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diff --git a/share/extensions/draw_from_triangle.py b/share/extensions/draw_from_triangle.py
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+#!/usr/bin/env python
+# coding=utf-8
+#
+# Copyright (C) 2007 John Beard john.j.beard@gmail.com
+#
+# This program is free software; you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 2 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program; if not, write to the Free Software
+# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+#
+"""
+This extension allows you to draw various triangle constructions
+It requires a path to be selected
+It will use the first three nodes of this path
+
+Dimensions of a triangle__
+
+ /`__
+ / a_c``--__
+ / ``--__ s_a
+s_b / ``--__
+ /a_a a_b`--__
+ /--------------------------------``B
+ A s_b
+"""
+
+from math import acos, cos, pi, sin, sqrt, tan
+
+import inkex
+from inkex import PathElement, Circle
+
+(X, Y) = range(2)
+
+# DRAWING ROUTINES
+
+# draw an SVG triangle given in trilinar coords
+def draw_SVG_circle(rad, centre, params, style, name, parent): # draw an SVG circle with a given radius as trilinear coordinates
+ if rad == 0: # we want a dot
+ r = style.d_rad # get the dot width from the style
+ circ_style = {'stroke': style.d_col, 'stroke-width': str(style.d_th), 'fill': style.d_fill}
+ else:
+ r = rad # use given value
+ circ_style = {'stroke': style.c_col, 'stroke-width': str(style.c_th), 'fill': style.c_fill}
+
+ cx, cy = get_cartesian_pt(centre, params)
+ circ_attribs = {'cx': str(cx), 'cy': str(cy), 'r': str(r)}
+ elem = parent.add(Circle(**circ_attribs))
+ elem.style = circ_style
+ elem.label = name
+
+
+# draw an SVG triangle given in trilinar coords
+def draw_SVG_tri(vert_mat, params, style, name, parent):
+ p1, p2, p3 = get_cartesian_tri(vert_mat, params) # get the vertex matrix in cartesian points
+ elem = parent.add(PathElement())
+ elem.path = 'M ' + str(p1[0]) + ',' + str(p1[1]) +\
+ ' L ' + str(p2[0]) + ',' + str(p2[1]) +\
+ ' L ' + str(p3[0]) + ',' + str(p3[1]) +\
+ ' L ' + str(p1[0]) + ',' + str(p1[1]) + ' z'
+ elem.style = {'stroke': style.l_col, 'stroke-width': str(style.l_th), 'fill': style.l_fill}
+ elem.label = name
+
+
+# draw an SVG line segment between the given (raw) points
+def draw_SVG_line(a, b, style, name, parent):
+ (x1, y1) = a
+ (x2, y2) = b
+ line = parent.add(PathElement())
+ line.style = {'stroke': style.l_col, 'stroke-width': str(style.l_th), 'fill': style.l_fill}
+ line.path = 'M ' + str(x1) + ',' + str(y1) + ' L ' + str(x2) + ',' + str(y2)
+ line.lavel = name
+
+
+# lines from each vertex to a corresponding point in trilinears
+def draw_vertex_lines(vert_mat, params, width, name, parent):
+ for i in range(3):
+ oppositepoint = get_cartesian_pt(vert_mat[i], params)
+ draw_SVG_line(params[3][-i % 3], oppositepoint, width, name + ':' + str(i), parent)
+
+
+# MATHEMATICAL ROUTINES
+
+def distance(a, b):
+ """find the pythagorean distance"""
+ (x0, y0) = a
+ (x1, y1) = b
+ return sqrt((x0 - x1) * (x0 - x1) + (y0 - y1) * (y0 - y1))
+
+
+def vector_from_to(a, b):
+ """get the vector from (x0,y0) to (x1,y1)"""
+ return b[X] - a[X], b[Y], a[Y]
+
+
+def get_cartesian_pt(t, p): # get the cartesian coordinates from a trilinear set
+ denom = p[0][0] * t[0] + p[0][1] * t[1] + p[0][2] * t[2]
+ c1 = p[0][1] * t[1] / denom
+ c2 = p[0][2] * t[2] / denom
+ return c1 * p[2][1][0] + c2 * p[2][0][0], c1 * p[2][1][1] + c2 * p[2][0][1]
+
+
+def get_cartesian_tri(arg, params):
+ """get the cartesian points from a trilinear vertex matrix"""
+ (t11, t12, t13), (t21, t22, t23), (t31, t32, t33) = arg
+ p1 = get_cartesian_pt((t11, t12, t13), params)
+ p2 = get_cartesian_pt((t21, t22, t23), params)
+ p3 = get_cartesian_pt((t31, t32, t33), params)
+ return p1, p2, p3
+
+
+def angle_from_3_sides(a, b, c): # return the angle opposite side c
+ cosx = (a * a + b * b - c * c) / (2 * a * b) # use the cosine rule
+ return acos(cosx)
+
+
+def translate_string(string, os): # translates s_a, a_a, etc to params[x][y], with cyclic offset
+ string = string.replace('s_a', 'params[0][' + str((os + 0) % 3) + ']') # replace with ref. to the relvant values,
+ string = string.replace('s_b', 'params[0][' + str((os + 1) % 3) + ']') # cycled by i
+ string = string.replace('s_c', 'params[0][' + str((os + 2) % 3) + ']')
+ string = string.replace('a_a', 'params[1][' + str((os + 0) % 3) + ']')
+ string = string.replace('a_b', 'params[1][' + str((os + 1) % 3) + ']')
+ string = string.replace('a_c', 'params[1][' + str((os + 2) % 3) + ']')
+ string = string.replace('area', 'params[4][0]')
+ string = string.replace('semiperim', 'params[4][1]')
+ return string
+
+
+def pt_from_tcf(tcf, params): # returns a trilinear triplet from a triangle centre function
+ trilin_pts = [] # will hold the final points
+ for i in range(3):
+ temp = tcf # read in the tcf
+ temp = translate_string(temp, i)
+ func = eval('lambda params: ' + temp.strip('"')) # the function leading to the trilinar element
+ trilin_pts.append(func(params)) # evaluate the function for the first trilinear element
+ return trilin_pts
+
+
+# SVG DATA PROCESSING
+
+def get_n_points_from_path(node, n):
+ """returns a list of first n points (x,y) in an SVG path-representing node"""
+ points = list(node.path.control_points)
+ if len(points) < 3:
+ return []
+ return points[:3]
+
+# EXTRA MATHS FUNCTIONS
+def sec(x): # secant(x)
+ if x == pi / 2 or x == -pi / 2 or x == 3 * pi / 2 or x == -3 * pi / 2: # sec(x) is undefined
+ return 100000000000
+ else:
+ return 1 / cos(x)
+
+
+def csc(x): # cosecant(x)
+ if x == 0 or x == pi or x == 2 * pi or x == -2 * pi: # csc(x) is undefined
+ return 100000000000
+ else:
+ return 1 / sin(x)
+
+
+def cot(x): # cotangent(x)
+ if x == 0 or x == pi or x == 2 * pi or x == -2 * pi: # cot(x) is undefined
+ return 100000000000
+ else:
+ return 1 / tan(x)
+
+
+class Style(object): # container for style information
+ def __init__(self, svg):
+ # dot markers
+ self.d_rad = svg.unittouu('4px') # dot marker radius
+ self.d_th = svg.unittouu('2px') # stroke width
+ self.d_fill = '#aaaaaa' # fill colour
+ self.d_col = '#000000' # stroke colour
+
+ # lines
+ self.l_th = svg.unittouu('2px')
+ self.l_fill = 'none'
+ self.l_col = '#000000'
+
+ # circles
+ self.c_th = svg.unittouu('2px')
+ self.c_fill = 'none'
+ self.c_col = '#000000'
+
+
+class DrawFromTriangle(inkex.EffectExtension):
+ def add_arguments(self, pars):
+ pars.add_argument("--tab")
+ # PRESET POINT OPTIONS
+ pars.add_argument("--circumcircle", type=inkex.Boolean, default=False)
+ pars.add_argument("--circumcentre", type=inkex.Boolean, default=False)
+ pars.add_argument("--incircle", type=inkex.Boolean, default=False)
+ pars.add_argument("--incentre", type=inkex.Boolean, default=False)
+ pars.add_argument("--contact_tri", type=inkex.Boolean, default=False)
+ pars.add_argument("--excircles", type=inkex.Boolean, default=False)
+ pars.add_argument("--excentres", type=inkex.Boolean, default=False)
+ pars.add_argument("--extouch_tri", type=inkex.Boolean, default=False)
+ pars.add_argument("--excentral_tri", type=inkex.Boolean, default=False)
+ pars.add_argument("--orthocentre", type=inkex.Boolean, default=False)
+ pars.add_argument("--orthic_tri", type=inkex.Boolean, default=False)
+ pars.add_argument("--altitudes", type=inkex.Boolean, default=False)
+ pars.add_argument("--anglebisectors", type=inkex.Boolean, default=False)
+ pars.add_argument("--centroid", type=inkex.Boolean, default=False)
+ pars.add_argument("--ninepointcentre", type=inkex.Boolean, default=False)
+ pars.add_argument("--ninepointcircle", type=inkex.Boolean, default=False)
+ pars.add_argument("--symmedians", type=inkex.Boolean, default=False)
+ pars.add_argument("--sym_point", type=inkex.Boolean, default=False)
+ pars.add_argument("--sym_tri", type=inkex.Boolean, default=False)
+ pars.add_argument("--gergonne_pt", type=inkex.Boolean, default=False)
+ pars.add_argument("--nagel_pt", type=inkex.Boolean, default=False)
+ # CUSTOM POINT OPTIONS
+ pars.add_argument("--mode", default='trilin')
+ pars.add_argument("--cust_str", default='s_a')
+ pars.add_argument("--cust_pt", type=inkex.Boolean, default=False)
+ pars.add_argument("--cust_radius", type=inkex.Boolean, default=False)
+ pars.add_argument("--radius", default='s_a')
+ pars.add_argument("--isogonal_conj", type=inkex.Boolean, default=False)
+ pars.add_argument("--isotomic_conj", type=inkex.Boolean, default=False)
+
+ def effect(self):
+ so = self.options # shorthand
+
+ pts = [] # initialise in case nothing is selected and following loop is not executed
+ for node in self.svg.selection.filter(inkex.PathElement).values():
+ # find the (x,y) coordinates of the first 3 points of the path
+ pts = get_n_points_from_path(node, 3)
+
+ if len(pts) == 3: # if we have right number of nodes, else skip and end program
+ st = Style(self.svg) # style for dots, lines and circles
+
+ # CREATE A GROUP TO HOLD ALL GENERATED ELEMENTS IN
+ # Hold relative to point A (pt[0])
+ layer = self.svg.get_current_layer().add(inkex.Group.new('TriangleElements'))
+ layer.transform = 'translate(' + str(pts[0][0]) + ',' + str(pts[0][1]) + ')'
+
+ # GET METRICS OF THE TRIANGLE
+ # vertices in the local coordinates (set pt[0] to be the origin)
+ vtx = [[0, 0],
+ [pts[1][0] - pts[0][0], pts[1][1] - pts[0][1]],
+ [pts[2][0] - pts[0][0], pts[2][1] - pts[0][1]]]
+
+ s_a = distance(vtx[1], vtx[2]) # get the scalar side lengths
+ s_b = distance(vtx[0], vtx[1])
+ s_c = distance(vtx[0], vtx[2])
+ sides = (s_a, s_b, s_c) # side list for passing to functions easily and for indexing
+
+ a_a = angle_from_3_sides(s_b, s_c, s_a) # angles in radians
+ a_b = angle_from_3_sides(s_a, s_c, s_b)
+ a_c = angle_from_3_sides(s_a, s_b, s_c)
+ angles = (a_a, a_b, a_c)
+
+ ab = vector_from_to(vtx[0], vtx[1]) # vector from a to b
+ ac = vector_from_to(vtx[0], vtx[2]) # vector from a to c
+ bc = vector_from_to(vtx[1], vtx[2]) # vector from b to c
+ vecs = (ab, ac) # vectors for finding cartesian point from trilinears
+
+ semiperim = (s_a + s_b + s_c) / 2.0 # semiperimeter
+ area = sqrt(semiperim * (semiperim - s_a) * (semiperim - s_b) * (semiperim - s_c)) # area of the triangle by heron's formula
+ uvals = (area, semiperim) # useful values
+
+ params = (sides, angles, vecs, vtx, uvals) # all useful triangle parameters in one object
+
+ # BEGIN DRAWING
+ if so.circumcentre or so.circumcircle:
+ r = s_a * s_b * s_c / (4 * area)
+ pt = (cos(a_a), cos(a_b), cos(a_c))
+ if so.circumcentre:
+ draw_SVG_circle(0, pt, params, st, 'Circumcentre', layer)
+ if so.circumcircle:
+ draw_SVG_circle(r, pt, params, st, 'Circumcircle', layer)
+
+ if so.incentre or so.incircle:
+ pt = [1, 1, 1]
+ if so.incentre:
+ draw_SVG_circle(0, pt, params, st, 'Incentre', layer)
+ if so.incircle:
+ r = area / semiperim
+ draw_SVG_circle(r, pt, params, st, 'Incircle', layer)
+
+ if so.contact_tri:
+ t1 = s_b * s_c / (-s_a + s_b + s_c)
+ t2 = s_a * s_c / (s_a - s_b + s_c)
+ t3 = s_a * s_b / (s_a + s_b - s_c)
+ v_mat = ((0, t2, t3), (t1, 0, t3), (t1, t2, 0))
+ draw_SVG_tri(v_mat, params, st, 'ContactTriangle', layer)
+
+ if so.extouch_tri:
+ t1 = (-s_a + s_b + s_c) / s_a
+ t2 = (s_a - s_b + s_c) / s_b
+ t3 = (s_a + s_b - s_c) / s_c
+ v_mat = ((0, t2, t3), (t1, 0, t3), (t1, t2, 0))
+ draw_SVG_tri(v_mat, params, st, 'ExtouchTriangle', layer)
+
+ if so.orthocentre:
+ pt = pt_from_tcf('cos(a_b)*cos(a_c)', params)
+ draw_SVG_circle(0, pt, params, st, 'Orthocentre', layer)
+
+ if so.orthic_tri:
+ v_mat = [[0, sec(a_b), sec(a_c)], [sec(a_a), 0, sec(a_c)], [sec(a_a), sec(a_b), 0]]
+ draw_SVG_tri(v_mat, params, st, 'OrthicTriangle', layer)
+
+ if so.centroid:
+ pt = [1 / s_a, 1 / s_b, 1 / s_c]
+ draw_SVG_circle(0, pt, params, st, 'Centroid', layer)
+
+ if so.ninepointcentre or so.ninepointcircle:
+ pt = [cos(a_b - a_c), cos(a_c - a_a), cos(a_a - a_b)]
+ if so.ninepointcentre:
+ draw_SVG_circle(0, pt, params, st, 'NinePointCentre', layer)
+ if so.ninepointcircle:
+ r = s_a * s_b * s_c / (8 * area)
+ draw_SVG_circle(r, pt, params, st, 'NinePointCircle', layer)
+
+ if so.altitudes:
+ v_mat = [[0, sec(a_b), sec(a_c)], [sec(a_a), 0, sec(a_c)], [sec(a_a), sec(a_b), 0]]
+ draw_vertex_lines(v_mat, params, st, 'Altitude', layer)
+
+ if so.anglebisectors:
+ v_mat = ((0, 1, 1), (1, 0, 1), (1, 1, 0))
+ draw_vertex_lines(v_mat, params, st, 'AngleBisectors', layer)
+
+ if so.excircles or so.excentres or so.excentral_tri:
+ v_mat = ((-1, 1, 1), (1, -1, 1), (1, 1, -1))
+ if so.excentral_tri:
+ draw_SVG_tri(v_mat, params, st, 'ExcentralTriangle', layer)
+ for i in range(3):
+ if so.excircles:
+ r = area / (semiperim - sides[i])
+ draw_SVG_circle(r, v_mat[i], params, st, 'Excircle:' + str(i), layer)
+ if so.excentres:
+ draw_SVG_circle(0, v_mat[i], params, st, 'Excentre:' + str(i), layer)
+
+ if so.sym_tri or so.symmedians:
+ v_mat = ((0, s_b, s_c), (s_a, 0, s_c), (s_a, s_b, 0))
+ if so.sym_tri:
+ draw_SVG_tri(v_mat, params, st, 'SymmedialTriangle', layer)
+ if so.symmedians:
+ draw_vertex_lines(v_mat, params, st, 'Symmedian', layer)
+
+ if so.sym_point:
+ pt = (s_a, s_b, s_c)
+ draw_SVG_circle(0, pt, params, st, 'SymmmedianPoint', layer)
+
+ if so.gergonne_pt:
+ pt = pt_from_tcf('1/(s_a*(s_b+s_c-s_a))', params)
+ draw_SVG_circle(0, pt, params, st, 'GergonnePoint', layer)
+
+ if so.nagel_pt:
+ pt = pt_from_tcf('(s_b+s_c-s_a)/s_a', params)
+ draw_SVG_circle(0, pt, params, st, 'NagelPoint', layer)
+
+ if so.cust_pt or so.cust_radius or so.isogonal_conj or so.isotomic_conj:
+ pt = [] # where we will store the point in trilinears
+ if so.mode == 'trilin': # if we are receiving from trilinears
+ for i in range(3):
+ strings = so.cust_str.split(':') # get split string
+ strings[i] = translate_string(strings[i], 0)
+ func = eval('lambda params: ' + strings[i].strip('"')) # the function leading to the trilinar element
+ pt.append(func(params)) # evaluate the function for the trilinear element
+ else: # we need a triangle function
+ string = so.cust_str # don't need to translate, as the pt_from_tcf function does that for us
+ pt = pt_from_tcf(string, params) # get the point from the tcf directly
+
+ if so.cust_pt: # draw the point
+ draw_SVG_circle(0, pt, params, st, 'CustomTrilinearPoint', layer)
+ if so.cust_radius: # draw the circle with given radius
+ strings = translate_string(so.radius, 0)
+ func = eval('lambda params: ' + strings.strip('"')) # the function leading to the radius
+ r = func(params)
+ draw_SVG_circle(r, pt, params, st, 'CustomTrilinearCircle', layer)
+ if so.isogonal_conj:
+ isogonal = [0, 0, 0]
+ for i in range(3):
+ isogonal[i] = 1 / pt[i]
+ draw_SVG_circle(0, isogonal, params, st, 'CustomIsogonalConjugate', layer)
+ if so.isotomic_conj:
+ isotomic = [0, 0, 0]
+ for i in range(3):
+ isotomic[i] = 1 / (params[0][i] * params[0][i] * pt[i])
+ draw_SVG_circle(0, isotomic, params, st, 'CustomIsotomicConjugate', layer)
+
+
+if __name__ == '__main__':
+ DrawFromTriangle().run()
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