Geometry values

All values are immutable: operations return new objects. Coordinates must be finite; NaN and infinities raise ValueError when a value is created.

Points and vectors

Point(float, ...)
Vector(float, ...)

coords

The coordinate tuple.

dimension

The dimension \(d\).

x

The first coordinate, when it exists.

y

The second coordinate, when it exists.

z

The third coordinate, when it exists.

dot()

The inner product of two vectors.

norm()

The Euclidean length of a vector.

normalized()

The unit vector in the direction of a vector; a zero vector cannot be normalized.

A point or a vector in \(\mathbb{R}^d\), given by its \(d \ge 1\) coordinates. Points and vectors combine as in affine geometry (Arithmetic of points and vectors).

Expression	Result
point - point	A Vector
point + vector, point - vector	A Point
vector + vector, vector * scalar	A Vector; scalar * vector works too

Mixing dimensions raises DimensionMismatch. point + point is not rejected: it adds the coordinates and returns a Point, which is meaningful only in combinations whose weights sum to one, such as the averages inside de Casteljau's algorithm.

from bezierkit import Point, Vector

p = Point(1, 2)
# Point(coords=(7.0, 0.0))
q = p + Vector(3, -1) * 2
# Vector(coords=(6.0, -2.0))
v = q - p
# 6.324555320336759
print(v.norm())

Point sets

PointSet(points)

An immutable batch of points backed by a read-only \((\text{count}, d)\) NumPy array, as returned by batch evaluation and sampling. It offers count, dimension, array (a read-only copy), the columns x, y, z, iteration over Points and indexing.

Parameters

Interval

Interval(start, end) is a closed interval with contains(), clamp() and linspace().

ParameterValues

Validates a scalar or a one-dimensional array of parameters against a domain. Every curve uses it, so at(1.2) on a curve over \([0, 1]\) raises ParameterOutOfDomain.

Errors

BezierKitError

Base class of the exceptions below

DimensionMismatch

Points, vectors or segments of different dimensions are combined

DegreeError

A curve has the wrong degree for an operation, or no control points

ParameterOutOfDomain

A parameter lies outside the curve's domain \([0, 1]\)

ToleranceNotMet

Adaptive fitting cannot reach its tolerance within its limits (Fitting)

Invalid arguments that are not geometry, such as a negative tolerance, raise ValueError.

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