232 lines
7.9 KiB
Python
232 lines
7.9 KiB
Python
#!/usr/bin/env python3
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# Copyright (c) 2012 Stuart Pernsteiner
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions are met:
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#
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# 1. Redistributions of source code must retain the above copyright notice,
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# this list of conditions and the following disclaimer.
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# 2. Redistributions in binary form must reproduce the above copyright notice,
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# this list of conditions and the following disclaimer in the documentation
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# and/or other materials provided with the distribution.
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#
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# THIS SOFTWARE IS PROVIDED BY THE AUTHOR "AS IS" AND ANY EXPRESS OR IMPLIED
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# WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
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# MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
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# EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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# PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
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# OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
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# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
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# OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
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# ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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import sys
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import inkex
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from inkex.paths import Path
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import gettext
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_ = gettext.gettext
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from copy import deepcopy
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import math
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from math import sqrt
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class EllipseSolveEffect(inkex.Effect):
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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.svg.selected) == 0:
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sys.exit(_("Error: You must select at least one path"))
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for pathId in self.svg.selected:
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path = self.svg.selected[pathId]
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pathdata = Path(path.get('d')).to_arrays()
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if len(pathdata) < 5:
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sys.exit(_("Error: The selected path has %d points, " +
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"but 5 are needed.") % len(pathdata))
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points = []
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for i in range(5):
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# pathdata[i] is the i'th segment of the path
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# pathdata[i][1] is the list of coordinates for the segment
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# pathdata[i][1][-2] is the x-coordinate of the last x,y pair
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# in the segment definition
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segpoints = pathdata[i][1]
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x = segpoints[-2]
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y = segpoints[-1]
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points.append((x,y))
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conic = solve_conic(points)
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[a,b,c,d,e,f] = conic
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if bareiss_determinant([[a,b/2,d/2],[b/2,c,e/2],[d/2,e/2,f]]) == 0 or a*c - b*b/4 <= 0:
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sys.exit(_("Error: Could not find an ellipse that passes " +
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"through the provided points"))
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center = ellipse_center(conic)
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[ad1, ad2] = ellipse_axes(conic)
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al1 = ellipse_axislen(conic, center, ad1)
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al2 = ellipse_axislen(conic, center, ad2)
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# Create an <svg:ellipse> object with the appropriate cx,cy and
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# with the major axis in the x direction. Then add a transform to
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# rotate it to the correct angle.
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if al1 > al2:
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major_dir = ad1
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major_len = al1
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minor_len = al2
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else:
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major_dir = ad2
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major_len = al2
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minor_len = al1
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# add sodipodi magic to turn the path into an ellipse
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def sodi(x):
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return inkex.addNS(x, 'sodipodi')
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path.set(sodi('cx'), str(center[0]))
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path.set(sodi('cy'), str(center[1]))
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path.set(sodi('rx'), str(major_len))
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path.set(sodi('ry'), str(minor_len))
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path.set(sodi('type'), 'arc')
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#inkex.utils.debug(str(center[0]))
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#inkex.utils.debug(str(center[1]))
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angle = math.atan2(major_dir[1], major_dir[0])
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if angle > math.pi / 2:
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angle -= math.pi
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if angle < -math.pi / 2:
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angle += math.pi
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path.apply_transform()
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path.set('transform', 'rotate(%f %f %f)' % (angle * 180 / math.pi, center[0], center[1]))
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# NASTY BUGFIX: We do apply_transform and path.set twice because otherwise the ellipse will not be rendered correctly. Reason unknown!
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path.apply_transform()
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path.set('transform', 'rotate(%f %f %f)' % (angle * 180 / math.pi, center[0], center[1]))
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def solve_conic(pts):
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# Find the equation of the conic section passing through the five given
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# points.
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#
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# This technique is from
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# http://math.fullerton.edu/mathews/n2003/conicfit/ConicFitMod/Links/ConicFitMod_lnk_9.html
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# (retrieved 31 Jan 2012)
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rowmajor_matrix = []
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for i in range(5):
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(x,y) = pts[i]
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row = [x*x, x*y, y*y, x, y, 1]
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rowmajor_matrix.append(row)
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full_matrix = []
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for i in range(6):
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col = []
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for j in range(5):
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col.append(rowmajor_matrix[j][i])
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full_matrix.append(col);
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coeffs = []
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sign = 1
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for i in range(6):
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mat = []
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for j in range(6):
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if j == i:
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continue
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mat.append(full_matrix[j])
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coeffs.append(bareiss_determinant(mat) * sign)
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sign = -sign
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return coeffs
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def bareiss_determinant(mat_orig):
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# Compute the determinant of the matrix using Bareiss's algorithm. It
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# doesn't matter whether 'mat' is in row-major or column-major layout,
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# because det(A) = det(A^T)
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# Algorithm from:
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# Yap, Chee, "Linear Systems", Fundamental Problems of Algorithmic Algebra
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# Lecture X, Section 2
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# http://cs.nyu.edu/~yap/book/alge/ftpSite/l10.ps.gz
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mat = deepcopy(mat_orig);
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size = len(mat)
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last_akk = 1
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for k in range(size-1):
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if last_akk == 0:
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return 0
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for i in range(k+1, size):
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for j in range(k+1, size):
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mat[i][j] = (mat[i][j] * mat[k][k] - mat[i][k] * mat[k][j]) / last_akk
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last_akk = mat[k][k]
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return mat[size-1][size-1]
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def ellipse_center(conic):
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# From
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# http://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections#Center
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[a,b,c,d,e,f] = conic
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x = (b*e - 2*c*d) / (4*a*c - b*b);
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y = (d*b - 2*a*e) / (4*a*c - b*b);
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return (x,y)
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def ellipse_axes(conic):
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# Compute the axis directions of the ellipse.
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# This technique is from
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# http://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections#Axes
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[a,b,c,d,e,f] = conic
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# Compute the eigenvalues of
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# / a b/2 \
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# \ b/2 c /
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# This algorithm is from
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# http://www.math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/index.html
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# (retrieved 31 Jan 2012)
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ma = a
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mb = b/2
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mc = b/2
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md = c
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mdet = ma*md - mb*mc
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mtrace = ma + md
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(l1,l2) = solve_quadratic(1, -mtrace, mdet);
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# Eigenvalues (\lambda_1, \lambda_2)
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#l1 = mtrace / 2 + sqrt(mtrace*mtrace/4 - mdet)
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#l2 = mtrace / 2 - sqrt(mtrace*mtrace/4 - mdet)
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if mb == 0:
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return [(0,1), (1,0)]
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else:
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return [(mb, l1-ma), (mb, l2-ma)]
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def ellipse_axislen(conic, center, direction):
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# Compute the axis length as a multiple of the magnitude of 'direction'
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[a,b,c,d,e,f] = conic
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(cx,cy) = center
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(dx,dy) = direction
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dlen = sqrt(dx*dx + dy*dy)
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dx /= dlen
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dy /= dlen
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# Solve for t:
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# a*x^2 + b*x*y + c*y^2 + d*x + e*y + f = 0
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# x = cx + t * dx
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# y = cy + t * dy
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# by substituting, we get qa*t^2 + qb*t + qc = 0, where:
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qa = a*dx*dx + b*dx*dy + c*dy*dy
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qb = a*2*cx*dx + b*(cx*dy + cy*dx) + c*2*cy*dy + d*dx + e*dy
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qc = a*cx*cx + b*cx*cy + c*cy*cy + d*cx + e*cy + f
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(t1,t2) = solve_quadratic(qa,qb,qc)
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return max(t1,t2)
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def solve_quadratic(a,b,c):
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disc = b*b - 4*a*c
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disc_root = sqrt(b*b - 4*a*c)
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x1 = (-b + disc_root) / (2*a)
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x2 = (-b - disc_root) / (2*a)
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return (x1,x2)
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if __name__ == '__main__':
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EllipseSolveEffect().run() |