src/reportlab/pdfgen/pdfgeom.py
author robin
Mon, 12 Sep 2022 09:33:45 +0100
changeset 4737 e39e4741759a
parent 4528 e09377955af8
permissions -rwxr-xr-x
nano bugfix in rl_addons/renderPM/_renderPM.c

#Copyright ReportLab Europe Ltd. 2000-2017
#see license.txt for license details
#history https://hg.reportlab.com/hg-public/reportlab/log/tip/src/reportlab/pdfgen/pdfgeom.py
__version__='3.3.0'
__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