🔺 Geometry Solver — API Reference
All pre-loaded features available in the solver playground, with signatures, parameters, and examples.
Geometry configuration
Switch the active geometry type before building a scene.
The geometry affects how distances, areas, and angles are computed.
Supported: Euclidean geometry: GEOMETRY_TYPE_EUCLIDEAN.
Experimental (Proof of Concept) support: Hyperbolic (Lobachevskian): GEOMETRY_TYPE_HYPERBOLIC
Experimental (Proof of Concept) support: Spherical (Riemann): GEOMETRY_TYPE_SPHERICAL
Important:
- when switching to Hyperbolic - define "curvature" parameter, or it will be default -1.0
- when switching to Spherical - define "sphere_radius" parameter, or it will be default 1.0
- when switching to Hyperbolic or Spherical - dimension is not configurable and defaulted to 2
Figure.set_geometry(geometry_type, curvature=None, sphere_radius=None, dimension=None )
classmethod
Set the active geometry. Use GEOMETRY_TYPE_* constants.
set_geometry(GEOMETRY_TYPE_SPHERICAL, sphere_radius=6371)
# Now distances are great-circle distances in km
get_geometry()
classmethod
Return the current Geometry parameters (has "geometry_type", "curvature", "sphere_radius", "dimension").
geometry = Figure.get_geometry()
print(geometry["geometry_type"], geometry["sphere_radius"])
get_geometry_type()
classmethod
Get current geometry type.
geometry_type = Figure.get_geometry_type()
get_geometry_curvature()
classmethod
Get current curvature of Hyperbolic geometry. Can be None if geometry is not Hyperbolic.
curvature = Figure.get_geometry_curvature()
get_geometry_sphere_radius()
classmethod
Get current sphere radius of Spherical geometry. Can be None if geometry is not Spherical.
sphere_radius = Figure.get_geometry_sphere_radius()
get_dimension_space()
classmethod
Get current dimension space. Minimum allowed: 2. Maximum allowed: MAX_DIMENSIONS (15), Default: 3
dimensions = Figure.get_dimension_space()
Geometry type constants
GEOMETRY_TYPE_EUCLIDEAN = 1
Flat plane — default.
GEOMETRY_TYPE_HYPERBOLIC = 2
Lobachevskian / Poincaré model.
GEOMETRY_TYPE_SPHERICAL = 3
Riemannian — requires sphere_radius.
Figure — base class
Manages all common figure operations, topology and general actions.
These class-methods operate on any figure regardless of figure type.
Most important are:
Geometry: set_geometry(), get_geometry_type(), get_geometry_dimension()...
CRUD: set_param(), get_param(), del_param()...
Interactions: add_interaction(), find_interaction()...
General: clear_all(), calculate_all(), describe_all(), display_theorem_trace()...
Figure.list_param(oid)
classmethod
List parameters names for a figure id.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Figure identifier returned by .create(). |
Returns: List of parameter names. Note: all defined parameters name will be displayed.
Figure.set_param(segment_ab, "length", 5)
Figure.set_param(point_a, "coordinates", {0: 1.0, 1: 2.0})
Figure.set_param(oid, param, value)
classmethod
Write one parameter value for figure oid.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Figure identifier returned by .create() |
| param | str | Parameter name, e.g. "length", "size", "coordinates". |
| value | any | Value to store. Use None to clear. |
Returns: None
Figure.set_param(segment_ab, "length", 5)
Figure.set_param(point_a, "coordinates", {0: 1.0, 1: 2.0})
Figure.get_param(oid, param) → value
classmethod
Read one parameter value from the registry. Returns None if the parameter is not set.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Figure identifier returned by .create() |
| param | str | Parameter name. |
Returns: Stored value, or None.
length = Figure.get_param(segment_ab, "length")
sides = Figure.get_param(triangle_abc, "sides") # Note: sides is a list of ids
Figure.calculate_all(max_iterations=100)
classmethod
Run constraint propagation to a fixed point across all figures in the registry. Calls each figure's calculate() repeatedly until no new values are set or max_iterations is reached. Always call this after setting up initial parameters.
| Parameter | Type | Description |
|---|---|---|
| max_iterations | int | Safety cap — default 100. |
Returns: None
Figure.set_param(pt, "coordinates", {0: 0.0, 1: 0.0})
Figure.calculate_all()
# All derived params (area, angles, radii…) are now set.
Figure.clear_all()
classmethod
Wipe the entire geometry constraints, return type of geometry to default Euclidean with dimension space =3. Call this at the start of each new problem.
Returns: None
Figure.clear_all() # always call before building a new scene
Figure.add_interaction(oid_1, oid_2, interact_oid, interact_type)
classmethod
Record a geometric relationship between two figures. The solver reads interactions to propagate constraints across figure boundaries (e.g. circumscribed circle radius = triangle circumradius).
| Parameter | Type | Description |
|---|---|---|
| oid_1 | int | First figure OID. |
| oid_2 | int | Second figure OID. |
| interact_oid | int|None | OID of the interaction figure itself (usually None). |
| interact_type | int | INTERACTION_* or POINT_ON_* constant. |
Returns: None
Figure.add_interaction(circle, triangle, None, INTERACTION_CIRCUMSCRIBED)
Figure.add_interaction(pt, circle, None, POINT_ON_CIRCLE_OUTLINE)
Figure.bulk_get_param(oids, param) → list
classmethod
Fetch the same parameter from a list of OIDs in one call. Returns a list of values (None where not set). Useful for collecting all side lengths or angle sizes from a figure.
| Parameter | Type | Description |
|---|---|---|
| oids | list[int] | List of OIDs. |
| param | str | Parameter name. |
Returns: list — one value per OID.
sides = Figure.get_param(tri, "sides")
lengths = Figure.bulk_get_param(sides, "length")
# → [3.0, 5.0, 4.0]
FigurePlane
Represents a plane in space. Parameters of 3D function Ax + By +Cz + D = 0 are stored as coefficients List [A, B, C, D].
FigurePlane.create() → int
classmethod
Contains parameters and methods of Plane in 3D.
| Parameter | Type | Description |
|---|---|---|
| name | sting | Display label, e.g. "Plane_A". |
| oid | int | Plane OID. |
| type | int | ELEMENT_TYPE_PLANE. |
| function | list[int] | Function that defines thePlane. keeps [A,B,C,D] of A*x + B*y + C*z + D = 0. |
FigurePlane.setup_instance(plane, points=[A,B,C])
FigurePlane.setup_instance(plane, points=[A,B,C])
classmethod
Calculates Plane's "function" based on coordinates of those 3 Points.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Plane OID. |
| points | list[int] | Three Points with all coordinates known to calculate Plane's function. |
FigurePlane.setup_instance(plane, points=[point_a, point_b, point_c])
FigurePlane.is_point_on_plane(oid, point) → bool
classmethod
If point's coordinates are set, checks is point situated on given plane.Return False if Point is not on Plane or if no enough parameters to check this.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Plane OID. |
| point | int | Point OID. |
FigurePlane.is_point_on_plane(plane, point_a)
FigurePlane.is_orientation_crossing(oid, points) → bool
classmethod
4 points A,B,C,D will form opposite segments AB|CD and BC|AD. Function checks if those segments are crossing on Plane.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Plane OID. |
| points | list[int] | Points OIDs. 4 points should be provided - [A,B,C,D] |
FigurePlane.is_orienttion_crossing(plane, [A,B,C,D])
FigurePoint
Represents a point in space. Coordinates are stored as {0: x, 1: y} or {0: x, 1: y, 2: z}. Use None for an unknown coordinate — the solver will fill it in if enough constraints are set.
FigurePoint.create() → int
classmethod
Contains parameters and methods of Point.
| Parameter | Type | Description |
|---|---|---|
| name | str | Display label, e.g. "A". |
| oid | int | Point OID. |
| type | int | ELEMENT_TYPE_POINT |
| coordinates | Dict[int] | Coordinates of Point: {0: int|None, 2: int|None, 3: int| None..} where 0 means x axis, 1 means y axi, 2 means z axis and so on up to 15 axis. |
A = FigurePoint.create()
FigurePoint.setup_instance(oid, name=None)
classmethod
Assign a label to a point. Coordinates are set separately with
Figure.set_param.| Parameter | Type | Description |
|---|---|---|
| oid | int | Point OID. |
| name | str | Display label, e.g. "A". |
A = FigurePoint.create()
FigurePoint.setup_instance(A, name='A')
Figure.set_param(A, 'coordinates', {0: 0.0, 1: 0.0}) # x=0, y=0
Figure.set_param(B, 'coordinates', {0: 3.0, 1: None}) # y unknown
FigurePoint.get_or_create(name=None, x=None, y=None, z=0.0) → int
classmethod
Create a point and optionally set its coordinates in one call. Returns the OID.
A = FigurePoint.get_or_create(name='A', x=0.0, y=0.0)
FigureSegment
A line segment between two endpoints. Length is derived from coordinates, or coordinates can be derived from length if one endpoint and direction are known.
FigureSegment.create() → int
classmethod
Contains parameters and methods of Segment.
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "AB". |
| oid | int | Segment OID. |
| type | int | ELEMENT_TYPE_SEGMENT. |
| ends | list[int] | Two point OIDs — [start_oid, end_oid]. |
| points | list[int] | Intermediate point OIDs between "ends" in orded from left to right — [point_a, point_b, point_c]. |
| length | float | Known length. Derived automatically if both endpoints have coordinates. |
| subsegments | list[int] | <TBD> List of segments made by intermediate points. |
| line | int | <TBD> Parent line OID. |
p1 = FigurePoint.create(); FigurePoint.setup_instance(p1, name='P')
p2 = FigurePoint.create(); FigurePoint.setup_instance(p2, name='Q')
seg = FigureSegment.create()
FigureSegment.setup_instance(oid, name=None, ends=None, length=None)
classmethod
Initialise a segment.
ends is a list of two point OIDs. Either ends, length, or both may be provided.| Parameter | Type | Description |
|---|---|---|
| ends | list[int] | Two point OIDs — [start_oid, end_oid]. |
| length | float | Known length. Derived automatically if both endpoints have coordinates. |
p1 = FigurePoint.create(); FigurePoint.setup_instance(p1, name='P')
p2 = FigurePoint.create(); FigurePoint.setup_instance(p2, name='Q')
seg = FigureSegment.create()
FigureSegment.setup_instance(seg, name='PQ', ends=[p1, p2], length=5)
FigureSegment.get_or_create(ends=None) → int
classmethod
Return an existing segment with these endpoints if one exists, otherwise create a new one. Avoids duplicate segments when figures share sides.
| Parameter | Type | Description |
|---|---|---|
| ends | list[int] | Two Points OIDs that are ends of this Segment. |
seg = FigureSegment.get_or_create(ends=[p1, p2])
FigureSegment.add_point(segment, point_to_add, between=None, after=None, before=None)
classmethod
Adds intermediate Point to the Segment and creates sub-segments from end points to added point. Interaction of type POINT_ON_SEGMENT is create automatically.
| Parameter | Type | Description |
|---|---|---|
| segment | int | Segment's OID. |
| point_to_add | int | OID of Point to add. |
| between | list[int] | Two Points OIDs between which to add a point. |
| before | int | Point OID before which to add new point. |
| after | int | Point OID after which to add new point. |
p1 = FigurePoint.create()
p2 = FigurePoint.create()
p3 = FigurePoint.create()
seg = FigureSegment.get_or_create(ends=[p1, p2])
FigureSegment.add_point(seg, p3, after=p1)
FigureAngle
FigureAngle.create() → int
classmethod
Contains parameters and methods of Angle.
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "ABC" |
| oid | int | Angle OID. |
| type | int | ELEMENT_TYPE_ANGLE. |
| angle_type | int | Standard Angle type depends on size(acute, right, obtuse, straight). |
| formed_by | lsit[int] | Two OID of elements creating this Angle. Use Segments for now. |
| vertex | int | OID of Point - vertex of the Angle. |
| size | float | Angle size in degrees. |
| bisector | int | <TBD> OID of element - bisector of the Angle |
angleA = FigureAngle.create()
FigureAngle.setup_instance(oid, name=None, formed_by=None, vertex=None, size=None)
classmethod
Initialise an angle. Usually you access angles from a triangle or polygon via
Figure.get_param(tri, "angles") rather than creating them manually.| Parameter | Type | Description |
|---|---|---|
| formed_by | list[int] | Two segment OIDs that form the angle. |
| vertex | int | Point OID at the vertex of the angle. |
| size | float | Angle size in degrees. |
angleA = FigureAngle.create()
FigureAngle.setup_instance(angleA, formed_by=[segment ab, segment_bc])
FigureAngle.setup_instance(angleA, formed_by=[segment ab, segment_bc])
FigureAngle.get_or_create(formed_by=None, vertex=None)
classmethod
Returns existent Angle OID if it already exists, or creates a new one. If you need to operate with exact triangle's or polygon's angle that was created when triangle or polygon created.
| Parameter | Type | Description |
|---|---|---|
| formed_by | list[int] | Two segment OIDs that form the angle. Should be defined with vertex. |
| vertex | int | Point OID at the vertex of the angle. Should be defined with formed_by |
angle = Figure.get_or_create(formed_by=[AB, BC], vertex=B)
FigureCircle
FigureCircle.create() → int
classmethod
Contains parameters and methods of Circle.
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "Circ_O". |
| oid | int | Triangle OID. |
| type | int | ELEMENT_TYPE_CIRCLE. |
| center | int | OID of Point - center of the Circle. |
| radius | float | Known radius length. |
| diameter | float | Known diameter length. |
| circumference | float | Known circumference length. |
| area | float | Known area size. |
| points | list[inf] | list of points on the circumference. |
O = FigurePoint.create()
FigurePoint.setup_instance(O, name='O')
circ_O = FigureCircle.create()
FigureCircle.setup_instance(oid, name=None, center=None, radius=None, diameter=None, circumference=None, area=None)
classmethod
Initialise a circle. Provide one known metric (radius, diameter, area, or circumference) and the solver derives the rest. Link to a triangle via
add_interaction to have the circumradius/inradius computed automatically.| Parameter | Type | Description |
|---|---|---|
| center | int | OID of a FigurePoint for the centre. |
| radius | float | Known radius. |
| diameter | float | Known diameter (= 2r). |
Derived params (after calculate_all): radius, diameter, area, circumference.
O = FigurePoint.create(); FigurePoint.setup_instance(O, name='O')
circ = FigureCircle.create()
FigureCircle.setup_instance(circ, name='C', center=O)
# Link to triangle so circumradius is derived automatically
Figure.add_interaction(circ, tri, None, INTERACTION_CIRCUMSCRIBED)
Figure.add_interaction(tri, circ, None, INTERACTION_INSCRIBED)
for pt in [A, B, C]:
Figure.add_interaction(pt, circ, None, POINT_ON_CIRCLE_OUTLINE)
FigureCircle.add_point_to_circumference(oid, point2add, between=None, after=None, before=None)
classmethod
Add points to Circle's circumference. Interaction type POINT_ON_CIRCLE_OUTLINE is created automatically.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Circle OID. |
| point2add | int | OID of Point to be added to circumference. Note: if non of between, after, before is specificed- point is added as last in the list.. |
| between | list[int] | OIDs of 2 neighboring Points between which to add a new point. |
| after | int | OID of Point after which to add a new point. |
| before | int | OID of Point before which to add a new point. |
Derived params (after calculate_all): radius, diameter, area, circumference.
O = FigurePoint.create()
FigurePoint.setup_instance(O, name='O')
circ = FigureCircle.create()
FigureCircle.setup_instance(circ, name='C', center=O)
A = FigurePoint.create()
B = FigurePoint.create()
FigureCircle.add_point(circ, A)
FigureCircle.add_point(circ, B, after=A)
FigureTriangle
FigureTriangle.create() → int
classmethod
Contains parameters and methods of Triangle.
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "ABC". |
| oid | int | Triangle OID. |
| type | int | ELEMENT_TYPE_TRIANGLE. |
| type_by_angle | int | TRIANGLE_ANGLE_TYPE_ACUTE, TRIANGLE_ANGLE_TYPE_RIGHT, TRIANGLE_ANGLE_TYPE_OBTUSE. |
| type_by_side | int | TRIANGLE_SIDE_TYPE_GENERAL, TRIANGLE_SIDE_TYPE_ISOSCELES, TRIANGLE_SIDE_TYPE_EQUILATERAL. |
| angles | list[int] | Exactly 3 Angle OIDs - angles of the Triangle. |
| sides | list[int] | Exactly 3 Segment OIDs - sides of the Triangle. |
| heights | list[int] | <TBD>Exactly 3 Segment OIDs - heights of the Triangle. |
| medians | list[int] | <TBD>Exactly 3 Segment OIDs - medians of the Triangle. |
| isosceles_sides | list[int] | Exactly 2 Segment OIDs - isosceles sides if Triangle is ISOSCELES. |
| isosceles_angles | list[int] | Exactly 2 Angle OIDs - isosceles angles if Triangle is ISOSCELES.. |
| isosceles_vertex | int | OID of Angle - vertex of ISOSCELES Triangle. |
| isosceles_base | int | OID of Segment - base of ISOSCELES Triangle]. |
| obtuse_angle | int | OID of Obtuse Angle if Triangle is OBTUSE. |
| right_angle | int | OID of Right Angle if Triangle is RIGHT. |
| right_hypotenuse | int | OID of Segment that is Hypotenuse of Right Triangle if it is RIGHT. |
| right_legs | list[int] | Exactly 2 Segment OIDs - legs of Right Triangle if it is RIGHT. |
| perimeter | float | Perimeter of Triangle. |
| area | float | Area of Triangle. |
tri = FigureTriangle.create()
FigureTriangle.setup_instance(oid, name=None, points=None)
classmethod
Initialise a triangle from three vertex point OIDs. Automatically creates three FigureSegment sides and three FigureAngle angles. Access them via
Figure.get_param(oid, "sides") and Figure.get_param(oid, "angles").| Parameter | Type | Description |
|---|---|---|
| points | list[int] | Exactly 3 FigurePoint OIDs — [A, B, C]. |
Accessible after setup:
sides (list of 3 segment OIDs), angles (list of 3 angle OIDs),
area, perimeter, type_by_side, type_by_angle.
A = FigurePoint.create(); FigurePoint.setup_instance(A, name='A')
B = FigurePoint.create(); FigurePoint.setup_instance(B, name='B')
C = FigurePoint.create(); FigurePoint.setup_instance(C, name='C')
tri = FigureTriangle.create()
FigureTriangle.setup_instance(tri, name='ABC', points=[A, B, C])
sides = Figure.get_param(tri, 'sides') # [AB, AC, BC]
angles = Figure.get_param(tri, 'angles') # [∠A, ∠B, ∠C]
Figure.set_param(angles[1], 'size', 90) # right angle at B
Figure.set_param(sides[0], 'length', 3) # |AB| = 3
Figure.set_param(sides[2], 'length', 4) # |BC| = 4
Figure.calculate_all()
# → Figure.get_param(tri, "area")=6.0, Figure.get_param(tri, "perimeter")=12.0, Figure.get_param(sides[1], "length")=5.0 (Pythagorean theorem)
Triangle sub-type by angle constants
TRIANGLE_ANGLE_TYPE_ACUTE = 1
All angles are less then 90.
TRIANGLE_ANGLE_TYPE_RIGHT = 2
One angle is Right (90).
TRIANGLE_ANGLE_TYPE_OBTUSE = 3
One angle is Obtuse (more than 90).
Triangle sub-type by sides constants
TRIANGLE_SIDE_TYPE_GENERAL = 1
No special structure.
TRIANGLE_SIDE_TYPE_ISOSCELES = 2
Two sides are equal.
TRIANGLE_SIDE_TYPE_EQUILATERAL = 3
All 3 sides are equal.
FigurePolygon
A general polygon with 4 or more vertices. Set sub-type to a
POLYGON_SUBTYPE_* constant to activate specialised calculations.
FigurePolygon.create() → int
classmethod
Contains parameters and methods of Polygon.
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "ABCD". |
| oid | int | Polygon OID. |
| type | int | ELEMENT_TYPE_POLYGON. |
| sub-type | int | POLYGON_SUBTYPE_GENERAL, POLYGON_SUBTYPE_PARALLELOGRAM, POLYGON_SUBTYPE_SQUARE... e.t.c.. |
| angles | list[int] | List of Angle OIDs - angles of the Polygon. |
| sides | list[int] | List of Segment OIDs - sides of the Polygon. |
| heights | list[int] | <TBD>List of Segment OIDs - heights of the Polygon. |
| medians | list[int] | <TBD>List of Segment OIDs - medians of the Polygon. |
| diagonals | list[int] | List of Segment OIDs - diagonals of the Polygon. |
| type_by_angle | int | POLYGON_BY_ANGLE_CONVEX, POLYGON_BY_ANGLE_CONCAVE. |
| type_by_equality | int | POLYGON_BY_EQUALITY_REGULAR, POLYGON_BY_EQUALITY_IRREGULAR. |
| type_by_shape | int | POLYGON_BY_SHAPE_SIMPLE, POLYGON_BY_SHAPE_SELFINTERSECTING. |
| inscription | bool | Condition - is Polygon "inscriptable" into some circle. |
| sides_number | int | Number of sides. n-lygon |
| perimeter | float | Perimetr of Polygon. |
| area | float | Area of Polygon. |
A = FigurePoint.create()
FigurePolygon.setup_instance(oid, name=None, points=None)
classmethod
Initialise a polygon from ordered vertex OIDs. Creates sides and angles automatically. Then set
Figure.set_param(oid, "sub-type", POLYGON_SUBTYPE_SQUARE) to activate square-specific propagation (all sides equal, all angles 90°).| Parameter | Type | Description |
|---|---|---|
| points | list[int] | Ordered vertex OIDs (≥ 4), listed in winding order. |
Derived params: area, perimeter, diagonal. Sides and angles are linked OIDs.
A = FigurePoint.create(); FigurePoint.setup_instance(A, name='A')
B = FigurePoint.create(); FigurePoint.setup_instance(B, name='B')
C = FigurePoint.create(); FigurePoint.setup_instance(C, name='C')
D = FigurePoint.create(); FigurePoint.setup_instance(D, name='D')
sq = FigurePolygon.create()
FigurePolygon.setup_instance(sq, name='ABCD', points=[A, B, C, D])
Figure.set_polygon_type(sq, POLYGON_SUBTYPE_SQUARE)
# Set 3 known corners — 4th is computed
Figure.set_param(A, 'coordinates', {0: 0.0, 1: 0.0})
Figure.set_param(B, 'coordinates', {0: 4.0, 1: 0.0})
Figure.set_param(C, 'coordinates', {0: 4.0, 1: 4.0})
Figure.calculate_all() # D=(0,4) derived; area=16
FigurePolygon.set_polygon_type(oid, sub_type)
classmethod
Defines subtype of Polygon if it is a part of task condition. For example: Define a Square ABCD.... Must be used instead of set_param to define necessary interactions automatically.
| Parameter | Type | Description |
|---|---|---|
| oid | int | Polygon OID. |
| sub_type | int | Supported Sub-type: POLYGON_SUBTYPE_RECTANGLE, POLYGON_SUBTYPE_PARALLELOGRAM, e.t.c. |
Derived params: area, perimeter, diagonal. Sides and angles are linked OIDs.
A = FigurePoint.create(); FigurePoint.setup_instance(A, name='A')
B = FigurePoint.create(); FigurePoint.setup_instance(B, name='B')
C = FigurePoint.create(); FigurePoint.setup_instance(C, name='C')
D = FigurePoint.create(); FigurePoint.setup_instance(D, name='D')
sq = FigurePolygon.create()
FigurePolygon.setup_instance(sq, name='ABCD', points=[A, B, C, D])
Figure.set_polygon_type(sq, POLYGON_SUBTYPE_SQUARE)
Polygon sub-type constants
POLYGON_SUBTYPE_GENERAL = 0
No special structure assumed.
POLYGON_SUBTYPE_QUADRILATERAL = 1
Polygon with 2 sides without special structure.
POLYGON_SUBTYPE_RECTANGLE = 2
Rectangle.
POLYGON_SUBTYPE_SQUARE = 3
Square.
POLYGON_SUBTYPE_PARALLELOGRAM = 4
Parallelogram.
POLYGON_SUBTYPE_RHOMBUS = 5
All 4 sides equal.
FigureEllipse
FigureEllipse.create() → int
classmethod
Contains parameters and methods of Ellipse..
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "ell_E". |
| oid | int | Ellipse OID. |
| type | int | ELEMENT_TYPE_ELLIPSE. |
| semi_major | float | Length of the major semi-axis (a). |
| semi_minor | float | Length of the minor semi-axis (b). |
| center | int | OID of Point - center of the Ellipse. |
| area | float | Area size of the Ellipse. |
| circumference | float | Circumference length of the Ellipse. |
| eccentricity | float | . |
| focal_distance | float | <TBD>Focal distance of the Ellipse. |
O = FigurePoint.create(); FigurePoint.setup_instance(O, name='O')
Figure.set_param(O, 'coordinates', {0: 0.0, 1: 0.0})
el = FigureEllipse.create()
FigureEllipse.setup_instance(el, name='E', semi_major=5, semi_minor=3, center=O)
FigureEllipse.calculate(el)
FigureEllipse.setup_instance(oid, name=None, semi_major=None, semi_minor=None, center=None)
classmethod
Initialise an ellipse. Provide the two semi-axes and optionally a centre point OID.
| Parameter | Type | Description |
|---|---|---|
| semi_major | float | Length of the major semi-axis (a). |
| semi_minor | float | Length of the minor semi-axis (b). |
| center | int | FigurePoint OID for the centre. |
Derived params: area = πab, eccentricity = √(1−b²/a²), focal_distance.
O = FigurePoint.create(); FigurePoint.setup_instance(O, name='O')
Figure.set_param(O, 'coordinates', {0: 0.0, 1: 0.0})
el = FigureEllipse.create()
FigureEllipse.setup_instance(el, name='E', semi_major=5, semi_minor=3, center=O)
FigureEllipse.calculate(el)
FigureFunction
Define a 1-D function f(x) or 2-D function f(x,y) over a bounded domain. The solver computes the definite integral numerically via Simpson's rule and attempts a symbolic antiderivative for polynomials.
FigureFunction.create() → int
classmethod
Contains parameters and methods of Function.
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "Parabola". |
| oid | int | Function OID. |
| type | int | ELEMENT_TYPE_FUNCTION |
| expression | str | callable | Function expression. |
| dim | int | 1 for f(x), 2 for f(x,y). Default 1. |
| ends | list[int] | Exactly 2 OIDs of Points - limits of the Function segment. |
| points | list[int] | <TBD> Intermediate points on Function graph between Ends. |
| x_min | float | Lesser integration bound in x. |
| x_max | float | Higher integration bound in x. |
| y_min | float | Lesser integration bound in y (dim=2 only). |
| y_max | float | Higher integration bound in y (dim=2 only). |
| n_points | int | Quadrature points. Default 1000. |
| integral_value | float | Function's segment Integral values (limited by end points). |
| integral_expression | str | callable | Function Integral expression. |
| base_value | float | Subtract from f(x) before integrating (area between two functions). Default 0.0. |
func_parab = FigureFunction.create()
FigureFunction.setup_instance(oid, name=None, expression=None, dim=1, ends=None, x_min=None, x_max=None, y_min=None, y_max=None, n_points=1000, base_value=0.0)
classmethod
Define the function and its domain.
expression is either a Python string ("sin(x)*exp(-x)") or a callable (lambda x: x**2). Available math functions in string expressions: sin, cos, tan, asin, acos, atan, exp, log, sqrt, pi, e, abs.| Parameter | Type | Description |
|---|---|---|
| expression | str | callable | Function expression. |
| dim | int | 1 for f(x), 2 for f(x,y). Default 1. |
| ends | list[point1,point2] | OIDs of Points that limit the Function segment. |
| x_min, x_max | float | Integration bounds in x. |
| y_min, y_max | float | Integration bounds in y (dim=2 only). |
| n_points | int | Quadrature points. Default 1000. |
| base_value | float | Subtract from f(x) before integrating (area between two functions). Default 0. |
After FigureFunction.calculate(oid): integral_value (float), integral_expression (str, polynomial antiderivative only).
# 1-D: area under parabola
point1 = FigurePoint.create()
point2 = FigurePoint.create()
f = FigureFunction.create()
FigureFunction.setup_instance(f, name='parabola',
expression='x**2', ends=[point1, point2], x_min=-2, x_max=2)
FigureFunction.calculate(f)
print(Figure.get_param(f, 'integral_value')) # ≈ 5.3333 (exact: 16/3)
# 2-D: volume under Gaussian surface
g = FigureFunction.create()
FigureFunction.setup_instance(g, name='gaussian',
expression='exp(-(x**2+y**2))', dim=2,
x_min=-3, x_max=3, y_min=-3, y_max=3)
FigureFunction.calculate(g)
print(Figure.get_param(g, 'integral_value')) # ≈ π
FigureFunction.evaluate(oid, *args) → float | None
classmethod
Evaluate the stored function at given coordinates. Returns None if the expression fails (domain error etc.).
y = FigureFunction.evaluate(f, 1.5) # f(1.5)
z = FigureFunction.evaluate(g, 1.0, 0.5) # g(1.0, 0.5) for dim=2
FigureConcyclicGroup
Define a Concyclic Group.
FigureConcyclicGroup.create() → int
classmethod
Contains parameters and methods of Concyclic Group.
| Parameter | Type | Description |
|---|---|---|
| name | string | Display label, e.g. "ConcGrp_1". |
| oid | int | ConcyclicGroup OID. |
| type | int | ELEMENT_TYPE_CONCYCLIC_GROUP |
| center | Dict[int] | Coordinates of the center of Concyclic Group. |
| radius | float | Radius lengths of Concyclic Group. |
| plane_function | list[int] | Plane function of the Concyclic Group, where stored [A, B,C,D] of function A*x + B*y + C*z + D =0. |
| points | list[int] | List of Point OID - memebrs of the Concyclic Group. |
concGrp_1 = FigureConcyclicGroup.create()
FigureConcyclicGroup.setup_instance(oid, poins, name=None)
classmethod
Define the Concyclic Group and it's params. From firs 3 points of the "points" finds if theare concyclic, and if yes - calculates parameters of Concyclic Group
| Parameter | Type | Description |
|---|---|---|
| oid | int | ConcyclicGroup OID. |
| points | list[int] | List of Point OIDs with known coordinates. |
| ends | list[point1,point2] | OIDs of Points that limit the Function segment. |
| name | string | Name of ConcyclicGroup. |
point1 = FigurePoint.create()
Figure.set_param(point1, "coordinates", <some coordinates>)
point2 = FigurePoint.create()
Figure.set_param(point2, "coordinates", <some coordinates>)
point3 = FigurePoint.create()
Figure.set_param(point4, "coordinates", <some coordinates>)
concGrp_1 = FigureConcyclicGroup.create()
FigureConcyclicGroup.setup_instance(concGrp_1, points=[poiny1, point2, point3], name='ConcGrp_1')
FigureConcyclicGroup.is_point_in_group(oid, point) → bool
classmethod
Checks are Point's coordinates meet requirements of Concyclic Group.
| Parameter | Type | Description |
|---|---|---|
| oid | int | ConcyclicGroup OID. |
| point | int | Point OID to measure is it's coordinates meet requirements of tho\is Concyclic Group. |
point1 = FigurePoint.create()
Figure.set_param(point1, "coordinates", <some coordinates>)
point2 = FigurePoint.create()
Figure.set_param(point2, "coordinates", <some coordinates>)
point3 = FigurePoint.create()
Figure.set_param(point3, "coordinates", <some coordinates>)
point4 = FigurePoint.create()
Figure.set_param(point4, "coordinates", <some coordinates>)
concGrp_1 = FigureConcyclicGroup.create()
FigureConcyclicGroup.setup_instance(concGrp_1, points=[poiny1, point2, point3], name='ConcGrp_1')
result = FigureConcyclicGroup.is_point_in_group(concGrp_1,point4)
Interaction constants
Pass these to Figure.add_interaction(oid_1, oid_2, None, CONSTANT)
to declare geometric relationships the solver should propagate.
POINT_END_OF_SEGMENT = 4
Point is the end of a Segment
POINT_ON_SEGMENT = 5
Point on the Segment, but not the end of Segment. (Intermediate point)
POINT_CENTER_OF_CIRCLE = 7
Point is the center of a Circle
POINT_ON_CIRCLE_OUTLINE = 8
Point is on Circle outline
POINT_ON_FIGURE_OUTLINE = 9
Point is on Figure outline, nota Vertex of end of side
POINT_APEX_OF_ANGLE = 10
Apex of an Angle
POINT_ON_PLANE = 12
Point on Plane
POINT_IN_CONCYCLIC_GROUP = 13
Point in Concyclic Group
INTERACTION_INSCRIBED = 15
Element is inscribed in other element (now supported - inscribed in Circle)
INTERACTION_CIRCUMSCRIBED = 16
Element is circumscribed by a Circle
INTERACTION_INTERSECTION = 17
Two elements (segments) intersected at Point
INTERACTION_RADIUS = 21
Segment is a Radius of a Circle
INTERACTION_DIAMETER = 22
Segment is a Diameter of a Circle
INTERACTION_APOTHEM = 23
Segment is an Apothem of a Polygon
INTERACTION_CONCYCLIC_WITH = 25
Element is Circumscribed by the same Circle as other element
INTERACTION_PARALLEL = 26
Segment is parallel to a Segment
INTERACTION_EQUAL = 27
Element parameter value is equal to same parameter value of other Element
Figure type constants
These identify figure types in Figure.get_type(oid) results
and in interaction filtering calls. They are pre-loaded in the playground namespace.
ELEMENT_TYPE_PLANE = 1
ELEMENT_TYPE_POINT = 2
ELEMENT_TYPE_SEGMENT = 5
ELEMENT_TYPE_SIDE = 6
ELEMENT_TYPE_ANGLE = 7
ELEMENT_TYPE_TRIANGLE = 8
ELEMENT_TYPE_CIRCLE = 9
ELEMENT_TYPE_POLYGON = 11
ELEMENT_TYPE_ELLIPSE = 12
ELEMENT_TYPE_CONCYCLIC_GROUP = 22
ELEMENT_TYPE_FUNCTION = 28
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