Spline Shapes

IPKISS has a number of classes for shapes built from splines. Splines are used in many graphical design and CAD tools. They are polynomial parametric functions that can be used to perform a smooth interpolation between a small set of control points.

ShapeFitNaturalCubicSpline	Shape fitting a natural spline through all points of the original_shape.
ShapeFitClampedCubicSpline	Shape fitting a spline through all points of the original_shape.

ShapeFitNaturalCubicSpline

class ipkiss3.all.ShapeFitNaturalCubicSpline

Shape fitting a natural spline through all points of the original_shape. The end points are ‘natural’, i.e. they have zero curvature. A third-order spline is used to guarantee continuity of tangent and curvature.

The start_face_angle and end_face_angle of the original_shape are not taken into account.

When original shape is closed, the spline will also be closed, and continuous in curvature and tangent in the start/end point, rather than having zero curvature in those points.

Parameters:

original_shape: Shape, required

discretisation: float and number > 0, optional

default (approximate) distance between evaluated points. Default is 100 grid spaces

end_face_angle: float, optional

start_face_angle: float, optional

points: optional

points of this shape

Other Parameters:

size_info: SizeInfo, locked

get the size information on this Shape

closed: locked

Examples

from ipkiss3 import all as i3
from matplotlib import pyplot as plt

s = i3.Shape([(0.0, 0.0), (10.0, 0.0), (10.0, 20.0), (30.0, 15.0), (30.0, 30.0)])
s2 = i3.ShapeFitNaturalCubicSpline(original_shape=s, discretisation=0.1)

# plot control shape
x, y = s.points.transpose()
plt.plot(x, y, "bo-")
# plot spline
x2, y2 = s2.points.transpose()
plt.plot(x2, y2, "r-")

plt.axis("equal")
plt.show()

ShapeFitClampedCubicSpline

class ipkiss3.all.ShapeFitClampedCubicSpline

Shape fitting a spline through all points of the original_shape. A third-order spline is used to guarantee continuity in both tangent and curvature.

The start and end angle are clamped to match the start_face_angle and end_face_angle of the original shape, as well as zero curvature in those points.

If the original_shape is closed, the spline will also be closed, but will still adhere to the clamped conditions (i.e. tangent and zero curvature) in the start/end point. Unless the start_face_angle and end_face_angle are identical, the spline will not be smooth (continuous in tangent and curvature) in those points.

Parameters:

original_shape: Shape, required

discretisation: float and number > 0, optional

default (approximate) distance between evaluated points. Default is 100 grid spaces

end_face_angle: float, optional

start_face_angle: float, optional

points: optional

points of this shape

Other Parameters:

size_info: SizeInfo, locked

get the size information on this Shape

closed: locked

Examples

from ipkiss3 import all as i3
from matplotlib import pyplot as plt

s = i3.Shape(
    [(0.0, 0.0), (10.0, 0.0), (10.0, 20.0), (30.0, 15.0), (30.0, 30.0)],
    start_face_angle=-20.0,
    end_face_angle=80.0,
)
s2 = i3.ShapeFitClampedCubicSpline(original_shape=s, discretisation=0.1)

# plot control shape
x, y = s.points.transpose()
plt.plot(x, y, "bo-")
# plot spline
x2, y2 = s2.points.transpose()
plt.plot(x2, y2, "r-")

plt.axis("equal")
plt.show()