77 lines
3.0 KiB
Python
Executable File
77 lines
3.0 KiB
Python
Executable File
#Copyright ReportLab Europe Ltd. 2000-2004
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#see license.txt for license details
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#history http://www.reportlab.co.uk/cgi-bin/viewcvs.cgi/public/reportlab/trunk/reportlab/pdfgen/pdfgeom.py
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__version__=''' $Id: pdfgeom.py 2385 2004-06-17 15:26:05Z rgbecker $ '''
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__doc__="""
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This module includes any mathematical methods needed for PIDDLE.
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It should have no dependencies beyond the Python library.
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So far, just Robert Kern's bezierArc.
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"""
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from math import sin, cos, pi, ceil
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def bezierArc(x1,y1, x2,y2, startAng=0, extent=90):
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"""bezierArc(x1,y1, x2,y2, startAng=0, extent=90) --> List of Bezier
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curve control points.
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(x1, y1) and (x2, y2) are the corners of the enclosing rectangle. The
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coordinate system has coordinates that increase to the right and down.
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Angles, measured in degress, start with 0 to the right (the positive X
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axis) and increase counter-clockwise. The arc extends from startAng
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to startAng+extent. I.e. startAng=0 and extent=180 yields an openside-down
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semi-circle.
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The resulting coordinates are of the form (x1,y1, x2,y2, x3,y3, x4,y4)
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such that the curve goes from (x1, y1) to (x4, y4) with (x2, y2) and
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(x3, y3) as their respective Bezier control points."""
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x1,y1, x2,y2 = min(x1,x2), max(y1,y2), max(x1,x2), min(y1,y2)
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if abs(extent) <= 90:
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arcList = [startAng]
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fragAngle = float(extent)
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Nfrag = 1
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else:
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arcList = []
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Nfrag = int(ceil(abs(extent)/90.))
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fragAngle = float(extent) / Nfrag
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x_cen = (x1+x2)/2.
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y_cen = (y1+y2)/2.
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rx = (x2-x1)/2.
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ry = (y2-y1)/2.
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halfAng = fragAngle * pi / 360.
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kappa = abs(4. / 3. * (1. - cos(halfAng)) / sin(halfAng))
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if fragAngle < 0:
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sign = -1
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else:
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sign = 1
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pointList = []
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for i in range(Nfrag):
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theta0 = (startAng + i*fragAngle) * pi / 180.
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theta1 = (startAng + (i+1)*fragAngle) *pi / 180.
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if fragAngle > 0:
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pointList.append((x_cen + rx * cos(theta0),
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y_cen - ry * sin(theta0),
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x_cen + rx * (cos(theta0) - kappa * sin(theta0)),
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y_cen - ry * (sin(theta0) + kappa * cos(theta0)),
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x_cen + rx * (cos(theta1) + kappa * sin(theta1)),
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y_cen - ry * (sin(theta1) - kappa * cos(theta1)),
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x_cen + rx * cos(theta1),
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y_cen - ry * sin(theta1)))
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else:
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pointList.append((x_cen + rx * cos(theta0),
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y_cen - ry * sin(theta0),
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x_cen + rx * (cos(theta0) + kappa * sin(theta0)),
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y_cen - ry * (sin(theta0) - kappa * cos(theta0)),
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x_cen + rx * (cos(theta1) - kappa * sin(theta1)),
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y_cen - ry * (sin(theta1) + kappa * cos(theta1)),
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x_cen + rx * cos(theta1),
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y_cen - ry * sin(theta1)))
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return pointList |