Utility functions and classes located in module ezdxf.math.

Functions

ezdxf.math.is_close_points(p1: Vertex, p2: Vertex, abs_tol=1e-10) → bool

Returns True if p1 is very close to p2.

Parameters
  • p1 – first vertex as Vector compatible object

  • p2 – second vertex as Vector compatible object

  • abs_tol – absolute tolerance

Raises

TypeError – for incompatible vertices

ezdxf.math.closest_point(base: Vertex, points: Iterable[Vertex]) → Vector

Returns closest point to base.

Parameters
  • base – base point as Vector compatible object

  • points – iterable of points as Vector compatible object

ezdxf.math.uniform_knot_vector(count: int, order: int, normalize=False) → List[float]

Returns an uniform knot vector for a B-spline of order and count control points.

order = degree + 1

Parameters
  • count – count of control points

  • order – spline order

  • normalize – normalize values in range [0, 1] if True

ezdxf.math.open_uniform_knot_vector(count: int, order: int, normalize=False) → List[float]

Returns an open (clamped) uniform knot vector for a B-spline of order and count control points.

order = degree + 1

Parameters
  • count – count of control points

  • order – spline order

  • normalize – normalize values in range [0, 1] if True

ezdxf.math.required_knot_values(count: int, order: int) → int

Returns the count of required knot values for a B-spline of order and count control points.

Parameters
  • count – count of control points, in text-books referred as “n + 1”

  • order – order of B-Spline, in text-books referred as “k”

Relationship:

“p” is the degree of the B-spline, text-book notation.

  • k = p + 1

  • 2 ≤ k ≤ n + 1

ezdxf.math.xround(value: float, rounding: float = 0.0) → float

Extended rounding function, argument rounding defines the rounding limit:

0

remove fraction

0.1

round next to x.1, x.2, … x.0

0.25

round next to x.25, x.50, x.75 or x.00

0.5

round next to x.5 or x.0

1.0

round to a multiple of 1: remove fraction

2.0

round to a multiple of 2: xxx2, xxx4, xxx6 …

5.0

round to a multiple of 5: xxx5 or xxx0

10.0

round to a multiple of 10: xx10, xx20, …

Parameters
  • value – float value to round

  • rounding – rounding limit

ezdxf.math.linspace(start: float, stop: float, num: int, endpoint=True) → Iterable[float]

Return evenly spaced numbers over a specified interval, like numpy.linspace().

Returns num evenly spaced samples, calculated over the interval [start, stop]. The endpoint of the interval can optionally be excluded.

New in version 0.12.3.

2D Functions

ezdxf.math.distance_point_line_2d(point: Vec2, start: Vec2, end: Vec2) → float

Returns distance from point to line defined by start- and end point.

Parameters
  • point – 2D point to test as Vec2 or tuple of float

  • start – line definition point as Vec2 or tuple of float

  • end – line definition point as Vec2 or tuple of float

New in version 0.11.

ezdxf.math.point_to_line_relation(point: Vec2, start: Vec2, end: Vec2, abs_tol=1e-10) → int

Returns -1 if point is left line, +1 if point is right of line and 0 if point is on the line. The line is defined by two vertices given as arguments start and end.

Parameters
  • point – 2D point to test as Vec2

  • start – line definition point as Vec2

  • end – line definition point as Vec2

  • abs_tol – tolerance for minimum distance to line

New in version 0.11.

ezdxf.math.is_point_on_line_2d(point: Vec2, start: Vec2, end: Vec2, ray=True, abs_tol=1e-10) → bool

Returns True if point is on line.

Parameters
  • point – 2D point to test as Vec2

  • start – line definition point as Vec2

  • end – line definition point as Vec2

  • ray – if True point has to be on the infinite ray, if False point has to be on the line segment

  • abs_tol – tolerance for on line test

New in version 0.11.

ezdxf.math.is_point_left_of_line(point: Vec2, start: Vec2, end: Vec2, colinear=False) → bool

Returns True if point is “left of line” defined by start- and end point, a colinear point is also “left of line” if argument colinear is True.

Parameters
  • point – 2D point to test as Vec2

  • start – line definition point as Vec2

  • end – line definition point as Vec2

  • colinear – a colinear point is also “left of line” if True

Changed in version 0.11: renamed from is_left_of_line()

ezdxf.math.is_point_in_polygon_2d(point: Vec2, polygon: Iterable[Vec2], abs_tol=1e-10) → int

Test if point is inside polygon.

Parameters
  • point – 2D point to test as Vec2

  • polygon – iterable of 2D points as Vec2

  • abs_tol – tolerance for distance check

Returns

+1 for inside, 0 for on boundary line, -1 for outside

New in version 0.11.

ezdxf.math.convex_hull_2d(points: Iterable[Vertex]) → List[Vertex]

Returns 2D convex hull for points.

Parameters

points – iterable of points as Vector compatible objects, z-axis is ignored

ezdxf.math.intersection_line_line_2d(line1: Sequence[Vec2], line2: Sequence[Vec2], virtual=True, abs_tol=1e-10) → Optional[Vec2]

Compute the intersection of two lines in the xy-plane.

Parameters
  • line1 – start- and end point of first line to test e.g. ((x1, y1), (x2, y2)).

  • line2 – start- and end point of second line to test e.g. ((x3, y3), (x4, y4)).

  • virtualTrue returns any intersection point, False returns only real intersection points.

  • abs_tol – tolerance for intersection test.

Returns

None if there is no intersection point (parallel lines) or intersection point as Vec2

New in version 0.11.

ezdxf.math.rytz_axis_construction(d1: Vector, d2: Vector) → Tuple[Vector, Vector, float]

The Rytz’s axis construction is a basic method of descriptive Geometry to find the axes, the semi-major axis and semi-minor axis, starting from two conjugated half-diameters.

Source: Wikipedia

Given conjugated diameter d1 is the vector from center C to point P and the given conjugated diameter d2 is the vector from center C to point Q. Center of ellipse is always (0, 0, 0). This algorithm works for 2D/3D vectors.

Parameters
  • d1 – conjugated semi-major axis as Vector

  • d2 – conjugated semi-minor axis as Vector

Returns

Tuple of (major axis, minor axis, ratio)

ezdxf.math.offset_vertices_2d(vertices: Iterable[Vertex], offset: float, closed: bool = False) → Iterable[Vec2]

Yields vertices of the offset line to the shape defined by vertices. The source shape consist of straight segments and is located in the xy-plane, the z-axis of input vertices is ignored. Takes closed shapes into account if argument closed is True, which yields intersection of first and last offset segment as first vertex for a closed shape. For closed shapes the first and last vertex can be equal, else an implicit closing segment from last to first vertex is added. A shape with equal first and last vertex is not handled automatically as closed shape.

Warning

Adjacent collinear segments in opposite directions, same as a turn by 180 degree (U-turn), leads to unexpected results.

New in version 0.11.

Parameters
  • vertices – source shape defined by vertices

  • offset – line offset perpendicular to direction of shape segments defined by vertices order, offset > 0 is ‘left’ of line segment, offset < 0 is ‘right’ of line segment

  • closedTrue to handle as closed shape

source = [(0, 0), (3, 0), (3, 3), (0, 3)]
result = list(offset_vertices_2d(source, offset=0.5, closed=True))
_images/offset_vertices_2d_1.png

Example for a closed collinear shape, which creates 2 additional vertices and the first one has an unexpected location:

source = [(0, 0), (0, 1), (0, 2), (0, 3)]
result = list(offset_vertices_2d(source, offset=0.5, closed=True))
_images/offset_vertices_2d_2.png

3D Functions

ezdxf.math.normal_vector_3p(a: Vector, b: Vector, c: Vector) → Vector

Returns normal vector for 3 points, which is the normalized cross product for: a->b x a->c.

New in version 0.11.

ezdxf.math.is_planar_face(face: Sequence[Vector], abs_tol=1e-09) → bool

Returns True if sequence of vectors is a planar face.

Parameters
  • face – sequence of Vector objects

  • abs_tol – tolerance for normals check

New in version 0.11.

ezdxf.math.subdivide_face(face: Sequence[Union[Vector, Vec2]], quads=True) → Iterable[List[Vector]]

Yields new subdivided faces. Creates new faces from subdivided edges and the face midpoint by linear interpolation.

Parameters
  • face – a sequence of vertices, Vec2 and Vector objects supported.

  • quads – create quad faces if True else create triangles

New in version 0.11.

ezdxf.math.subdivide_ngons(faces: Iterable[Sequence[Union[Vector, Vec2]]]) → Iterable[List[Vector]]

Yields only triangles or quad faces, subdivides ngons into triangles.

Parameters

faces – iterable of faces as sequence of Vec2 and Vector objects

New in version 0.12.

ezdxf.math.intersection_ray_ray_3d(ray1: Tuple[Vector, Vector], ray2: Tuple[Vector, Vector], abs_tol=1e-10) → Sequence[Vector]

Calculate intersection of two rays, returns a 0-tuple for parallel rays, a 1-tuple for intersecting rays and a 2-tuple for not intersecting and not parallel rays with points of closest approach on each ray.

Parameters
  • ray1 – first ray as tuple of two points on the ray as Vector objects

  • ray2 – second ray as tuple of two points on the ray as Vector objects

  • abs_tol – absolute tolerance for comparisons

New in version 0.11.

ezdxf.math.estimate_tangents(points: List[Vector], method: str = '5-points', normalize=True) → List[Vector]

Estimate tangents for curve defined by given fit points. Calculated tangents are normalized (unit-vectors).

Available tangent estimation methods:

  • “3-points”: 3 point interpolation

  • “5-points”: 5 point interpolation

  • “bezier”: tangents from an interpolated cubic bezier curve

  • “diff”: finite difference

Parameters
  • points – start-, end- and passing points of curve

  • method – tangent estimation method

  • normalize – normalize tangents if True

Returns

tangents as list of Vector objects

ezdxf.math.estimate_end_tangent_magnitude(points: List[Vector], method: str = 'chord') → List[Vector]

Estimate tangent magnitude of start- and end tangents.

Available estimation methods:

  • “chord”: total chord length, curve approximation by straight segments

  • “arc”: total arc length, curve approximation by arcs

  • “bezier-n”: total length from cubic bezier curve approximation, n segments per section

Parameters
  • points – start-, end- and passing points of curve

  • method – tangent magnitude estimation method

ezdxf.math.fit_points_to_cad_cv(fit_points: Iterable[Vertex], degree: int = 3, method='chord', tangents: Iterable[Vertex] = None) → BSpline

Returns the control vertices and knot vector configuration for DXF SPLINE entities defined only by fit points as close as possible to common CAD applications like BricsCAD.

There exist infinite numerical correct solution for this setup, but some facts are known:

  • Global curve interpolation with start- and end derivatives, e.g. 6 fit points creates 8 control vertices in BricsCAD

  • Degree of B-spline is limited to 2 or 3, a stored degree of >3 is ignored, this limit exist only for B-splines defined by fit points

  • Knot parametrization method is “chord”

  • Knot distribution is “natural”

The last missing parameter is the start- and end tangents estimation method used by BricsCAD, if these tangents are stored in the DXF file provide them as argument tangents as 2-tuple (start, end) and the interpolated control vertices will match the BricsCAD calculation, except for floating point imprecision.

Parameters
  • fit_points – points the spline is passing through

  • degree – degree of spline, only 2 or 3 is supported by BricsCAD, default = 3

  • method – knot parametrization method, default = ‘chord’

  • tangents – start- and end tangent, default is autodetect

Returns

BSpline

New in version 0.13.

ezdxf.math.global_bspline_interpolation(fit_points: Iterable[Vertex], degree: int = 3, tangents: Iterable[Vertex] = None, method: str = 'chord') → BSpline

B-spline interpolation by Global Curve Interpolation. Given are the fit points and the degree of the B-spline. The function provides 3 methods for generating the parameter vector t:

  • “uniform”: creates a uniform t vector, from 0 to 1 evenly spaced, see uniform method

  • “chord”, “distance”: creates a t vector with values proportional to the fit point distances, see chord length method

  • “centripetal”, “sqrt_chord”: creates a t vector with values proportional to the fit point sqrt(distances), see centripetal method

  • “arc”: creates a t vector with values proportional to the arc length between fit points.

It is possible to constraint the curve by tangents, by start- and end tangent if only two tangents are given or by one tangent for each fit point.

If tangents are given, they represent 1st derivatives and and should be scaled if they are unit vectors, if only start- and end tangents given the function estimate_end_tangent_magnitude() helps with an educated guess, if all tangents are given, scaling by chord length is a reasonable choice (Piegl & Tiller).

Parameters
  • fit_points – fit points of B-spline, as list of Vector compatible objects

  • tangents – if only two vectors are given, take the first and the last vector as start- and end tangent constraints or if for all fit points a tangent is given use all tangents as interpolation constraints (optional)

  • degree – degree of B-spline

  • method – calculation method for parameter vector t

Returns

BSpline

ezdxf.math.local_cubic_bspline_interpolation(fit_points: Iterable[Vertex], method: str = '5-points', tangents: Iterable[Vertex] = None) → BSpline

B-spline interpolation by ‘Local Cubic Curve Interpolation’, which creates B-spline from fit points and estimated tangent direction at start-, end- and passing points.

Source: Piegl & Tiller: “The NURBS Book” - chapter 9.3.4

Available tangent estimation methods:

  • “3-points”: 3 point interpolation

  • “5-points”: 5 point interpolation

  • “bezier”: cubic bezier curve interpolation

  • “diff”: finite difference

or pass pre-calculated tangents, which overrides tangent estimation.

Parameters
  • fit_points – all B-spline fit points as Vector compatible objects

  • method – tangent estimation method

  • tangents – tangents as Vector compatible objects (optional)

Returns

BSpline

ezdxf.math.rational_spline_from_arc(center: Vector = 0, 0, radius: float = 1, start_angle: float = 0, end_angle: float = 360, segments: int = 1) → BSpline

Returns a rational B-splines for a circular 2D arc.

Parameters
  • center – circle center as Vector compatible object

  • radius – circle radius

  • start_angle – start angle in degrees

  • end_angle – end angle in degrees

  • segments – count of spline segments, at least one segment for each quarter (90 deg), 1 for as few as needed.

New in version 0.13.

ezdxf.math.rational_spline_from_ellipse(ellipse: ConstructionEllipse, segments: int = 1) → BSpline

Returns a rational B-splines for an elliptic arc.

Parameters
  • ellipse – ellipse parameters as ConstructionEllipse object

  • segments – count of spline segments, at least one segment for each quarter (pi/2), 1 for as few as needed.

New in version 0.13.

ezdxf.math.cubic_bezier_from_arc(center: Vector = 0, 0, radius: float = 1, start_angle: float = 0, end_angle: float = 360, segments: int = 1) → Iterable[Bezier4P]

Returns an approximation for a circular 2D arc by multiple cubic Bézier-curves.

Parameters
  • center – circle center as Vector compatible object

  • radius – circle radius

  • start_angle – start angle in degrees

  • end_angle – end angle in degrees

  • segments – count of Bèzier-curve segments, at least one segment for each quarter (90 deg), 1 for as few as possible.

New in version 0.13.

ezdxf.math.cubic_bezier_from_ellipse(ellipse: ConstructionEllipse, segments: int = 1) → Iterable[Bezier4P]

Returns an approximation for an elliptic arc by multiple cubic Bézier-curves.

Parameters
  • ellipse – ellipse parameters as ConstructionEllipse object

  • segments – count of Bèzier-curve segments, at least one segment for each quarter (pi/2),

  • for as few as possible. (1) –

New in version 0.13.

ezdxf.math.cubic_bezier_interpolation(points: Iterable[Vertex]) → List[Bezier4P]

Returns an interpolation curve for given data points as multiple cubic Bézier-curves. Returns n-1 cubic Bézier-curves for n given data points, curve i goes from point[i] to point[i+1].

Parameters

points – data points

New in version 0.13.

Transformation Classes

OCS Class

class ezdxf.math.OCS(extrusion: Vertex = Vector(0.0, 0.0, 1.0))

Establish an OCS for a given extrusion vector.

Parameters

extrusion – extrusion vector.

ux

x-axis unit vector

uy

y-axis unit vector

uz

z-axis unit vector

from_wcs(point: Vertex) → Vertex

Returns OCS vector for WCS point.

points_from_wcs(points: Iterable[Vertex]) → Iterable[Vertex]

Returns iterable of OCS vectors from WCS points.

to_wcs(point: Vertex) → Vertex

Returns WCS vector for OCS point.

points_to_wcs(points: Iterable[Vertex]) → Iterable[Vertex]

Returns iterable of WCS vectors for OCS points.

render_axis(layout: BaseLayout, length: float = 1, colors: Tuple[int, int, int] = 1, 3, 5)

Render axis as 3D lines into a layout.

UCS Class

class ezdxf.math.UCS(origin: Vertex = 0, 0, 0, ux: Vertex = None, uy: Vertex = None, uz: Vertex = None)

Establish an user coordinate system (UCS). The UCS is defined by the origin and two unit vectors for the x-, y- or z-axis, all axis in WCS. The missing axis is the cross product of the given axis.

If x- and y-axis are None: ux = (1, 0, 0), uy = (0, 1, 0), uz = (0, 0, 1).

Unit vectors don’t have to be normalized, normalization is done at initialization, this is also the reason why scaling gets lost by copying or rotating.

Parameters
  • origin – defines the UCS origin in world coordinates

  • ux – defines the UCS x-axis as vector in WCS

  • uy – defines the UCS y-axis as vector in WCS

  • uz – defines the UCS z-axis as vector in WCS

ux

x-axis unit vector

uy

y-axis unit vector

uz

z-axis unit vector

is_cartesian

Returns True if cartesian coordinate system.

copy() → UCS

Returns a copy of this UCS.

New in version 0.11.

to_wcs(point: Vertex) → Vector

Returns WCS point for UCS point.

points_to_wcs(points: Iterable[Vertex]) → Iterable[Vector]

Returns iterable of WCS vectors for UCS points.

direction_to_wcs(vector: Vertex) → Vector

Returns WCS direction for UCS vector without origin adjustment.

from_wcs(point: Vertex) → Vector

Returns UCS point for WCS point.

points_from_wcs(points: Iterable[Vertex]) → Iterable[Vector]

Returns iterable of UCS vectors from WCS points.

direction_from_wcs(vector: Vertex) → Vector

Returns UCS vector for WCS vector without origin adjustment.

to_ocs(point: Vertex) → Vector

Returns OCS vector for UCS point.

The OCS is defined by the z-axis of the UCS.

points_to_ocs(points: Iterable[Vertex]) → Iterable[Vector]

Returns iterable of OCS vectors for UCS points.

The OCS is defined by the z-axis of the UCS.

Parameters

points – iterable of UCS vertices

to_ocs_angle_deg(angle: float) → float

Transforms angle from current UCS to the parent coordinate system (most likely the WCS) including the transformation to the OCS established by the extrusion vector UCS.uz.

Parameters

angle – in UCS in degrees

rotate(axis: Vertex, angle: float) → UCS

Returns a new rotated UCS, with the same origin as the source UCS. The rotation vector is located in the origin and has WCS coordinates e.g. (0, 0, 1) is the WCS z-axis as rotation vector.

New in version 0.11.

Parameters
  • axis – arbitrary rotation axis as vector in WCS

  • angle – rotation angle in radians

rotate_local_x(angle: float) → UCS

Returns a new rotated UCS, rotation axis is the local x-axis.

New in version 0.11.

Parameters

angle – rotation angle in radians

rotate_local_y(angle: float) → UCS

Returns a new rotated UCS, rotation axis is the local y-axis.

New in version 0.11.

Parameters

angle – rotation angle in radians

rotate_local_z(angle: float) → UCS

Returns a new rotated UCS, rotation axis is the local z-axis.

New in version 0.11.

Parameters

angle – rotation angle in radians

shift(delta: Vertex) → UCS

Shifts current UCS by delta vector and returns self.

New in version 0.11.

Parameters

delta – shifting vector

moveto(location: Vertex) → UCS

Place current UCS at new origin location and returns self.

New in version 0.11.

Parameters

location – new origin in WCS

static from_x_axis_and_point_in_xy(origin: Vertex, axis: Vertex, point: Vertex) → UCS

Returns an new UCS defined by the origin, the x-axis vector and an arbitrary point in the xy-plane.

Parameters
  • origin – UCS origin as (x, y, z) tuple in WCS

  • axis – x-axis vector as (x, y, z) tuple in WCS

  • point – arbitrary point unlike the origin in the xy-plane as (x, y, z) tuple in WCS

static from_x_axis_and_point_in_xz(origin: Vertex, axis: Vertex, point: Vertex) → UCS

Returns an new UCS defined by the origin, the x-axis vector and an arbitrary point in the xz-plane.

Parameters
  • origin – UCS origin as (x, y, z) tuple in WCS

  • axis – x-axis vector as (x, y, z) tuple in WCS

  • point – arbitrary point unlike the origin in the xz-plane as (x, y, z) tuple in WCS

static from_y_axis_and_point_in_xy(origin: Vertex, axis: Vertex, point: Vertex) → UCS

Returns an new UCS defined by the origin, the y-axis vector and an arbitrary point in the xy-plane.

Parameters
  • origin – UCS origin as (x, y, z) tuple in WCS

  • axis – y-axis vector as (x, y, z) tuple in WCS

  • point – arbitrary point unlike the origin in the xy-plane as (x, y, z) tuple in WCS

static from_y_axis_and_point_in_yz(origin: Vertex, axis: Vertex, point: Vertex) → UCS

Returns an new UCS defined by the origin, the y-axis vector and an arbitrary point in the yz-plane.

Parameters
  • origin – UCS origin as (x, y, z) tuple in WCS

  • axis – y-axis vector as (x, y, z) tuple in WCS

  • point – arbitrary point unlike the origin in the yz-plane as (x, y, z) tuple in WCS

static from_z_axis_and_point_in_xz(origin: Vertex, axis: Vertex, point: Vertex) → UCS

Returns an new UCS defined by the origin, the z-axis vector and an arbitrary point in the xz-plane.

Parameters
  • origin – UCS origin as (x, y, z) tuple in WCS

  • axis – z-axis vector as (x, y, z) tuple in WCS

  • point – arbitrary point unlike the origin in the xz-plane as (x, y, z) tuple in WCS

static from_z_axis_and_point_in_yz(origin: Vertex, axis: Vertex, point: Vertex) → UCS

Returns an new UCS defined by the origin, the z-axis vector and an arbitrary point in the yz-plane.

Parameters
  • origin – UCS origin as (x, y, z) tuple in WCS

  • axis – z-axis vector as (x, y, z) tuple in WCS

  • point – arbitrary point unlike the origin in the yz-plane as (x, y, z) tuple in WCS

render_axis(layout: BaseLayout, length: float = 1, colors: Tuple[int, int, int] = 1, 3, 5)

Render axis as 3D lines into a layout.

Matrix44

class ezdxf.math.Matrix44(*args)

This is a pure Python implementation for 4x4 transformation matrices, to avoid dependency to big numerical packages like numpy, before binary wheels, installation of these packages wasn’t always easy on Windows.

The utility functions for constructing transformations and transforming vectors and points assumes that vectors are stored as row vectors, meaning when multiplied, transformations are applied left to right (e.g. vAB transforms v by A then by B).

Matrix44 initialization:

  • Matrix44() returns the identity matrix.

  • Matrix44(values) values is an iterable with the 16 components of the matrix.

  • Matrix44(row1, row2, row3, row4) four rows, each row with four values.

__repr__() → str

Returns the representation string of the matrix: Matrix44((col0, col1, col2, col3), (...), (...), (...))

set(*args) → None

Set matrix values.

  • set() creates the identity matrix.

  • set(values) values is an iterable with the 16 components of the matrix.

  • set(row1, row2, row3, row4) four rows, each row with four values.

get_row(row: int) → Tuple[float, …]

Get row as list of of four float values.

Parameters

row – row index [0 .. 3]

set_row(row: int, values: Sequence[float]) → None

Sets the values in a row.

Parameters
  • row – row index [0 .. 3]

  • values – iterable of four row values

get_col(col: int) → Tuple[float, …]

Returns a column as a tuple of four floats.

Parameters

col – column index [0 .. 3]

set_col(col: int, values: Sequence[float])

Sets the values in a column.

Parameters
  • col – column index [0 .. 3]

  • values – iterable of four column values

copy() → Matrix44

Returns a copy of same type.

__copy__() → Matrix44

Returns a copy of same type.

classmethod scale(sx: float, sy: float = None, sz: float = None) → Matrix44

Returns a scaling transformation matrix. If sy is None, sy = sx, and if sz is None sz = sx.

classmethod translate(dx: float, dy: float, dz: float) → Matrix44

Returns a translation matrix for translation vector (dx, dy, dz).

classmethod x_rotate(angle: float) → Matrix44

Returns a rotation matrix about the x-axis.

Parameters

angle – rotation angle in radians

classmethod y_rotate(angle: float) → Matrix44

Returns a rotation matrix about the y-axis.

Parameters

angle – rotation angle in radians

classmethod z_rotate(angle: float) → Matrix44

Returns a rotation matrix about the z-axis.

Parameters

angle – rotation angle in radians

classmethod axis_rotate(axis: Vertex, angle: float) → Matrix44

Returns a rotation matrix about an arbitrary axis.

Parameters
  • axis – rotation axis as (x, y, z) tuple or Vector object

  • angle – rotation angle in radians

classmethod xyz_rotate(angle_x: float, angle_y: float, angle_z: float) → Matrix44

Returns a rotation matrix for rotation about each axis.

Parameters
  • angle_x – rotation angle about x-axis in radians

  • angle_y – rotation angle about y-axis in radians

  • angle_z – rotation angle about z-axis in radians

classmethod perspective_projection(left: float, right: float, top: float, bottom: float, near: float, far: float) → Matrix44

Returns a matrix for a 2D projection.

Parameters
  • left – Coordinate of left of screen

  • right – Coordinate of right of screen

  • top – Coordinate of the top of the screen

  • bottom – Coordinate of the bottom of the screen

  • near – Coordinate of the near clipping plane

  • far – Coordinate of the far clipping plane

classmethod perspective_projection_fov(fov: float, aspect: float, near: float, far: float) → Matrix44

Returns a matrix for a 2D projection.

Parameters
  • fov – The field of view (in radians)

  • aspect – The aspect ratio of the screen (width / height)

  • near – Coordinate of the near clipping plane

  • far – Coordinate of the far clipping plane

static chain(*matrices: Iterable[Matrix44]) → Matrix44

Compose a transformation matrix from one or more matrices.

static ucs(ux: Vertex, uy: Vertex, uz: Vertex) → Matrix44

Returns a matrix for coordinate transformation from WCS to UCS. For transformation from UCS to WCS, transpose the returned matrix.

Parameters
  • ux – x-axis for UCS as unit vector

  • uy – y-axis for UCS as unit vector

  • uz – z-axis for UCS as unit vector

  • origin – UCS origin as location vector

__hash__() → int

Returns hash value of matrix.

__getitem__(index: Tuple[int, int])

Get (row, column) element.

__setitem__(index: Tuple[int, int], value: float)

Set (row, column) element.

__iter__() → Iterable[float]

Iterates over all matrix values.

rows() → Iterable[Tuple[float, …]]

Iterate over rows as 4-tuples.

columns() → Iterable[Tuple[float, …]]

Iterate over columns as 4-tuples.

__mul__(other: Matrix44) → Matrix44

Returns a new matrix as result of the matrix multiplication with another matrix.

__imul__(other: Matrix44) → Matrix44

Inplace multiplication with another matrix.

fast_mul(other: Matrix44) → Matrix44

Multiplies this matrix with other matrix.

Assumes that both matrices have a right column of (0, 0, 0, 1). This is True for matrices composed of rotations, translations and scales. fast_mul is approximately 25% quicker than the *= operator.

transform(vector: Vertex) → ezdxf.math.vector.Vector

Returns a transformed vertex.

transform_direction(vector: Vertex, normalize=False) → ezdxf.math.vector.Vector

Returns a transformed direction vector without translation.

transform_vertices(vectors: Iterable[Vertex]) → Iterable[ezdxf.math.vector.Vector]

Returns an iterable of transformed vertices.

transform_directions(vectors: Iterable[Vertex], normalize=False) → Iterable[ezdxf.math.vector.Vector]

Returns an iterable of transformed direction vectors without translation.

transpose() → None

Swaps the rows for columns inplace.

determinant() → float

Returns determinant.

inverse() → None

Calculates the inverse of the matrix.

Raises

ZeroDivisionError – if matrix has no inverse.

Construction Tools

Vector

class ezdxf.math.Vector(*args)

This is an immutable universal 3D vector object. This class is optimized for universality not for speed. Immutable means you can’t change (x, y, z) components after initialization:

v1 = Vector(1, 2, 3)
v2 = v1
v2.z = 7  # this is not possible, raises AttributeError
v2 = Vector(v2.x, v2.y, 7)  # this creates a new Vector() object
assert v1.z == 3  # and v1 remains unchanged

Vector initialization:

  • Vector(), returns Vector(0, 0, 0)

  • Vector((x, y)), returns Vector(x, y, 0)

  • Vector((x, y, z)), returns Vector(x, y, z)

  • Vector(x, y), returns Vector(x, y, 0)

  • Vector(x, y, z), returns Vector(x, y, z)

Addition, subtraction, scalar multiplication and scalar division left and right handed are supported:

v = Vector(1, 2, 3)
v + (1, 2, 3) == Vector(2, 4, 6)
(1, 2, 3) + v == Vector(2, 4, 6)
v - (1, 2, 3) == Vector(0, 0, 0)
(1, 2, 3) - v == Vector(0, 0, 0)
v * 3 == Vector(3, 6, 9)
3 * v == Vector(3, 6, 9)
Vector(3, 6, 9) / 3 == Vector(1, 2, 3)
-Vector(1, 2, 3) == (-1, -2, -3)

Comparison between vectors and vectors or tuples is supported:

Vector(1, 2, 3) < Vector (2, 2, 2)
(1, 2, 3) < tuple(Vector(2, 2, 2))  # conversion necessary
Vector(1, 2, 3) == (1, 2, 3)

bool(Vector(1, 2, 3)) is True
bool(Vector(0, 0, 0)) is False
x

x-axis value

y

y-axis value

z

z-axis value

xy

Vector as (x, y, 0), projected on the xy-plane.

xyz

Vector as (x, y, z) tuple.

vec2

Real 2D vector as Vec2 object.

magnitude

Length of vector.

magnitude_xy

Length of vector in the xy-plane.

magnitude_square

Square length of vector.

is_null

True for Vector(0, 0, 0).

angle

Angle between vector and x-axis in the xy-plane in radians.

angle_deg

Returns angle of vector and x-axis in the xy-plane in degrees.

spatial_angle

Spatial angle between vector and x-axis in radians.

spatial_angle_deg

Spatial angle between vector and x-axis in degrees.

__str__() → str

Return '(x, y, z)' as string.

__repr__() → str

Return 'Vector(x, y, z)' as string.

__len__() → int

Returns always 3.

__hash__() → int

Returns hash value of vector, enables the usage of vector as key in set and dict.

copy() → Vector

Returns a copy of vector as Vector object.

__copy__() → Vector

Returns a copy of vector as Vector object.

__deepcopy__(memodict: dict) → Vector

copy.deepcopy() support.

__getitem__(index: int) → float

Support for indexing:

  • v[0] is v.x

  • v[1] is v.y

  • v[2] is v.z

__iter__() → Iterable[float]

Returns iterable of x-, y- and z-axis.

__abs__() → float

Returns length (magnitude) of vector.

replace(x: float = None, y: float = None, z: float = None) → Vector

Returns a copy of vector with replaced x-, y- and/or z-axis.

classmethod generate(items: Iterable[Vertex]) → Iterable[Vector]

Returns an iterable of Vector objects.

classmethod list(items: Iterable[Vertex]) → List[Vector]

Returns a list of Vector objects.

classmethod from_angle(angle: float, length: float = 1.0) → Vector

Returns a Vector object from angle in radians in the xy-plane, z-axis = 0.

classmethod from_deg_angle(angle: float, length: float = 1.0) → Vector

Returns a Vector object from angle in degrees in the xy-plane, z-axis = 0.

orthogonal(ccw: bool = True) → Vector

Returns orthogonal 2D vector, z-axis is unchanged.

Parameters

ccw – counter clockwise if True else clockwise

lerp(other: Any, factor=0.5) → Vector

Returns linear interpolation between self and other.

Parameters
  • other – end point as Vector compatible object

  • factor – interpolation factor (0 = self, 1 = other, 0.5 = mid point)

is_parallel(other: Vector, abs_tolr=1e-12) → bool

Returns True if self and other are parallel to vectors.

project(other: Any) → Vector

Returns projected vector of other onto self.

normalize(length: float = 1.0) → Vector

Returns normalized vector, optional scaled by length.

reversed() → Vector

Returns negated vector (-self).

isclose(other: Any, abs_tol: float = 1e-12) → bool

Returns True if self is close to other. Uses math.isclose() to compare all axis.

__neg__() → Vector

Returns negated vector (-self).

__bool__() → bool

Returns True if vector is not (0, 0, 0).

__eq__(other: Any) → bool

Equal operator.

Parameters

otherVector compatible object

__lt__(other: Any) → bool

Lower than operator.

Parameters

otherVector compatible object

__add__(other: Any) → Vector

Add operator: self + other

Parameters

otherVector compatible object

__radd__(other: Any) → Vector

RAdd operator: other + self

Parameters

otherVector compatible object

__sub__(other: Any) → Vector

Sub operator: self - other

Parameters

otherVector compatible object

__rsub__(other: Any) → Vector

RSub operator: other - self

Parameters

otherVector compatible object

__mul__(other: float) → Vector

Mul operator: self * other

Parameters

other – scale factor

__rmul__(other: float) → Vector

RMul operator: other * self

Parameters

other – scale factor

__truediv__(other: float) → Vector

Div operator: self / other

Parameters

other – scale factor

__div__(other: float) → Vector

Div operator: self / other

Parameters

other – scale factor

__rtruediv__(other: float) → Vector

RDiv operator: other / self

Parameters

other – scale factor

__rdiv__(other: float) → Vector

RDiv operator: other / self

Parameters

other – scale factor

dot(other: Any) → float

Dot operator: self . other

Parameters

otherVector compatible object

cross(other: Any) → Vector

Dot operator: self x other

Parameters

otherVector compatible object

distance(other: Any) → float

Returns distance between self and other vector.

angle_about(base: Vector, target: Vector) → float

Returns counter clockwise angle in radians about self from base to target when projected onto the plane defined by self as the normal vector.

Parameters
  • base – base vector, defines angle 0

  • target – target vector

angle_between(other: Any) → float

Returns angle between self and other in radians. +angle is counter clockwise orientation.

Parameters

otherVector compatible object

rotate(angle: float) → Vector

Returns vector rotated about angle around the z-axis.

Parameters

angle – angle in radians

rotate_deg(angle: float) → Vector

Returns vector rotated about angle around the z-axis.

Parameters

angle – angle in degrees

ezdxf.math.X_AXIS

Vector(1, 0, 0)

ezdxf.math.Y_AXIS

Vector(0, 1, 0)

ezdxf.math.Z_AXIS

Vector(0, 0, 1)

ezdxf.math.NULLVEC

Vector(0, 0, 0)

Vec2

class ezdxf.math.Vec2(v)

Vec2 represents a special 2D vector (x, y). The Vec2 class is optimized for speed and not immutable, iadd(), isub(), imul() and idiv() modifies the vector itself, the Vector class returns a new object.

Vec2 initialization accepts float-tuples (x, y[, z]), two floats or any object providing x and y attributes like Vec2 and Vector objects.

Parameters
  • v – vector object with x and y attributes/properties or a sequence of float [x, y, ...] or x-axis as float if argument y is not None

  • y – second float for Vec2(x, y)

Vec2 implements a subset of Vector.

Plane

class ezdxf.math.Plane(normal: Vector, distance: float)

Represents a plane in 3D space as normal vector and the perpendicular distance from origin.

New in version 0.11.

normal

Normal vector of the plane.

distance_from_origin

The (perpendicular) distance of the plane from origin (0, 0, 0).

vector

Returns the location vector.

classmethod from_3p(a: Vector, b: Vector, c: Vector) → Plane

Returns a new plane from 3 points in space.

classmethod from_vector(vector) → Plane

Returns a new plane from a location vector.

copy() → Plane

Returns a copy of the plane.

signed_distance_to(v: Vector) → float

Returns signed distance of vertex v to plane, if distance is > 0, v is in ‘front’ of plane, in direction of the normal vector, if distance is < 0, v is at the ‘back’ of the plane, in the opposite direction of the normal vector.

distance_to(v: Vector) → float

Returns absolute (unsigned) distance of vertex v to plane.

is_coplanar_vertex(v: Vector, abs_tol=1e-09) → bool

Returns True if vertex v is coplanar, distance from plane to vertex v is 0.

is_coplanar_plane(p: Plane, abs_tol=1e-09) → bool

Returns True if plane p is coplanar, normal vectors in same or opposite direction.

BoundingBox

class ezdxf.math.BoundingBox(vertices: Iterable[Vertex] = None)

3D bounding box.

Parameters

vertices – iterable of (x, y, z) tuples or Vector objects

extmin

“lower left” corner of bounding box

extmax

“upper right” corner of bounding box

property center

Returns center of bounding box.

extend(vertices: Iterable[Vertex]) → None

Extend bounds by vertices.

Parameters

vertices – iterable of (x, y, z) tuples or Vector objects

property has_data

Returns True if data is available

inside(vertex: Vertex) → bool

Returns True if vertex is inside bounding box.

property size

Returns size of bounding box.

BoundingBox2d

class ezdxf.math.BoundingBox2d(vertices: Iterable[Vertex] = None)

Optimized 2D bounding box.

Parameters

vertices – iterable of (x, y[, z]) tuples or Vector objects

extmin

“lower left” corner of bounding box

extmax

“upper right” corner of bounding box

property center

Returns center of bounding box.

extend(vertices: Iterable[Vertex]) → None

Extend bounds by vertices.

Parameters

vertices – iterable of (x, y[, z]) tuples or Vector objects

property has_data

Returns True if data is available

inside(vertex: Vertex) → bool

Returns True if vertex is inside bounding box.

property size

Returns size of bounding box.

ConstructionRay

class ezdxf.math.ConstructionRay(p1: Vertex, p2: Vertex = None, angle: float = None)

Infinite 2D construction ray as immutable object.

Parameters
  • p1 – definition point 1

  • p2 – ray direction as 2nd point or None

  • angle – ray direction as angle in radians or None

location

Location vector as Vec2.

direction

Direction vector as Vec2.

slope

Slope of ray or None if vertical.

angle

Angle between x-axis and ray in radians.

angle_deg

Angle between x-axis and ray in degrees.

is_vertical

True if ray is vertical (parallel to y-axis).

is_horizontal

True if ray is horizontal (parallel to x-axis).

__str__()

Return str(self).

is_parallel(self, other: ConstructionRay) → bool

Returns True if rays are parallel.

intersect(other: ConstructionRay) → Vec2

Returns the intersection point as (x, y) tuple of self and other.

Raises

ParallelRaysError – if rays are parallel

orthogonal(location: ‘Vertex’) → ConstructionRay

Returns orthogonal ray at location.

bisectrix(other: ConstructionRay) → ConstructionRay:

Bisectrix between self and other.

yof(x: float) → float

Returns y-value of ray for x location.

Raises

ArithmeticError – for vertical rays

xof(y: float) → float

Returns x-value of ray for y location.

Raises

ArithmeticError – for horizontal rays

ConstructionLine

class ezdxf.math.ConstructionLine(start: Vertex, end: Vertex)

2D ConstructionLine is similar to ConstructionRay, but has a start- and endpoint. The direction of line goes from start- to endpoint, “left of line” is always in relation to this line direction.

Parameters
  • start – start point of line as Vec2 compatible object

  • end – end point of line as Vec2 compatible object

start

start point as Vec2

end

end point as Vec2

bounding_box

bounding box of line as BoundingBox2d object.

ray

collinear ConstructionRay.

is_vertical

True if line is vertical.

__str__()

Return str(self).

translate(dx: float, dy: float) → None

Move line about dx in x-axis and about dy in y-axis.

Parameters
  • dx – translation in x-axis

  • dy – translation in y-axis

length() → float

Returns length of line.

midpoint() → Vec2

Returns mid point of line.

inside_bounding_box(point: Vertex) → bool

Returns True if point is inside of line bounding box.

intersect(other: ConstructionLine, abs_tol: float = 1e-10) → Optional[Vec2]

Returns the intersection point of to lines or None if they have no intersection point.

Parameters
has_intersection(other: ConstructionLine, abs_tol: float = 1e-10) → bool

Returns True if has intersection with other line.

is_point_left_of_line(point: Vertex, colinear=False) → bool

Returns True if point is left of construction line in relation to the line direction from start to end.

If colinear is True, a colinear point is also left of the line.

ConstructionCircle

class ezdxf.math.ConstructionCircle(center: Vertex, radius: float = 1.0)

Circle construction tool.

Parameters
  • center – center point as Vec2 compatible object

  • radius – circle radius > 0

center

center point as Vec2

radius

radius as float

bounding_box

2D bounding box of circle as BoundingBox2d object.

static from_3p(p1: Vertex, p2: Vertex, p3: Vertex) → ConstructionCircle

Creates a circle from three points, all points have to be compatible to Vec2 class.

__str__() → str

Returns string representation of circle ConstructionCircle(center, radius).

translate(dx: float, dy: float) → None

Move circle about dx in x-axis and about dy in y-axis.

Parameters
  • dx – translation in x-axis

  • dy – translation in y-axis

point_at(angle: float) → Vec2

Returns point on circle at angle as Vec2 object.

Parameters

angle – angle in radians

inside(point: Vertex) → bool

Returns True if point is inside circle.

tangent(angle: float) → ConstructionRay

Returns tangent to circle at angle as ConstructionRay object.

Parameters

angle – angle in radians

intersect_ray(ray: ConstructionRay, abs_tol: float = 1e-10) → Sequence[Vec2]

Returns intersection points of circle and ray as sequence of Vec2 objects.

Parameters
  • ray – intersection ray

  • abs_tol – absolute tolerance for tests (e.g. test for tangents)

Returns

tuple of Vec2 objects

tuple size

Description

0

no intersection

1

ray is a tangent to circle

2

ray intersects with the circle

intersect_circle(other: ConstructionCircle, abs_tol: float = 1e-10) → Sequence[Vec2]

Returns intersection points of two circles as sequence of Vec2 objects.

Parameters
  • other – intersection circle

  • abs_tol – absolute tolerance for tests (e.g. test for circle touch point)

Returns

tuple of Vec2 objects

tuple size

Description

0

no intersection

1

circle touches the other circle at one point

2

circle intersects with the other circle

ConstructionArc

class ezdxf.math.ConstructionArc(center: Vertex = 0, 0, radius: float = 1, start_angle: float = 0, end_angle: float = 360, is_counter_clockwise: bool = True)

This is a helper class to create parameters for the DXF Arc class.

ConstructionArc represents a 2D arc in the xy-plane, use an UCS to place arc in 3D space, see method add_to_layout().

Implements the 2D transformation tools: translate(), scale_uniform() and rotate_z()

Parameters
  • center – center point as Vec2 compatible object

  • radius – radius

  • start_angle – start angle in degrees

  • end_angle – end angle in degrees

  • is_counter_clockwise – swaps start- and end angle if False

center

center point as Vec2

radius

radius as float

start_angle

start angle in degrees

end_angle

end angle in degrees

angle_span

Returns angle span of arc from start- to end param.

start_angle_rad

start angle in radians.

end_angle_rad

end angle in radians.

start_point

start point of arc as Vec2.

end_point

end point of arc as Vec2.

bounding_box

bounding box of arc as BoundingBox2d.

angles(num: int) → Iterable[float]

Returns num angles from start- to end angle in degrees in counter clockwise order.

All angles are normalized in the range from [0, 360).

vertices(a: Iterable[float]) → Iterable[ezdxf.math.vector.Vec2]

Yields vertices on arc for angles in iterable a in WCS as location vectors.

Parameters

a – angles in the range from 0 to 360 in degrees, arc goes counter clockwise around the z-axis, WCS x-axis = 0 deg.

tangents(a: Iterable[float]) → Iterable[ezdxf.math.vector.Vec2]

Yields tangents on arc for angles in iterable a in WCS as direction vectors.

Parameters

a – angles in the range from 0 to 360 in degrees, arc goes counter clockwise around the z-axis, WCS x-axis = 0 deg.

translate(dx: float, dy: float) → ConstructionArc

Move arc about dx in x-axis and about dy in y-axis, returns self (floating interface).

Parameters
  • dx – translation in x-axis

  • dy – translation in y-axis

scale_uniform(s: float) → ConstructionArc

Scale arc inplace uniform about s in x- and y-axis, returns self (floating interface).

rotate_z(angle: float) → ConstructionArc

Rotate arc inplace about z-axis, returns self (floating interface).

Parameters

angle – rotation angle in degrees

classmethod from_2p_angle(start_point: Vertex, end_point: Vertex, angle: float, ccw: bool = True) → ConstructionArc

Create arc from two points and enclosing angle. Additional precondition: arc goes by default in counter clockwise orientation from start_point to end_point, can be changed by ccw = False.

Parameters
  • start_point – start point as Vec2 compatible object

  • end_point – end point as Vec2 compatible object

  • angle – enclosing angle in degrees

  • ccw – counter clockwise direction if True

classmethod from_2p_radius(start_point: Vertex, end_point: Vertex, radius: float, ccw: bool = True, center_is_left: bool = True) → ConstructionArc

Create arc from two points and arc radius. Additional precondition: arc goes by default in counter clockwise orientation from start_point to end_point can be changed by ccw = False.

The parameter center_is_left defines if the center of the arc is left or right of the line from start_point to end_point. Parameter ccw = False swaps start- and end point, which inverts the meaning of center_is_left.

Parameters
  • start_point – start point as Vec2 compatible object

  • end_point – end point as Vec2 compatible object

  • radius – arc radius

  • ccw – counter clockwise direction if True

  • center_is_left – center point of arc is left of line from start- to end point if True

classmethod from_3p(start_point: Vertex, end_point: Vertex, def_point: Vertex, ccw: bool = True) → ConstructionArc

Create arc from three points. Additional precondition: arc goes in counter clockwise orientation from start_point to end_point.

Parameters
  • start_point – start point as Vec2 compatible object

  • end_point – end point as Vec2 compatible object

  • def_point – additional definition point as Vec2 compatible object

  • ccw – counter clockwise direction if True

add_to_layout(layout: BaseLayout, ucs: UCS = None, dxfattribs: dict = None) → Arc

Add arc as DXF Arc entity to a layout.

Supports 3D arcs by using an UCS. An ConstructionArc is always defined in the xy-plane, but by using an arbitrary UCS, the arc can be placed in 3D space, automatically OCS transformation included.

Parameters
  • layout – destination layout as BaseLayout object

  • ucs – place arc in 3D space by UCS object

  • dxfattribs – additional DXF attributes for DXF Arc entity

ConstructionEllipse

class ezdxf.math.ConstructionEllipse(center: Vertex = Vector(0.0, 0.0, 0.0), major_axis: Vertex = Vector(1.0, 0.0, 0.0), extrusion: Vertex = Vector(0.0, 0.0, 1.0), ratio: float = 1, start_param: float = 0, end_param: float = 6.283185307179586, ccw: bool = True)

This is a helper class to create parameters for 3D ellipses.

Parameters
  • center – 3D center point

  • major_axis – major axis as 3D vector

  • extrusion – normal vector of ellipse plane

  • ratio – ratio of minor axis to major axis

  • start_param – start param in radians

  • end_param – end param in radians

  • ccw – is counter clockwise flag - swaps start- and end param if False

center

center point as Vector

major_axis

major axis as Vector

minor_axis

minor axis as Vector, automatically calculated from major_axis and extrusion.

extrusion

extrusion vector (normal of ellipse plane) as Vector

ratio

ratio of minor axis to major axis (float)

start

start param in radians (float)

end

end param in radians (float)

start_point

Returns start point of ellipse as Vector.

end_point

Returns end point of ellipse as Vector.

to_ocs() → ConstructionEllipse

Returns ellipse parameters as OCS representation.

OCS elevation is stored in center.z.

params(num: int) → Iterable[float]

Returns num params from start- to end param in counter clockwise order.

All params are normalized in the range from [0, 2pi).

vertices(params: Iterable[float]) → Iterable[ezdxf.math.vector.Vector]

Yields vertices on ellipse for iterable params in WCS.

Parameters

params – param values in the range from 0 to 2*pi in radians, param goes counter clockwise around the extrusion vector, major_axis = local x-axis = 0 rad.

params_from_vertices(vertices: Iterable[Vertex]) → Iterable[float]

Yields ellipse params for all given vertices.

The vertex don’t has to be exact on the ellipse curve or in the range from start- to end param or even in the ellipse plane. Param is calculated from the intersection point of the ray projected on the ellipse plane from the center of the ellipse through the vertex.

Warning

An input for start- and end vertex at param 0 and 2*pi return unpredictable results because of floating point inaccuracy, sometimes 0 and sometimes 2*pi.

dxfattribs() → Dict

Returns required DXF attributes to build an ELLIPSE entity.

Entity ELLIPSE has always a ratio in range from 1e-6 to 1.

main_axis_points() → Iterable[ezdxf.math.vector.Vector]

Yields main axis points of ellipse in the range from start- to end param.

classmethod from_arc(center: Vertex = 0, 0, 0, radius: float = 1, extrusion: Vertex = 0, 0, 1, start_angle: float = 0, end_angle: float = 360, ccw: bool = True) → ConstructionEllipse

Returns ConstructionEllipse from arc or circle.

Arc and Circle parameters defined in OCS.

Parameters
  • center – center in OCS

  • radius – arc or circle radius

  • extrusion – OCS extrusion vector

  • start_angle – start angle in degrees

  • end_angle – end angle in degrees

  • ccw – arc curve goes counter clockwise from start to end if True

transform(m: Matrix44)

Transform ellipse in place by transformation matrix m.

swap_axis() → None

Swap axis and adjust start- and end parameter.

add_to_layout(layout: BaseLayout, dxfattribs: dict = None) → Ellipse

Add ellipse as DXF Ellipse entity to a layout.

Parameters
  • layout – destination layout as BaseLayout object

  • dxfattribs – additional DXF attributes for DXF Ellipse entity

ConstructionBox

class ezdxf.math.ConstructionBox(center: Vertex = 0, 0, width: float = 1, height: float = 1, angle: float = 0)

Helper class to create rectangles.

Parameters
  • center – center of rectangle

  • width – width of rectangle

  • height – height of rectangle

  • angle – angle of rectangle in degrees

center

box center

width

box width

height

box height

angle

rotation angle in degrees

corners

box corners as sequence of Vec2 objects.

bounding_box

BoundingBox2d

incircle_radius

incircle radius

circumcircle_radius

circum circle radius

__iter__() → Iterable[Vec2]

Iterable of box corners as Vec2 objects.

__getitem__(corner) → Vec2

Get corner by index corner, list like slicing is supported.

__repr__() → str

Returns string representation of box as ConstructionBox(center, width, height, angle)

classmethod from_points(p1: Vertex, p2: Vertex) → ConstructionBox

Creates a box from two opposite corners, box sides are parallel to x- and y-axis.

Parameters
  • p1 – first corner as Vec2 compatible object

  • p2 – second corner as Vec2 compatible object

translate(dx: float, dy: float) → None

Move box about dx in x-axis and about dy in y-axis.

Parameters
  • dx – translation in x-axis

  • dy – translation in y-axis

expand(dw: float, dh: float) → None

Expand box: dw expand width, dh expand height.

scale(sw: float, sh: float) → None

Scale box: sw scales width, sh scales height.

rotate(angle: float) → None

Rotate box by angle in degrees.

is_inside(point: Vertex) → bool

Returns True if point is inside of box.

is_any_corner_inside(other: ConstructionBox) → bool

Returns True if any corner of other box is inside this box.

is_overlapping(other: ConstructionBox) → bool

Returns True if this box and other box do overlap.

border_lines() → Sequence[ConstructionLine]

Returns border lines of box as sequence of ConstructionLine.

intersect(line: ConstructionLine) → List[Vec2]

Returns 0, 1 or 2 intersection points between line and box border lines.

Parameters

line – line to intersect with border lines

Returns

list of intersection points

list size

Description

0

no intersection

1

line touches box at one corner

2

line intersects with box

Shape2d

class ezdxf.math.Shape2d(vertices: Iterable[Vertex] = None)

2D geometry object as list of Vec2 objects, vertices can be moved, rotated and scaled.

Parameters

vertices – iterable of Vec2 compatible objects.

vertices

List of Vec2 objects

bounding_box

BoundingBox2d

__len__() → int

Returns count of vertices.

__getitem__(item) → Vec2

Get vertex by index item, supports list like slicing.

append(vertex: Vertex) → None

Append single vertex.

Parameters

vertex – vertex as Vec2 compatible object

extend(vertices: Iterable) → None

Append multiple vertices.

Parameters

vertices – iterable of vertices as Vec2 compatible objects

translate(vector: Vertex) → None

Translate shape about vector.

scale(sx: float = 1.0, sy: float = 1.0) → None

Scale shape about sx in x-axis and sy in y-axis.

scale_uniform(scale: float) → None

Scale shape uniform about scale in x- and y-axis.

rotate(angle: float, center: Vertex = None) → None

Rotate shape around rotation center about angle in degrees.

rotate_rad(angle: float, center: Vertex = None) → None

Rotate shape around rotation center about angle in radians.

offset(offset: float, closed: bool = False) → ezdxf.math.shape.Shape2d

Returns a new offset shape, for more information see also ezdxf.math.offset_vertices_2d() function.

New in version 0.11.

Parameters
  • offset – line offset perpendicular to direction of shape segments defined by vertices order, offset > 0 is ‘left’ of line segment, offset < 0 is ‘right’ of line segment

  • closedTrue to handle as closed shape

convex_hull() → ezdxf.math.shape.Shape2d

Returns convex hull as new shape.

Curves

BSpline

class ezdxf.math.BSpline(control_points: Iterable[Vertex], order: int = 4, knots: Iterable[float] = None, weights: Iterable[float] = None)

Representation of a B-spline curve, using an uniform open knot vector (“clamped”).

Parameters
  • control_points – iterable of control points as Vector compatible objects

  • order – spline order (degree + 1)

  • knots – iterable of knot values

  • weights – iterable of weight values

control_points

Control points as list of Vector

count

Count of control points, (n + 1 in text book notation).

degree

Degree (p) of B-spline = order - 1

order

Order of B-spline = degree + 1

max_t

Biggest knot value.

is_rational

Returns True if curve is a rational B-spline. (has weights)

knots() → List[float]

Returns a list of knot values as floats, the knot vector always has order + count values (n + p + 2 in text book notation).

normalize_knots()

Normalize knot vector into range [0, 1].

weights() → List[float]

Returns a list of weights values as floats, one for each control point or an empty list.

params(segments: int) → Iterable[float]

Yield evenly spaced parameters from 0 to max_t for given segment count.

reverse() → BSpline

Returns a new BSpline with reversed control point order.

point(t: float) → Vector

Returns point for parameter t.

Parameters

t – parameter in range [0, max_t]

points(t: float) → List[Vector]

Yields points for parameter vector t.

Parameters

t – parameters in range [0, max_t]

derivative(t: float, n: int = 2) → List[Vector]

Return point and derivatives up to n <= degree for parameter t.

e.g. n=1 returns point and 1st derivative.

Parameters
  • t – parameter in range [0, max_t]

  • n – compute all derivatives up to n <= degree

Returns

n+1 values as Vector objects

derivatives(t: Iterable[float], n: int = 2) → Iterable[List[Vector]]

Yields points and derivatives up to n <= degree for parameter vector t.

e.g. n=1 returns point and 1st derivative.

Parameters
  • t – parameters in range [0, max_t]

  • n – compute all derivatives up to n <= degree

Returns

List of n+1 values as Vector objects

insert_knot(t: float) → None

Insert additional knot, without altering the curve shape.

Parameters

t – position of new knot 0 < t < max_t

approximate(segments: int = 20) → Iterable[Vector]

Approximates curve by vertices as Vector objects, vertices count = segments + 1.

static from_ellipse(ellipse: ConstructionEllipse) → BSpline

Returns the ellipse as BSpline of 2nd degree with as few control points as possible.

static from_arc(arc: ConstructionArc) → BSpline

Returns the arc as BSpline of 2nd degree with as few control points as possible.

static from_fit_points(points: Iterable[Vertex], degree: int = 3, method='chord') → BSpline

Returns BSpline defined by fit points.

static ellipse_approximation(ellipse: ConstructionEllipse, num: int = 16) → BSpline

Returns an ellipse approximation as BSpline with num control points.

static arc_approximation(arc: ConstructionArc, num: int = 16) → BSpline

Returns an arc approximation as BSpline with num control points.

transform(m: Matrix44) → BSpline

Transform B-spline by transformation matrix m inplace.

New in version 0.13.

bezier_decomposition() → Iterable[List[Vector]]

Decompose a non-rational B-spline into multiple Bézier curves.

This is the preferred method to represent the most common non-rational B-splines of 3rd degree by cubic Bézier curves, which are often supported by render backends.

Returns

Yields control points of Bézier curves, each Bézier segment has degree+1 control points e.g. B-spline of 3rd degree yields cubic Bézier curves of 4 control points.

cubic_bezier_approximation(level: int = 3, segments: int = None) → Iterable[Bezier4P]

Approximate arbitrary B-splines (degree != 3 and/or rational) by multiple segments of cubic Bézier curves. The choice of cubic Bézier curves is based on the widely support of this curves by many render backends. For cubic non-rational B-splines, which is maybe the most common used B-spline, is bezier_decomposition() the better choice.

1. approximation by level: an educated guess, the first level of approximation segments is based on the count of control points and their distribution along the B-spline, every additional level is a subdivision of the previous level. E.g. a B-Spline of 8 control points has 7 segments at the first level, 14 at the 2nd level and 28 at the 3rd level, a level >= 3 is recommended.

  1. approximation by a given count of evenly distributed approximation segments.

Parameters
  • level – subdivision level of approximation segments (ignored if argument segments != None)

  • segments – absolute count of approximation segments

Returns

Yields control points of cubic Bézier curves as Bezier4P objects

BSplineU

class ezdxf.math.BSplineU(control_points: Iterable[Vertex], order: int = 4, knots: Iterable[float] = None, weights: Iterable[float] = None)

Representation of an uniform (periodic) B-spline curve (open curve).

BSplineClosed

class ezdxf.math.BSplineClosed(control_points: Iterable[Vertex], order: int = 4, knots: Iterable[float] = None, weights: Iterable[float] = None)

Representation of a closed uniform B-spline curve (closed curve).

Bezier

class ezdxf.math.Bezier(defpoints: Iterable[Vertex])

A Bézier curve is a parametric curve used in computer graphics and related fields. Bézier curves are used to model smooth curves that can be scaled indefinitely. “Paths”, as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves. Paths are not bound by the limits of rasterized images and are intuitive to modify. (Source: Wikipedia)

This is a general implementation which works with any count of definition points greater than 2, but it is a simple and slow implementation. For more performance look at the specialized Bezier4P class.

Parameters

defpoints – iterable of definition points as Vector compatible objects.

control_points

Control points as list of Vector objects.

params(segments: int) → Iterable[float]

Yield evenly spaced parameters from 0 to 1 for given segment count.

approximate(segments: int = 20) → Iterable[Vector]

Approximates curve by vertices as Vector objects, vertices count = segments + 1.

point(t: float) → Vector

Returns a point for parameter t in range [0, 1] as Vector object.

points(t: Iterable[float]) → Iterable[Vector]

Yields multiple points for parameters in vector t as Vector objects. Parameters have to be in range [0, 1].

derivative(t: float) → Tuple[Vector, Vector, Vector]

Returns (point, 1st derivative, 2nd derivative) tuple for parameter t in range [0, 1] as Vector objects.

derivatives(t: Iterable[float]) → Iterable[Tuple[Vector, Vector, Vector]]

Returns multiple (point, 1st derivative, 2nd derivative) tuples for parameter vector t as Vector objects. Parameters in range [0, 1]

Bezier4P

class ezdxf.math.Bezier4P(defpoints: Sequence[Vertex])

Implements an optimized cubic Bézier curve for exact 4 control points. A Bézier curve is a parametric curve, parameter t goes from 0 to 1, where 0 is the first control point and 1 is the fourth control point.

Special behavior:

  • 2D control points in, returns 2D results as Vec2 objects

  • 3D control points in, returns 3D results as Vector objects

Parameters

defpoints – iterable of definition points as Vec2 or Vector compatible objects.

control_points

control points as list of (x, y, z), z-axis is 0 for 2D curves.

to2d() → Bezier4P

Returns the Bèzier-curve with 2d control points. (discards the z-axis)

to3d() → Bezier4P

Returns the Bèzier-curve with 3d control points.

point(t: float) → Union[Vector, Vec2]

Returns point for location t` at the Bèzier-curve.

Parameters

t – curve position in the range [0, 1]

tangent(t: float) → Union[Vector, Vec2]

Returns direction vector of tangent for location t at the Bèzier-curve.

Parameters

t – curve position in the range [0, 1]

approximate(segments: int) → Iterable[Union[Vector, Vec2]]

Approximate Bézier curve by vertices, yields segments + 1 vertices as (x, y[, z]) tuples.

Parameters

segments – count of segments for approximation

approximated_length(segments: int = 100) → float

Returns estimated length of Bèzier-curve as approximation by line segments.

reverse() → Bezier4P

Returns a new Bèzier-curve with reversed control point order.

BezierSurface

class ezdxf.math.BezierSurface(defpoints: List[List[Sequence[float]]])

BezierSurface defines a mesh of m x n control points. This is a parametric surface, which means the m-dimension goes from 0 to 1 as parameter u and the n-dimension goes from 0 to 1 as parameter v.

Parameters

defpoints – matrix (list of lists) of m rows and n columns: [ [m1n1, m1n2, … ], [m2n1, m2n2, …] … ] each element is a 3D location as (x, y, z) tuple.

nrows

count of rows (m-dimension)

ncols

count of columns (n-dimension)

point(u: float, v: float) → Sequence[float]

Returns a point for location (u, v) at the Bézier surface as (x, y, z) tuple, parameters u and v in the range of [0, 1].

approximate(usegs: int, vsegs: int) → List[List[Sequence[float]]]

Approximate surface as grid of (x, y, z) tuples.

Parameters
  • usegs – count of segments in u-direction (m-dimension)

  • vsegs – count of segments in v-direction (n-dimension)

Returns

list of usegs + 1 rows, each row is a list of vsegs + 1 vertices as (x, y, z) tuples.

EulerSpiral

class ezdxf.math.EulerSpiral(curvature: float = 1.0)

This class represents an euler spiral (clothoid) for curvature (Radius of curvature).

This is a parametric curve, which always starts at the origin = (0, 0).

Parameters

curvature – radius of curvature

radius(t: float) → float

Get radius of circle at distance t.

tangent(t: float) → Vector

Get tangent at distance t as :class.`Vector` object.

distance(radius: float) → float

Get distance L from origin for radius.

point(t: float) → Vector

Get point at distance t as :class.`Vector`.

circle_center(t: float) → Vector

Get circle center at distance t.

Changed in version 0.10: renamed from circle_midpoint

approximate(length: float, segments: int) → Iterable[Vector]

Approximate curve of length with line segments.

Generates segments+1 vertices as Vector objects.

bspline(length: float, segments: int = 10, degree: int = 3, method: str = 'uniform') → BSpline

Approximate euler spiral as B-spline.

Parameters
  • length – length of euler spiral

  • segments – count of fit points for B-spline calculation

  • degree – degree of BSpline

  • method – calculation method for parameter vector t

Returns

BSpline

Linear Algebra

Functions

ezdxf.math.gauss_jordan_solver(A: Iterable[Iterable[float]], B: Iterable[Iterable[float]]) → Tuple[Matrix, Matrix]

Solves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B by the Gauss-Jordan algorithm, which is the slowest of all, but it is very reliable. Returns a copy of the modified input matrix A and the result matrix x.

Internally used for matrix inverse calculation.

Parameters
  • A – matrix [[a11, a12, …, a1n], [a21, a22, …, a2n], [a21, a22, …, a2n], … [an1, an2, …, ann]]

  • B – matrix [[b11, b12, …, b1m], [b21, b22, …, b2m], … [bn1, bn2, …, bnm]]

Returns

2-tuple of Matrix objects

Raises

ZeroDivisionError – singular matrix

New in version 0.13.

ezdxf.math.gauss_jordan_inverse(A: Iterable[Iterable[float]]) → Matrix

Returns the inverse of matrix A as Matrix object.

Hint

For small matrices (n<10) is this function faster than LUDecomposition(m).inverse() and as fast even if the decomposition is already done.

Raises

ZeroDivisionError – singular matrix

New in version 0.13.

ezdxf.math.gauss_vector_solver(A: Iterable[Iterable[float]], B: Iterable[float]) → List[float]

Solves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as vector B with n elements by the Gauss-Elimination algorithm, which is faster than the Gauss-Jordan algorithm. The speed improvement is more significant for solving multiple right-hand side quantities as matrix at once.

Reference implementation for error checking.

Parameters
  • A – matrix [[a11, a12, …, a1n], [a21, a22, …, a2n], [a21, a22, …, a2n], … [an1, an2, …, ann]]

  • B – vector [b1, b2, …, bn]

Returns

vector as list of floats

Raises

ZeroDivisionError – singular matrix

New in version 0.13.

ezdxf.math.gauss_matrix_solver(A: Iterable[Iterable[float]], B: Iterable[Iterable[float]]) → Matrix

Solves the linear equation system given by a nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B by the Gauss-Elimination algorithm, which is faster than the Gauss-Jordan algorithm.

Reference implementation for error checking.

Parameters
  • A – matrix [[a11, a12, …, a1n], [a21, a22, …, a2n], [a21, a22, …, a2n], … [an1, an2, …, ann]]

  • B – matrix [[b11, b12, …, b1m], [b21, b22, …, b2m], … [bn1, bn2, …, bnm]]

Returns

matrix as Matrix object

Raises

ZeroDivisionError – singular matrix

New in version 0.13.

ezdxf.math.tridiagonal_vector_solver(A: Iterable[Iterable[float]], B: Iterable[float]) → List[float]

Solves the linear equation system given by a tri-diagonal nxn Matrix A . x = B, right-hand side quantities as vector B. Matrix A is diagonal matrix defined by 3 diagonals [-1 (a), 0 (b), +1 (c)].

Note: a0 is not used but has to be present, cn-1 is also not used and must not be present.

If an ZeroDivisionError exception occurs, the equation system can possibly be solved by BandedMatrixLU(A, 1, 1).solve_vector(B)

Parameters
  • A

    diagonal matrix [[a0..an-1], [b0..bn-1], [c0..cn-1]]

    [[b0, c0, 0, 0, ...],
    [a1, b1, c1, 0, ...],
    [0, a2, b2, c2, ...],
    ... ]
    

  • B – iterable of floats [[b1, b1, …, bn]

Returns

list of floats

Raises

ZeroDivisionError – singular matrix

New in version 0.13.

ezdxf.math.tridiagonal_matrix_solver(A: Iterable[Iterable[float]], B: Iterable[Iterable[float]]) → Matrix

Solves the linear equation system given by a tri-diagonal nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B. Matrix A is diagonal matrix defined by 3 diagonals [-1 (a), 0 (b), +1 (c)].

Note: a0 is not used but has to be present, cn-1 is also not used and must not be present.

If an ZeroDivisionError exception occurs, the equation system can possibly be solved by BandedMatrixLU(A, 1, 1).solve_vector(B)

Parameters
  • A

    diagonal matrix [[a0..an-1], [b0..bn-1], [c0..cn-1]]

    [[b0, c0, 0, 0, ...],
    [a1, b1, c1, 0, ...],
    [0, a2, b2, c2, ...],
    ... ]
    

  • B – matrix [[b11, b12, …, b1m], [b21, b22, …, b2m], … [bn1, bn2, …, bnm]]

Returns

matrix as Matrix object

Raises

ZeroDivisionError – singular matrix

New in version 0.13.

ezdxf.math.banded_matrix(A: Matrix, check_all=True) → Tuple[int, int]

Transform matrix A into a compact banded matrix representation. Returns compact representation as Matrix object and lower- and upper band count m1 and m2.

Parameters
  • A – input Matrix

  • check_all – check all diagonals if True or abort testing after first all zero diagonal if False.

ezdxf.math.detect_banded_matrix(A: Matrix, check_all=True) → Tuple[int, int]

Returns lower- and upper band count m1 and m2.

Parameters
  • A – input Matrix

  • check_all – check all diagonals if True or abort testing after first all zero diagonal if False.

ezdxf.math.compact_banded_matrix(A: Matrix, m1: int, m2: int) → Matrix

Returns compact banded matrix representation as Matrix object.

Parameters
  • A – matrix to transform

  • m1 – lower band count, excluding main matrix diagonal

  • m2 – upper band count, excluding main matrix diagonal

ezdxf.math.freeze_matrix(A: Union[MatrixData, Matrix]) → Matrix

Returns a frozen matrix, all data is stored in immutable tuples.

Matrix Class

class ezdxf.math.Matrix(items: Any = None, shape: Tuple[int, int] = None, matrix: List[List[float]] = None)

Basic matrix implementation without any optimization for speed of memory usage. Matrix data is stored in row major order, this means in a list of rows, where each row is a list of floats. Direct access to the data is accessible by the attribute Matrix.matrix.

The matrix can be frozen by function freeze_matrix() or method Matrix.freeze(), than the data is stored in immutable tuples.

Initialization:

  • Matrix(shape=(rows, cols)) … new matrix filled with zeros

  • Matrix(matrix[, shape=(rows, cols)]) … from copy of matrix and optional reshape

  • Matrix([[row_0], [row_1], …, [row_n]]) … from Iterable[Iterable[float]]

  • Matrix([a1, a2, …, an], shape=(rows, cols)) … from Iterable[float] and shape

New in version 0.13.

nrows

Count of matrix rows.

ncols

Count of matrix columns.

shape

Shape of matrix as (n, m) tuple for n rows and m columns.

static reshape(items: Iterable[float], shape: Tuple[int, int]) → ezdxf.math.linalg.Matrix

Returns a new matrix for iterable items in the configuration of shape.

classmethod identity(shape: Tuple[int, int]) → ezdxf.math.linalg.Matrix

Returns the identity matrix for configuration shape.

row(index) → List[float]

Returns row index as list of floats.

iter_row(index) → Iterable[float]

Yield values of row index.

col(index) → List[float]

Return column index as list of floats.

iter_col(index) → Iterable[float]

Yield values of column index.

diag(index) → List[float]

Returns diagonal index as list of floats.

An index of 0 specifies the main diagonal, negative values specifies diagonals below the main diagonal and positive values specifies diagonals above the main diagonal.

e.g. given a 4x4 matrix: index 0 is [00, 11, 22, 33], index -1 is [10, 21, 32] and index +1 is [01, 12, 23]

iter_diag(index) → Iterable[float]

Yield values of diagonal index, see also diag().

rows() → List[List[float]]

Return a list of all rows.

cols() → List[List[float]]

Return a list of all columns.

set_row(index: int, items: Union[float, Iterable[float]] = 1.0) → None

Set row values to a fixed value or from an iterable of floats.

set_col(index: int, items: Union[float, Iterable[float]] = 1.0) → None

Set column values to a fixed value or from an iterable of floats.

set_diag(index: int = 0, items: Union[float, Iterable[float]] = 1.0) → None

Set diagonal values to a fixed value or from an iterable of floats.

An index of 0 specifies the main diagonal, negative values specifies diagonals below the main diagonal and positive values specifies diagonals above the main diagonal.

e.g. given a 4x4 matrix: index 0 is [00, 11, 22, 33], index -1 is [10, 21, 32] and index +1 is [01, 12, 23]

append_row(items: Sequence[float]) → None

Append a row to the matrix.

append_col(items: Sequence[float]) → None

Append a column to the matrix.

swap_rows(a: int, b: int) → None

Swap rows a and b inplace.

swap_cols(a: int, b: int) → None

Swap columns a and b inplace.

transpose() → Matrix

Returns a new transposed matrix.

inverse() → Matrix

Returns inverse of matrix as new object.

determinant() → float

Returns determinant of matrix, raises ZeroDivisionError if matrix is singular.

freeze() → Matrix

Returns a frozen matrix, all data is stored in immutable tuples.

lu_decomp() → LUDecomposition

Returns the LU decomposition as LUDecomposition object, a faster linear equation solver.

__getitem__(item: Tuple[int, int]) → float

Get value by (row, col) index tuple, fancy slicing as known from numpy is not supported.

__setitem__(item: Tuple[int, int], value: float)

Set value by (row, col) index tuple, fancy slicing as known from numpy is not supported.

__eq__(other: Matrix) → bool

Returns True if matrices are equal, tolerance value for comparision is adjustable by the attribute Matrix.abs_tol.

__add__(other: Union[Matrix, float]) → Matrix

Matrix addition by another matrix or a float, returns a new matrix.

__sub__(other: Union[Matrix, float]) → Matrix

Matrix subtraction by another matrix or a float, returns a new matrix.

__mul__(other: Union[Matrix, float]) → Matrix

Matrix multiplication by another matrix or a float, returns a new matrix.

LUDecomposition Class

class ezdxf.math.LUDecomposition(A: Iterable[Iterable[float]])

Represents a LU decomposition matrix of A, raise ZeroDivisionError for a singular matrix.

This algorithm is a little bit faster than the Gauss-Elimination algorithm using CPython and much faster when using pypy.

The LUDecomposition.matrix attribute gives access to the matrix data as list of rows like in the Matrix class, and the LUDecomposition.index attribute gives access to the swapped row indices.

Parameters

A – matrix [[a11, a12, …, a1n], [a21, a22, …, a2n], [a21, a22, …, a2n], … [an1, an2, …, ann]]

Raises

ZeroDivisionError – singular matrix

New in version 0.13.

nrows

Count of matrix rows (and cols).

solve_vector(B: Iterable[float]) → List[float]

Solves the linear equation system given by the nxn Matrix A . x = B, right-hand side quantities as vector B with n elements.

Parameters

B – vector [b1, b2, …, bn]

Returns

vector as list of floats

solve_matrix(B: Iterable[Iterable[float]]) → Matrix

Solves the linear equation system given by the nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B.

Parameters

B – matrix [[b11, b12, …, b1m], [b21, b22, …, b2m], … [bn1, bn2, …, bnm]]

Returns

matrix as Matrix object

inverse() → Matrix

Returns the inverse of matrix as Matrix object, raise ZeroDivisionError for a singular matrix.

determinant() → float

Returns the determinant of matrix, raises ZeroDivisionError if matrix is singular.

BandedMatrixLU Class

class ezdxf.math.BandedMatrixLU(A: ezdxf.math.linalg.Matrix, m1: int, m2: int)

Represents a LU decomposition of a compact banded matrix.

upper

Upper triangle

lower

Lower triangle

m1

Lower band count, excluding main matrix diagonal

m2

Upper band count, excluding main matrix diagonal

index

Swapped indices

nrows

Count of matrix rows.

solve_vector(B: Iterable[float]) → List[float]

Solves the linear equation system given by the banded nxn Matrix A . x = B, right-hand side quantities as vector B with n elements.

Parameters

B – vector [b1, b2, …, bn]

Returns

vector as list of floats

solve_matrix(B: Iterable[Iterable[float]]) → Matrix

Solves the linear equation system given by the banded nxn Matrix A . x = B, right-hand side quantities as nxm Matrix B.

Parameters

B – matrix [[b11, b12, …, b1m], [b21, b22, …, b2m], … [bn1, bn2, …, bnm]]

Returns

matrix as Matrix object

determinant() → float

Returns the determinant of matrix.