations.
`CenterSymbolicRegistry`	Exact symbolic evaluator and persistent cache for ETC triangle centers.
`SymbolicCenterRecord`	Exact symbolic coordinates and invariants for center `X_num` on a triangle.
`SymbolicTriangle`	Exact symbolic reference triangle with side lengths, vertices, and invariants.

Functions¶

`extract_glossary_terms`(html_content) → dict[str, Any]	Extract all glossary terms, their rich RST bodies, and plain-text summaries from GLOSSARY HTML.
`generate_glossary_rst`(terms[, intro_rst, valid_centers]) → str	Generate rich docsrc/glossary.rst with deterministic #term-<slug> anchors.
`ingest_folder`(input_folder, output_folder) → dict[str, Any]	Ingest all ETC volume HTML files in input_folder and write split files to output_folder.
`bevan_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the Bevan point `X_40` (reflection of `X_1` across `X_3`).
`centroid`(model, A, B, C[, ID, classes, draw_medians]) → sympy.geometry.Point	Construct the centroid `X_2` of triangle `ABC`.
`circumcenter`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the circumcenter `X_3` of triangle `ABC` (Euclid IV.5).
`circumcircle_inverse_of_incenter`(model, A, B, C[, ID, ...]) → sympy.geometry.Point	Construct `X_36`, the circumcircle inverse of `X_1`.
`clawson_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the Clawson point `X_19`.
`construct_baseline_triangle`(model[, a, b, c, ...]) → tuple[sympy.geometry.Point, sympy.geometry.Point, sympy.geometry.Point]	Construct an exact symbolic triangle with side ratios `(a, b, c)`.
`construct_reference_triangle`(model[, preset, ...]) → tuple[sympy.geometry.Point, sympy.geometry.Point, sympy.geometry.Point]	Construct one of the 4 canonical exact symbolic reference triangles in `model`.
`create_model`([name]) → geometor.model.Model	Create a silent exact `geometor.model.Model` with `auto_intersect=False`.
`de_longchamps_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the de Longchamps point `X_20` (reflection of `X_4` in `X_3`).
`fermat_point`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the 1st isogonic center (Fermat point) `X_13`.
`feuerbach_point`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the Feuerbach point `X_11` of triangle `ABC`.
`first_isodynamic_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the 1st isodynamic point `X_15`.
`first_napoleon_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the 1st Napoleon point `X_17`.
`gergonne_point`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the Gergonne point `X_7` of triangle `ABC`.
`get_center_concordance`(num) → CenterConcordance \| None	Return the `CenterConcordance` for center `X_num`, if registered.
`harmonic_feuerbach_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct `X_12` (the `{X_1, X_5}`-harmonic conjugate of `X_11`).
`incenter`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the incenter `X_1` of triangle `ABC` (Euclid IV.4).
`isotomic_conjugate_of_incenter`(model, A, B, C[, ID, ...]) → sympy.geometry.Point	Construct `X_75`, the isotomic conjugate of `X_1`.
`mittenpunkt`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the Mittenpunkt `X_9` of triangle `ABC`.
`nagel_point`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the Nagel point `X_8` of triangle `ABC`.
`nine_point_center`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the nine-point center `X_5` of triangle `ABC`.
`orthocenter`(model, A, B, C[, ID, classes, draw_altitudes]) → sympy.geometry.Point	Construct the orthocenter `X_4` of triangle `ABC`.
`second_isodynamic_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the 2nd isodynamic point `X_16`.
`second_isogonic_center`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the 2nd isogonic center `X_14`.
`second_napoleon_point`(model, A, B, C[, ID, classes]) → sympy.geometry.Point	Construct the 2nd Napoleon point `X_18`.
`spieker_center`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the Spieker center `X_10` of triangle `ABC`.
`symmedian_point`(model, A, B, C[, ID, classes, ...]) → sympy.geometry.Point	Construct the symmedian (Lemoine) point `X_6` of triangle `ABC`.
`parse_center`(html_content) → dict[str, Any] \| None	Parse a center's HTML content into a rich structured dictionary.
`generate_rst_files`(centers, output_dir[, ...]) → None	Generate thematic collection folders (c-XXXXX-YYYYY/) and per-center folders (x-NNNNN/).
`get_canonical_triangle`([preset, unit_baseline]) → SymbolicTriangle	Return a canonical `SymbolicTriangle` by preset key.

Package Contents¶

geometor.etc.extract_glossary_terms(html_content: str) → dict[str, Any]¶: Extract all glossary terms, their rich RST bodies, and plain-text summaries from GLOSSARY HTML.

geometor.etc.generate_glossary_rst(terms: dict[str, Any], intro_rst: str = '', valid_centers: set[int] | None = None) → str¶: Generate rich docsrc/glossary.rst with deterministic #term-<slug> anchors.

geometor.etc.ingest_folder(input_folder: str | pathlib.Path, output_folder: str | pathlib.Path) → dict[str, Any]¶

Ingest all ETC volume HTML files in input_folder and write split files to output_folder.

Returns a summary dictionary with counts of centers, preambles, and intro sections.

geometor.etc.CANONICAL_CENTER_CONCORDANCE: dict[int, CenterConcordance]¶

class geometor.etc.CenterConcordance¶

Concordance entry linking canonical function names, Kimberling IDs, and classical citations.

num: int¶

function_name: str¶

etc_id: str¶

title: str¶

classical_ref: str¶

property signature: str¶: Return canonical functional signature string.

geometor.etc.bevan_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₄₀', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the Bevan point X_40 (reflection of X_1 across X_3).

geometor.etc.centroid(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₂', classes: list[str] | None = None, draw_medians: bool = False) → sympy.geometry.Point¶: Construct the centroid X_2 of triangle ABC.

geometor.etc.circumcenter(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₃', classes: list[str] | None = None, draw_bisectors: bool = False, draw_circumcircle: bool = False) → sympy.geometry.Point¶: Construct the circumcenter X_3 of triangle ABC (Euclid IV.5).

geometor.etc.circumcircle_inverse_of_incenter(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₃₆', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct X_36, the circumcircle inverse of X_1.

geometor.etc.clawson_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₉', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the Clawson point X_19.

geometor.etc.construct_baseline_triangle(model: geometor.model.Model, a: sympy.Expr | float = 15, b: sympy.Expr | float = 13, c: sympy.Expr | float = 14, show_guides: bool = False, *, unit_baseline: bool = True) → tuple[sympy.geometry.Point, sympy.geometry.Point, sympy.geometry.Point]¶

Construct an exact symbolic triangle with side ratios (a, b, c).

Preserves backward compatibility for scripts calling construct_baseline_triangle(model, 5, 6, 7) while computing exact algebraic coordinates without floating-point approximations.

geometor.etc.construct_reference_triangle(model: geometor.model.Model, preset: str | geometor.etc.triangles.SymbolicTriangle = 'heronian', *, unit_baseline: bool = False, show_guides: bool = False) → tuple[sympy.geometry.Point, sympy.geometry.Point, sympy.geometry.Point]¶

Construct one of the 4 canonical exact symbolic reference triangles in model.

Parameters:

model – Target geometor.model.Model.
preset – Canonical preset key ("heronian", "right", "kepler", "kimberling") or a SymbolicTriangle.
unit_baseline – When True, normalizes side \(AB = 1\). Defaults to False so Heronian \((15, 13, 14)\) and Right \((3, 4, 5)\) preserve exact integer vertex and center coordinates.
show_guides – When True, includes Euclid I.22 compass guide circles centered at \(A\) and \(B\).

geometor.etc.create_model(name: str = 'ETC Construction') → geometor.model.Model¶: Create a silent exact geometor.model.Model with auto_intersect=False.

geometor.etc.de_longchamps_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₂₀', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the de Longchamps point X_20 (reflection of X_4 in X_3).

geometor.etc.fermat_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₃', classes: list[str] | None = None, draw_equilaterals: bool = False) → sympy.geometry.Point¶: Construct the 1st isogonic center (Fermat point) X_13.

geometor.etc.feuerbach_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₁', classes: list[str] | None = None, draw_circles: bool = False) → sympy.geometry.Point¶: Construct the Feuerbach point X_11 of triangle ABC.

geometor.etc.first_isodynamic_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₅', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the 1st isodynamic point X_15.

geometor.etc.first_napoleon_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₇', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the 1st Napoleon point X_17.

geometor.etc.gergonne_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₇', classes: list[str] | None = None, draw_cevians: bool = False, draw_intouch: bool = False) → sympy.geometry.Point¶: Construct the Gergonne point X_7 of triangle ABC.

geometor.etc.get_center_concordance(num: int) → CenterConcordance | None¶: Return the CenterConcordance for center X_num, if registered.

geometor.etc.harmonic_feuerbach_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₂', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct X_12 (the {X_1, X_5}-harmonic conjugate of X_11).

geometor.etc.incenter(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁', classes: list[str] | None = None, draw_bisectors: bool = False, draw_incircle: bool = False, draw_touchpoints: bool = False) → sympy.geometry.Point¶

Construct the incenter X_1 of triangle ABC (Euclid IV.4).

Parameters:

model – Target geometor.model.Model.
A – Vertices of reference triangle ABC.
B – Vertices of reference triangle ABC.
C – Vertices of reference triangle ABC.
ID – Element identifier (defaults to "X_1").
classes – Optional CSS/model classes.
draw_bisectors – When True, constructs exact internal angle bisector feet I_a, I_b, I_c and concurring bisector lines [ A I_a ], [ B I_b ], [ C I_c ].
draw_incircle – When True, constructs the inscribed circle incircle centered at X_1 through exact tangency foot T_c.
draw_touchpoints – When True, constructs all three right-spread touchpoints T_a, T_b, T_c.

geometor.etc.isotomic_conjugate_of_incenter(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₇₅', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct X_75, the isotomic conjugate of X_1.

geometor.etc.mittenpunkt(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₉', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the Mittenpunkt X_9 of triangle ABC.

geometor.etc.nagel_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₈', classes: list[str] | None = None, draw_cevians: bool = False, draw_extouch: bool = False) → sympy.geometry.Point¶: Construct the Nagel point X_8 of triangle ABC.

geometor.etc.nine_point_center(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₅', classes: list[str] | None = None, draw_circle: bool = False) → sympy.geometry.Point¶: Construct the nine-point center X_5 of triangle ABC.

geometor.etc.orthocenter(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₄', classes: list[str] | None = None, draw_altitudes: bool = False) → sympy.geometry.Point¶: Construct the orthocenter X_4 of triangle ABC.

geometor.etc.second_isodynamic_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₆', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the 2nd isodynamic point X_16.

geometor.etc.second_isogonic_center(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₄', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the 2nd isogonic center X_14.

geometor.etc.second_napoleon_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₈', classes: list[str] | None = None) → sympy.geometry.Point¶: Construct the 2nd Napoleon point X_18.

geometor.etc.spieker_center(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₁₀', classes: list[str] | None = None, draw_circle: bool = False, draw_bisectors: bool = False, draw_medial: bool = False) → sympy.geometry.Point¶: Construct the Spieker center X_10 of triangle ABC.

geometor.etc.symmedian_point(model: geometor.model.Model, A: sympy.geometry.Point, B: sympy.geometry.Point, C: sympy.geometry.Point, ID: str = 'X₆', classes: list[str] | None = None, draw_symmedians: bool = False) → sympy.geometry.Point¶: Construct the symmedian (Lemoine) point X_6 of triangle ABC.

geometor.etc.parse_center(html_content: str) → dict[str, Any] | None¶: Parse a center’s HTML content into a rich structured dictionary.

class geometor.etc.CenterSymbolicRegistry(triangle: geometor.etc.triangles.SymbolicTriangle | str = 'heronian', *, cache_dir: pathlib.Path | str | None = DEFAULT_SYMBOLIC_CACHE_DIR)¶

Exact symbolic evaluator and persistent cache for ETC triangle centers.

Parameters:

triangle – A SymbolicTriangle instance or canonical preset name ("heronian", "right", "kepler", "kimberling").
cache_dir – Directory where per-triangle JSON cache files are stored. Pass None to disable disk persistence (in-memory only).

cache_dir¶

property cache_file: pathlib.Path | None¶: Path to this triangle’s JSON cache file.

save_cache() → None¶: Persist cached symbolic center records to disk if modified.

has_exact_formula(num: int) → bool¶: Return whether center X_num has a built-in closed-form generator.

evaluate_barycentrics(num: int, raw_bary: tuple[sympy.Expr, sympy.Expr, sympy.Expr] | None = None) → SymbolicCenterRecord¶: Evaluate and cache a center from either EXACT_CYCLIC_BARYCENTRICS or raw_bary.

get(num: int) → SymbolicCenterRecord¶: Return the exact SymbolicCenterRecord for X_num.

evaluate_cyclic_sympy(num: int, first_component: sympy.Expr, *, is_trilinear: bool = False, cache: bool = True) → SymbolicCenterRecord¶: Evaluate an arbitrary cyclic SymPy expression in (a, b, c, A, B, C, S_A, S_B, S_C, S, r, R, s).

warm_collection_1() → dict[int, SymbolicCenterRecord]¶: Evaluate and cache all Collection 1 centers (X₁–X₁₉) plus key companions.

class geometor.etc.SymbolicCenterRecord¶

Exact symbolic coordinates and invariants for center X_num on a triangle.

num: int¶

triangle_key: str¶

bary: tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶

norm_bary: tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶

trilinear: tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶

xy: tuple[sympy.Expr, sympy.Expr]¶

sub_areas: tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶

search_value: sympy.Expr¶

property is_kepler: bool¶: Return whether this record belongs to the Kepler golden triangle.

xy_latex() → str¶: Return (x, y) formatted as LaTeX.

xy_pretty() → str¶: Return (x, y) formatted as compact Unicode.

trilinear_latex() → str¶: Return homogeneous trilinears formatted as LaTeX.

trilinear_pretty() → str¶: Return homogeneous trilinears formatted as Unicode.

bary_latex() → str¶: Return homogeneous barycentrics formatted as LaTeX.

bary_pretty() → str¶: Return homogeneous barycentrics formatted as Unicode.

search_latex() → str¶: Return the exact Kimberling search value as LaTeX.

approx_xy() → tuple[float, float]¶: Return secondary float approximation of (x, y) for SVG layout.

approx_search_value() → float¶: Return float approximation of search_value.

to_cache_dict() → dict[str, Any]¶: Serialize exact SymPy expressions via sp.srepr.

classmethod from_cache_dict(data: dict[str, Any]) → SymbolicCenterRecord¶: Deserialize exact SymPy expressions from sp.srepr strings.

geometor.etc.generate_rst_files(centers: list[dict[str, Any]], output_dir: str | pathlib.Path, glossary_terms: dict[str, Any] | list[str] | None = None, preambles_by_center: dict[str, list[dict[str, Any]]] | None = None, valid_centers: set[int] | None = None, render_graphics: bool = True, constructions_dir: str | pathlib.Path | None = None) → None¶: Generate thematic collection folders (c-XXXXX-YYYYY/) and per-center folders (x-NNNNN/).

geometor.etc.CANONICAL_TRIANGLES: dict[str, SymbolicTriangle]¶

class geometor.etc.SymbolicTriangle¶

Exact symbolic reference triangle with side lengths, vertices, and invariants.

Parameters:

key – Preset identifier ("heronian", "right", "kepler", "kimberling", or "acute").
label – Short human-readable title (e.g. "Heronian (15, 13, 14)").
field_latex – LaTeX string naming the ambient algebraic field (e.g. r"\mathbb{Q}").
a – Exact side lengths \(a = |BC|\), \(b = |CA|\), \(c = |AB|\).
b – Exact side lengths \(a = |BC|\), \(b = |CA|\), \(c = |AB|\).
c – Exact side lengths \(a = |BC|\), \(b = |CA|\), \(c = |AB|\).
A_xy – Exact Cartesian coordinates of vertices \(A\), \(B\), \(C\).
B_xy – Exact Cartesian coordinates of vertices \(A\), \(B\), \(C\).
C_xy – Exact Cartesian coordinates of vertices \(A\), \(B\), \(C\).
area – Exact area \(\Delta = \operatorname{Area}(\triangle ABC)\).
simplify_fn – Field-aware exact simplification callable.

key: str¶

label: str¶

field_latex: str¶

a: sympy.Expr¶

b: sympy.Expr¶

c: sympy.Expr¶

A_xy: tuple[sympy.Expr, sympy.Expr]¶

B_xy: tuple[sympy.Expr, sympy.Expr]¶

C_xy: tuple[sympy.Expr, sympy.Expr]¶

area: sympy.Expr¶

simplify_fn: collections.abc.Callable[[sympy.Expr], sympy.Expr]¶

simplify(expr: sympy.Expr | int) → sympy.Expr¶: Simplify expr in this triangle’s algebraic field.

property Q_a: sympy.Expr¶: Exact quadrance \(Q_a = a^2\) of side \(BC\).

property Q_b: sympy.Expr¶: Exact quadrance \(Q_b = b^2\) of side \(CA\).

property Q_c: sympy.Expr¶: Exact quadrance \(Q_c = c^2\) of side \(AB\).

property s: sympy.Expr¶: Exact semiperimeter \(s = (a + b + c)/2\).

property two_area: sympy.Expr¶: Conway doubled area \(S = 2\Delta\).

property r: sympy.Expr¶: Exact inradius \(r = \Delta / s\).

property Q_r: sympy.Expr¶: Exact incircle quadrance \(Q_r = r^2\).

property R: sympy.Expr¶: Exact circumradius \(R = abc / (4\Delta)\).

property Q_R: sympy.Expr¶: Exact circumcircle quadrance \(Q_R = R^2\).

property S_A: sympy.Expr¶: Conway symbol \(S_A = (b^2 + c^2 - a^2)/2\).

property S_B: sympy.Expr¶: Conway symbol \(S_B = (c^2 + a^2 - b^2)/2\).

property S_C: sympy.Expr¶: Conway symbol \(S_C = (a^2 + b^2 - c^2)/2\).

unit_baseline() → SymbolicTriangle¶: Return a homothetic copy scaled by \(1/c\) so \(A=(0,0), B=(1,0)\).

trilinear_to_bary(alpha: sympy.Expr, beta: sympy.Expr, gamma: sympy.Expr) → tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶: Convert homogeneous trilinears \((\alpha : \beta : \gamma)\) to barycentrics.

bary_to_trilinear(u: sympy.Expr, v: sympy.Expr, w: sympy.Expr) → tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶: Convert homogeneous barycentrics \((u : v : w)\) to trilinears.

normalize_bary(u: sympy.Expr, v: sympy.Expr, w: sympy.Expr) → tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶: Normalize homogeneous barycentrics so \(u + v + w = 1\).

bary_to_cartesian(u: sympy.Expr, v: sympy.Expr, w: sympy.Expr) → tuple[sympy.Expr, sympy.Expr]¶: Map homogeneous barycentrics \((u : v : w)\) to exact Cartesian \((x, y)\).

cartesian_to_sub_areas(x: sympy.Expr, y: sympy.Expr) → tuple[sympy.Expr, sympy.Expr, sympy.Expr]¶: Return exact signed sub-triangle areas \((\Delta_a, \Delta_b, \Delta_c)\).

kimberling_search_value(u: sympy.Expr, v: sympy.Expr, w: sympy.Expr) → sympy.Expr¶: Return exact directed distance \(h_a = 2\Delta u / (a(u + v + w))\) to \(BC\).

geometor.etc.get_canonical_triangle(preset: str = 'heronian', *, unit_baseline: bool = False) → SymbolicTriangle¶

Return a canonical SymbolicTriangle by preset key.

Parameters:

preset – One of "heronian", "right", "kepler", "kimberling" (or legacy "acute").
unit_baseline – When True, scales the triangle by \(1/c\) so \(AB = 1\).