reportlab/pdfgen/pdfgeom.py
 author dinu_gherman Fri, 12 Jan 2001 21:36:57 +0000 changeset 562 6c9408ec3302 parent 494 54257447cfe9 child 1683 7fa753e4420a permissions -rwxr-xr-x
Minor neglectable changes.

#copyright ReportLab Inc. 2000
#see license.txt for license details
#history http://cvs.sourceforge.net/cgi-bin/cvsweb.cgi/reportlab/pdfgen/pdfgeom.py?cvsroot=reportlab
#\$Header: /tmp/reportlab/reportlab/pdfgen/pdfgeom.py,v 1.7 2001/01/12 21:36:57 dinu_gherman Exp \$
__version__=''' \$Id: pdfgeom.py,v 1.7 2001/01/12 21:36:57 dinu_gherman Exp \$ '''
__doc__="""
This module includes any mathematical methods needed for PIDDLE.
It should have no dependencies beyond the Python library.

So far, just Robert Kern's bezierArc.
"""

from math import sin, cos, pi, ceil

def bezierArc(x1,y1, x2,y2, startAng=0, extent=90):
"""bezierArc(x1,y1, x2,y2, startAng=0, extent=90) --> List of Bezier
curve control points.

(x1, y1) and (x2, y2) are the corners of the enclosing rectangle.  The
coordinate system has coordinates that increase to the right and down.
Angles, measured in degress, start with 0 to the right (the positive X
axis) and increase counter-clockwise.  The arc extends from startAng
to startAng+extent.  I.e. startAng=0 and extent=180 yields an openside-down
semi-circle.

The resulting coordinates are of the form (x1,y1, x2,y2, x3,y3, x4,y4)
such that the curve goes from (x1, y1) to (x4, y4) with (x2, y2) and
(x3, y3) as their respective Bezier control points."""

x1,y1, x2,y2 = min(x1,x2), max(y1,y2), max(x1,x2), min(y1,y2)

if abs(extent) <= 90:
arcList = [startAng]
fragAngle = float(extent)
Nfrag = 1
else:
arcList = []
Nfrag = int(ceil(abs(extent)/90.))
fragAngle = float(extent) / Nfrag

x_cen = (x1+x2)/2.
y_cen = (y1+y2)/2.
rx = (x2-x1)/2.
ry = (y2-y1)/2.
halfAng = fragAngle * pi / 360.
kappa = abs(4. / 3. * (1. - cos(halfAng)) / sin(halfAng))

if fragAngle < 0:
sign = -1
else:
sign = 1

pointList = []

for i in range(Nfrag):
theta0 = (startAng + i*fragAngle) * pi / 180.
theta1 = (startAng + (i+1)*fragAngle) *pi / 180.
if fragAngle > 0:
pointList.append((x_cen + rx * cos(theta0),
y_cen - ry * sin(theta0),
x_cen + rx * (cos(theta0) - kappa * sin(theta0)),
y_cen - ry * (sin(theta0) + kappa * cos(theta0)),
x_cen + rx * (cos(theta1) + kappa * sin(theta1)),
y_cen - ry * (sin(theta1) - kappa * cos(theta1)),
x_cen + rx * cos(theta1),
y_cen - ry * sin(theta1)))
else:
pointList.append((x_cen + rx * cos(theta0),
y_cen - ry * sin(theta0),
x_cen + rx * (cos(theta0) + kappa * sin(theta0)),
y_cen - ry * (sin(theta0) - kappa * cos(theta0)),
x_cen + rx * (cos(theta1) - kappa * sin(theta1)),
y_cen - ry * (sin(theta1) + kappa * cos(theta1)),
x_cen + rx * cos(theta1),
y_cen - ry * sin(theta1)))

return pointList