395 lines
15 KiB
Python
395 lines
15 KiB
Python
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#!/usr/bin/env python3
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'''
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Bezier Envelope extension for Inkscape
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Copyright (C) 2009 Gerrit Karius
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This program is free software; you can redistribute it and/or
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modify it under the terms of the GNU General Public License
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as published by the Free Software Foundation; either version 2
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of the License, or (at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program; if not, write to the Free Software
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Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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About the Bezier Envelope extension:
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This extension implements Bezier enveloping.
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It takes an arbitrary path (the "letter") and a 4-sided path (the "envelope") as input.
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The envelope must be 4 segments long. Unless the letter is to be rotated or flipped,
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the envelope should begin at the upper left corner and be drawn clockwise.
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The extension then attempts to squeeze the letter into the envelope
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by rearranging all anchor and handle points of the letter's path.
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In order to do this, the bounding box of the letter is used.
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All anchor and bezier handle points get new x and y coordinates between 0% and 100%
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according to their place inside the bounding box.
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The 4 sides of the envelope are then interpreted as deformed axes.
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Points at 0% or 100% could be placed along these axes, but because most points
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are somewhere inside the bounding box, some tweening of the axes must be done.
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The function mapPointsToMorph does the tweening.
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Say, some point is at x=30%, y=40%.
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For the tweening, the function tweenCubic first calculates a straight tween
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of the y axis at the x percentage of 30%.
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This tween axis now floats somewhere between the y axis keys at the x percentage,
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but is not necessarily inside the envelope, because the x axes are not straight.
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Now, the end points on the two x axes at 30% are calculated. The function match()
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takes these points and calculates a "stretch" transform which maps the two anchor
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points of the y axis tween to the two points on the x axes by rotating the tween and
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stretching it along its endpoints. This transform is then applied to the handle points,
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to get the entire tweened y axis to its x tweened position.
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Last, the point at the y percentage 40% of this y axis tween is calculated.
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That is the final point of the enveloped letter.
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Finally, after all of the letter's points have been recalculated in this manner,
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the resulting path is taken and replaces the letter's original path.
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TODO:
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* Currently, both letter and envelope must be paths to work.
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-> Arbitrary other shapes like circles and rectangles should be interpreted as paths.
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* It should be possible to select several letters, and squeeze them into one envelope as a group.
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* It should be possible to insert a clone of the letter, instead of replacing it.
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* This program was originally written in Java. Maybe for some code, Python shortcuts can be used.
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I hope the comments are not too verbose. Enjoy!
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'''
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import inkex
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from inkex import Transform
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from inkex.paths import Path
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import math
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import sys
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import ffgeom
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class BezierEnvelope(inkex.Effect):
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segmentTypes = ["move","line","quad","cubic","close"]
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def __init__(self):
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inkex.Effect.__init__(self)
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def effect(self):
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if len(self.options.ids) < 2:
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raise Exception("Two paths must be selected. The 1st is the letter, the 2nd is the envelope and must have 4 sides.")
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exit()
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letterElement = self.svg.selected[self.options.ids[0]]
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envelopeElement = self.svg.selected[self.options.ids[1]]
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if letterElement.tag != inkex.addNS('path','svg') or envelopeElement.tag != inkex.addNS('path','svg'):
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raise Exception("Both letter and envelope must be SVG paths.")
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exit()
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axes = extractMorphAxes( Path( envelopeElement.get('d') ).to_arrays() )
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if axes is None:
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raise Exception("No axes found on envelope.")
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axisCount = len(axes)
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if axisCount < 4:
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raise Exception("The envelope path has less than 4 segments.")
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for i in range( 0, 4 ):
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if axes[i] is None:
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raise Exception("axes[%i] is None" % i)
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# morph the enveloped element according to the axes
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morph_element( letterElement, envelopeElement, axes );
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def morph_element( letterElement, envelopeElement, axes ):
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path = Path( letterElement.get('d') ).to_arrays()
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morphedPath = morphPath( path, axes )
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letterElement.set("d", str(Path(morphedPath)))
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# Morphs a path into a new path, according to cubic curved bounding axes.
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def morphPath( path, axes ):
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bounds = [y for x in list(Path(path).bounding_box()) for y in list(x)]
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assert len(bounds) == 4
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new_path = []
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current = [ 0.0, 0.0 ]
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start = [ 0.0, 0.0 ]
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for cmd, params in path:
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segmentType = cmd
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points = params
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if segmentType == "M":
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start[0] = points[0]
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start[1] = points[1]
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segmentType = convertSegmentToCubic( current, segmentType, points, start )
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percentages = [0.0]*len(points)
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morphed = [0.0]*len(points)
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numPts = getNumPts( segmentType )
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normalizePoints( bounds, points, percentages, numPts )
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mapPointsToMorph( axes, percentages, morphed, numPts )
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addSegment( new_path, segmentType, morphed )
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if len(points) >= 2:
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current[0] = points[ len(points)-2 ]
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current[1] = points[ len(points)-1 ]
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return new_path
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def getNumPts( segmentType ):
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if segmentType == "M":
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return 1
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if segmentType == "L":
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return 1
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if segmentType == "Q":
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return 2
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if segmentType == "C":
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return 3
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if segmentType == "Z":
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return 0
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return -1
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def addSegment( path, segmentType, points ):
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path.append([segmentType,points])
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# Converts visible path segments (Z,L,Q) into absolute cubic segments (C).
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def convertSegmentToCubic( current, segmentType, points, start ):
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if segmentType == "H":
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# print(current, points, start)
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assert len(points) == 1
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points.insert(0, current[0])
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# points[0] += current[0]
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# print(segmentType, current, points, start)
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return convertSegmentToCubic(current, "L", points, start)
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elif segmentType == "V":
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# print(points)
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assert len(points) == 1
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points.append(current[1])
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# points[1] += current[1]
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# print(segmentType, current, points, start)
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return convertSegmentToCubic(current, "L", points, start)
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if segmentType == "M":
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return "M";
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if segmentType == "C":
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return "C";
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elif segmentType == "Z":
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for i in range(0,6):
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points.append(0.0)
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points[4] = start[0]
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points[5] = start[1]
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thirdX = (points[4] - current[0]) / 3.0
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thirdY = (points[5] - current[1]) / 3.0
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points[2] = points[4]-thirdX
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points[3] = points[5]-thirdY
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points[0] = current[0]+thirdX
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points[1] = current[1]+thirdY
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return "C"
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elif segmentType == "L":
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for i in range(0,4):
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points.append(0.0)
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points[4] = points[0]
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points[5] = points[1]
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thirdX = (points[4] - current[0]) / 3.0
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thirdY = (points[5] - current[1]) / 3.0
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points[2] = points[4]-thirdX
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points[3] = points[5]-thirdY
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points[0] = current[0]+thirdX
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points[1] = current[1]+thirdY
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return "C"
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elif segmentType == "Q":
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for i in range(0,2):
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points.append(0.0)
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firstThirdX = (points[0] - current[0]) * 2.0 / 3.0
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firstThirdY = (points[1] - current[1]) * 2.0 / 3.0
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secondThirdX = (points[2] - points[0]) * 2.0 / 3.0
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secondThirdY = (points[3] - points[1]) * 2.0 / 3.0
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points[4] = points[2]
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points[5] = points[3]
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points[0] = current[0] + firstThirdX
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points[1] = current[1] + firstThirdY
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points[2] = points[2] - secondThirdX
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points[3] = points[3] - secondThirdY
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return "C"
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else:
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sys.stderr.write("unsupported segment type: %s\n" % (segmentType))
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return segmentType
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# Normalizes the points of a path segment, so that they are expressed as percentage coordinates
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# relative to the bounding box axes of the total shape.
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# @param bounds The bounding box of the shape.
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# @param points The points of the segment.
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# @param percentages The returned points in normalized percentage form.
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# @param numPts
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def normalizePoints( bounds, points, percentages, numPts ):
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# bounds has structure xmin,xMax,ymin,yMax
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xmin,xMax,ymin,yMax = bounds
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for i in range( 0, numPts ):
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x = i*2
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y = i*2+1
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percentages[x] = (points[x] - xmin) / (xMax-xmin)
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percentages[y] = (points[y] - ymin) / (yMax-ymin)
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# Extracts 4 axes from a path. It is assumed that the path starts with a move, followed by 4 cubic paths.
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# The extraction reverses the last 2 axes, so that they run in parallel with the first 2.
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# @param path The path that is formed by the axes.
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# @return The definition points of the 4 cubic path axes as float arrays, bundled in another array.
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def extractMorphAxes( path ):
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points = []
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current = [ 0.0, 0.0 ]
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start = [ 0.0, 0.0 ]
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# the curved axis definitions go in here
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axes = [None]*4
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i = 0
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for cmd, params in path:
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points = params
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cmd = convertSegmentToCubic( current, cmd, points, start )
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if cmd == "M":
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current[0] = points[0]
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current[1] = points[1]
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start[0] = points[0]
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start[1] = points[1]
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elif cmd == "C":
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# 1st cubic becomes x axis 0
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# 2nd cubic becomes y axis 1
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# 3rd cubic becomes x axis 2 and is reversed
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# 4th cubic becomes y axis 3 and is reversed
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if i % 2 == 0:
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index = i
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else:
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index = 4-i
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if( i < 2 ):
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# axes 1 and 2
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axes[index] = [ current[0], current[1], points[0], points[1], points[2], points[3], points[4], points[5] ]
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elif( i < 4 ):
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# axes 3 and 4
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axes[index] = [ points[4], points[5], points[2], points[3], points[0], points[1], current[0], current[1] ]
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else:
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# more than 4 axes - hopefully it was an unnecessary trailing Z
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{}
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current[0] = points[4]
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current[1] = points[5]
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i = i + 1
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elif cmd == "Z":
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#do nothing
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{}
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else:
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raise Exception("Unsupported segment type: %s" % cmd)
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return None
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return axes
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# Projects points in percentage coordinates into a morphed coordinate system that is framed
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# by 2 x cubic curves (along the x axis) and 2 y cubic curves (along the y axis).
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# @param axes The x and y axes of the envelope.
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# @param percentage The current segment of the letter in normalized percentage form.
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# @param morphed The array to hold the returned morphed path.
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# @param numPts The number of points to be transformed.
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def mapPointsToMorph( axes, percentage, morphed, numPts ):
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# rename the axes for legibility
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yCubic0 = axes[1]
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yCubic1 = axes[3]
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xCubic0 = axes[0]
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xCubic1 = axes[2]
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# morph each point
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for i in range( 0, numPts ):
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x = i*2
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y = i*2+1
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# tween between the morphed y axes according to the x percentage
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tweenedY = tweenCubic( yCubic0, yCubic1, percentage[x] )
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# get 2 points on the morphed x axes
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xSpot0 = pointOnCubic( xCubic0, percentage[x] )
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xSpot1 = pointOnCubic( xCubic1, percentage[x] )
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# create a transform that stretches the y axis tween between these 2 points
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yAnchor0 = [ tweenedY[0], tweenedY[1] ]
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yAnchor1 = [ tweenedY[6], tweenedY[7] ]
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xTransform = match( yAnchor0, yAnchor1, xSpot0, xSpot1 )
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# map the y axis tween to the 2 points by applying the stretch transform
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for j in range(0,4):
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x2 = j*2
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y2 = j*2+1
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pointOnY = [tweenedY[x2],tweenedY[y2]]
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Transform(xTransform).apply_to_point(pointOnY)
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tweenedY[x2] = pointOnY[0]
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tweenedY[y2] = pointOnY[1]
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# get the point on the tweened and transformed y axis according to the y percentage
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morphedPoint = pointOnCubic( tweenedY, percentage[y] )
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morphed[x] = morphedPoint[0]
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morphed[y] = morphedPoint[1]
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# Calculates the point on a cubic bezier curve at the given percentage.
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def pointOnCubic( c, t ):
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point = [0.0,0.0]
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_t_2 = t*t
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_t_3 = _t_2*t
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_1_t = 1-t
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_1_t_2 = _1_t*_1_t
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_1_t_3 = _1_t_2*_1_t
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for i in range( 0, 2 ):
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point[i] = c[i]*_1_t_3 + 3*c[2+i]*_1_t_2*t + 3*c[4+i]*_1_t*_t_2 + c[6+i]*_t_3
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return point
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# Tweens 2 bezier curves in a straightforward way,
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# i.e. each of the points on the curve is tweened along a straight line
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# between the respective point on key1 and key2.
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def tweenCubic( key1, key2, percentage ):
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tween = [0.0]*len(key1)
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for i in range ( 0, len(key1) ):
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tween[i] = key1[i] + percentage * (key2[i] - key1[i])
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return tween
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# Calculates a transform that matches 2 points to 2 anchors
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# by rotating and scaling (up or down) along the axis that is formed by
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# a line between the two points.
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def match( p1, p2, a1, a2 ):
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x = 0
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y = 1
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# distances
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dp = [ p2[x]-p1[x], p2[y]-p1[y] ]
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da = [ a2[x]-a1[x], a2[y]-a1[y] ]
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# angles
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angle_p = math.atan2( dp[x], dp[y] )
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angle_a = math.atan2( da[x], da[y] )
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# radians
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#rp = math.sqrt( dp[x]*dp[x] + dp[y]*dp[y] )
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#ra = math.sqrt( da[x]*da[x] + da[y]*da[y] )
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rp = math.hypot( dp[x], dp[y] )
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ra = math.hypot( da[x], da[y] )
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# scale
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scale = ra / rp
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# transforms in the order they are applied
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t1 = Transform( "translate(%f,%f)"%(-p1[x],-p1[y]) ).matrix
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#t2 = Transform( "rotate(%f)"%(-angle_p) ).matrix
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#t3 = Transform( "scale(%f,%f)"%(scale,scale) ).matrix
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#t4 = Transform( "rotate(%f)"%angle_a ).matrix
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t2 = rotateTransform(-angle_p)
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t3 = scale_transform( scale, scale )
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t4 = rotateTransform( angle_a )
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t5 = Transform( "translate(%f,%f)"%(a1[x],a1[y]) ).matrix
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||
|
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# transforms in the order they are multiplied
|
||
|
|
t = t5
|
||
|
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t = Transform(t) * Transform(t4)
|
||
|
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t = Transform(t) * Transform(t3)
|
||
|
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t = Transform(t) * Transform(t2)
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||
|
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t = Transform(t) * Transform(t1)
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|
|
# return the combined transform
|
||
|
|
return t
|
||
|
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|
||
|
|
|
||
|
|
def rotateTransform( a ):
|
||
|
|
return [[math.cos(a),-math.sin(a),0],[math.sin(a),math.cos(a),0]]
|
||
|
|
|
||
|
|
def scale_transform( sx, sy ):
|
||
|
|
return [[sx,0,0],[0,sy,0]]
|
||
|
|
|
||
|
|
|
||
|
|
BezierEnvelope().run()
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