On Sun, Aug 23, 2009 at 7:45 PM, Chris Barker<[email protected]> wrote:
> This is a Bezier spline -- it can not exactly form a piece of a circle
> (though it can get pretty close). You can probably find the math
> somewhere for how to approximate a circle, but...
somewhere like ... matplotlib.path.unit_circle (thanks to Michael D)
@classmethod
def unit_circle(cls):
"""
(staticmethod) Returns a :class:`Path` of the unit circle.
The circle is approximated using cubic Bezier curves. This
uses 8 splines around the circle using the approach presented
here:
Lancaster, Don. `Approximating a Circle or an Ellipse Using Four
Bezier Cubic Splines <http://www.tinaja.com/glib/ellipse4.pdf>`_.
"""
if cls._unit_circle is None:
MAGIC = 0.2652031
SQRTHALF = np.sqrt(0.5)
MAGIC45 = np.sqrt((MAGIC*MAGIC) / 2.0)
vertices = np.array(
[[0.0, -1.0],
[MAGIC, -1.0],
[SQRTHALF-MAGIC45, -SQRTHALF-MAGIC45],
[SQRTHALF, -SQRTHALF],
[SQRTHALF+MAGIC45, -SQRTHALF+MAGIC45],
[1.0, -MAGIC],
[1.0, 0.0],
[1.0, MAGIC],
[SQRTHALF+MAGIC45, SQRTHALF-MAGIC45],
[SQRTHALF, SQRTHALF],
[SQRTHALF-MAGIC45, SQRTHALF+MAGIC45],
[MAGIC, 1.0],
[0.0, 1.0],
[-MAGIC, 1.0],
[-SQRTHALF+MAGIC45, SQRTHALF+MAGIC45],
[-SQRTHALF, SQRTHALF],
[-SQRTHALF-MAGIC45, SQRTHALF-MAGIC45],
[-1.0, MAGIC],
[-1.0, 0.0],
[-1.0, -MAGIC],
[-SQRTHALF-MAGIC45, -SQRTHALF+MAGIC45],
[-SQRTHALF, -SQRTHALF],
[-SQRTHALF+MAGIC45, -SQRTHALF-MAGIC45],
[-MAGIC, -1.0],
[0.0, -1.0],
[0.0, -1.0]],
np.float_)
codes = cls.CURVE4 * np.ones(26)
codes[0] = cls.MOVETO
codes[-1] = cls.CLOSEPOLY
cls._unit_circle = cls(vertices, codes)
return cls._unit_circle
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