bezier

Tools to work with Bezier curves.

getBezierPoint(t, pt1, pt2, pt3, pt4, reverse=True)

Use the Bernstein Basis Function to get a point in a Bezier curve.

Parameters

t (float) – A float representing the ratio of the desired point.
pt1 (tuple) – The x,y coordinate of the first point (on-curve).
pt2 (tuple) – The x,y coordinate of the second point (off-curve).
pt3 (tuple) – The x,y coordinate of the third point (off-curve).
pt4 (tuple) – The x,y coordinate of the last point (on-curve).
reverse (bool) – Get point for the reverse value of t.

>>> pt1 = 320, 162
>>> pt2 = 138, 528
>>> pt3 = 416, 856
>>> pt4 = 854, 794
>>> getBezierPoint(0.5, pt1, pt2, pt3, pt4, reverse=True)
(354.5, 638.5)

lerp(p1, p2, t)

Linear interpolation between two points.

Parameters

p1 (Point) – A Point object.
p2 (Point) – Another Point object.
t (float) – The interpolation factor.

Returns

A new Point object interpolated from p1 and p2.

glyphToBezierSegments(glyph): Convert an RGlyph into lists of BezierSegment objects.

class Point(pos)

A basic Bezier Point object with support for math operations and normalization.

__init__(pos)

Create a new Point object from x,y coordinates.

Parameters: pos (tuple) – A pair of x,y coordinates.
Returns: A new Point object.

>>> p = Point((100, 100))
>>> p.x, p.y
(100, 100)

mag()

normal()

normalise()

class BezierSegment(p0, p1, p2, p3)

A basic Bezier Segment object with support for point and curvature calculations.

__init__(p0, p1, p2, p3)

Initiliaze a BezierSegment from four Points (two on-curve, two off-curve).

Parameters

p0 (Point) – The first on-curve point.
p1 (Point) – The first off-curve point.
p2 (Point) – The second off-curve point.
p3 (Point) – The second on-curve point.

position(t)

Get a point on the curve based on a given factor.

Parameters: t (float) – A float representing the ratio of the desired point.
Returns: A Point object.

>>> p0 = Point((0, 0))
>>> p1 = Point((0, 60))
>>> p2 = Point((40, 100))
>>> p3 = Point((100, 100))
>>> B = BezierSegment(p0, p1, p2, p3)
>>> pt = B.position(0.5)
>>> pt.x, pt.y
(27.5, 72.5)

d(t): First derivative of the curve. Describes the tangent along the curve. Used to calculate the normal (line perpedincular to the curve).

dd(t): Second derivative of the curve. Describes how quickly the tangent is changing.

curvature(t)

Calculate the segments’s curvature at a given point.

Parameters: t (float) – A float representing the ratio of the desired point.
Returns: The curvature value.

>>> p0 = Point((0, 0))
>>> p1 = Point((0, 60))
>>> p2 = Point((40, 100))
>>> p3 = Point((100, 100))
>>> B = BezierSegment(p0, p1, p2, p3)
>>> B.curvature(0.5)
-0.011544600509168123