matplotlib.bezier — Matplotlib 3.10.1 documentation (original) (raw)
A module providing some utility functions regarding Bézier path manipulation.
class matplotlib.bezier.BezierSegment(control_points)[source]#
Bases: object
A d-dimensional Bézier segment.
Parameters:
control_points(N, d) array
Location of the N control points.
axis_aligned_extrema()[source]#
Return the dimension and location of the curve's interior extrema.
The extrema are the points along the curve where one of its partial derivatives is zero.
Returns:
dimsarray of int
Index \(i\) of the partial derivative which is zero at each interior extrema.
dzerosarray of float
Of same size as dims. The \(t\) such that \(d/dx_i B(t) = 0\)
property control_points#
The control points of the curve.
property degree#
Degree of the polynomial. One less the number of control points.
property dimension#
The dimension of the curve.
Evaluate the curve at a single point, returning a tuple of d floats.
property polynomial_coefficients#
The polynomial coefficients of the Bézier curve.
Returns:
(n+1, d) array
Coefficients after expanding in polynomial basis, where \(n\)is the degree of the Bézier curve and \(d\) its dimension. These are the numbers (\(C_j\)) such that the curve can be written \(\sum_{j=0}^n C_j t^j\).
Notes
The coefficients are calculated as
\[{n \choose j} \sum_{i=0}^j (-1)^{i+j} {j \choose i} P_i\]
where \(P_i\) are the control points of the curve.
exception matplotlib.bezier.NonIntersectingPathException[source]#
Bases: ValueError
matplotlib.bezier.check_if_parallel(dx1, dy1, dx2, dy2, tolerance=1e-05)[source]#
Check if two lines are parallel.
Parameters:
dx1, dy1, dx2, dy2float
The gradients dy/dx of the two lines.
tolerancefloat
The angular tolerance in radians up to which the lines are considered parallel.
Returns:
is_parallel
- 1 if two lines are parallel in same direction.
- -1 if two lines are parallel in opposite direction.
- False otherwise.
matplotlib.bezier.find_bezier_t_intersecting_with_closedpath(bezier_point_at_t, inside_closedpath, t0=0.0, t1=1.0, tolerance=0.01)[source]#
Find the intersection of the Bézier curve with a closed path.
The intersection point t is approximated by two parameters t0, _t1_such that t0 <= t <= t1.
Search starts from t0 and t1 and uses a simple bisecting algorithm therefore one of the end points must be inside the path while the other doesn't. The search stops when the distance of the points parametrized by_t0_ and t1 gets smaller than the given tolerance.
Parameters:
bezier_point_at_tcallable
A function returning x, y coordinates of the Bézier at parameter t. It must have the signature:
bezier_point_at_t(t: float) -> tuple[float, float]
inside_closedpathcallable
A function returning True if a given point (x, y) is inside the closed path. It must have the signature:
inside_closedpath(point: tuple[float, float]) -> bool
t0, t1float
Start parameters for the search.
tolerancefloat
Maximal allowed distance between the final points.
Returns:
t0, t1float
The Bézier path parameters.
matplotlib.bezier.find_control_points(c1x, c1y, mmx, mmy, c2x, c2y)[source]#
Find control points of the Bézier curve passing through (c1x, c1y), (mmx, mmy), and (c2x, c2y), at parametric values 0, 0.5, and 1.
matplotlib.bezier.get_cos_sin(x0, y0, x1, y1)[source]#
matplotlib.bezier.get_intersection(cx1, cy1, cos_t1, sin_t1, cx2, cy2, cos_t2, sin_t2)[source]#
Return the intersection between the line through (cx1, cy1) at angle_t1_ and the line through (cx2, cy2) at angle t2.
matplotlib.bezier.get_normal_points(cx, cy, cos_t, sin_t, length)[source]#
For a line passing through (cx, cy) and having an angle t, return locations of the two points located along its perpendicular line at the distance of length.
matplotlib.bezier.get_parallels(bezier2, width)[source]#
Given the quadratic Bézier control points bezier2, returns control points of quadratic Bézier lines roughly parallel to given one separated by width.
matplotlib.bezier.inside_circle(cx, cy, r)[source]#
Return a function that checks whether a point is in a circle with center (cx, cy) and radius r.
The returned function has the signature:
f(xy: tuple[float, float]) -> bool
matplotlib.bezier.make_wedged_bezier2(bezier2, width, w1=1.0, wm=0.5, w2=0.0)[source]#
Being similar to get_parallels, returns control points of two quadratic Bézier lines having a width roughly parallel to given one separated by_width_.
matplotlib.bezier.split_bezier_intersecting_with_closedpath(bezier, inside_closedpath, tolerance=0.01)[source]#
Split a Bézier curve into two at the intersection with a closed path.
Parameters:
bezier(N, 2) array-like
Control points of the Bézier segment. See BezierSegment.
inside_closedpathcallable
A function returning True if a given point (x, y) is inside the closed path. See also find_bezier_t_intersecting_with_closedpath.
tolerancefloat
The tolerance for the intersection. See alsofind_bezier_t_intersecting_with_closedpath.
Returns:
left, right
Lists of control points for the two Bézier segments.
matplotlib.bezier.split_de_casteljau(beta, t)[source]#
Split a Bézier segment defined by its control points beta into two separate segments divided at t and return their control points.
matplotlib.bezier.split_path_inout(path, inside, tolerance=0.01, reorder_inout=False)[source]#
Divide a path into two segments at the point where inside(x, y) becomes False.