Jordan Curve

Introduction

Jordan Curve is a continuous closed curve which doesn’t intersect itself.

For our purpose, we use oriented jordan curve by setting a positive direction as counter-clockwise.

Although a jordan curve can be very general, we restrict and use only jordan curves which are piecewise smooth curves. We call each piece as a segment, a planar bezier curve.

Creating a segment

A segment is a PlanarBezier instance. You create a new instance by passing the ctrlpoints of the curve. For example, we have a linear and a quadratic segment in the figure bellow

from shapepy import PlanarBezier
# Creates a liner segment between (1, 2) and (4, 0)
linear_segment = PlanarBezier([(1, 2),
                               (4, 0)])
# Creates a quadratic segment
quadratic_segment = PlanarBezier([(1, 2),
                                  (4, 2),
                                  (4, 0)])

Creating a jordan curve

There are 4 ways to create a JordanCurve instance:

• From segments: JordanCurve directly

• From vertices: FactoryJordan.polygon

• From spline curve: FactoryJordan.spline_curve

From vertices

This method creates polygonal shapes only

from shapepy import JordanCurve

# Create a list of vertices
vertices = [(1, 2), (4, 0), (-1, -1), (-3, 1)]
# Creates a quadrilateral jordan
jordan = FactoryJordan.polygon(vertices)

From segments

This method can create shape of any degree

from shapepy import Segment, JordanCurve
segment0 = Segment([(0, 0), (4, 0)])
segment1 = Segment([(4, 0), (4, 3), (0, 3)])
segment2 = Segment([(0, 3), (0, 0)])
segments = [segment0, segment1, segment2]
jordan = JordanCurve(segments)

From spline

For this case, we will use the package pynurbs

import pynurbs
from shapepy import Point2D, JordanCurve
knotvector = (0, 0, 0, 1/3, 1/3, 2/3, 2/3, 1, 1, 1)
ctrlpoints = [(0, 0), (2, 0), (4, 0), (4, 3),
              (0, 3), (0, 3/2), (0, 0)]
ctrlpoints = [cartesian(point) for point in ctrlpoints]
curve = pynurbs.Curve(knotvector, ctrlpoints)
jordan = FactoryJordan.spline_curve(curve)