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Diffstat (limited to 'share/extensions/triangle.py')
| -rwxr-xr-x | share/extensions/triangle.py | 188 |
1 files changed, 188 insertions, 0 deletions
diff --git a/share/extensions/triangle.py b/share/extensions/triangle.py new file mode 100755 index 0000000..dc8d6f2 --- /dev/null +++ b/share/extensions/triangle.py @@ -0,0 +1,188 @@ +#!/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 a triangle given certain information + about side length or angles. + +Measurements of the triangle + + C(x_c,y_c) + /`__ + / a_c``--__ + / ``--__ s_a + s_b / ``--__ + /a_a a_b`--__ + /--------------------------------``B(x_b, y_b) + A(x_a,y_a) s_b +""" + +import sys +from math import acos, asin, cos, pi, sin, sqrt + +import inkex + +X, Y = range(2) + +def draw_SVG_tri(point1, point2, point3, offset, width, name, parent): + style = {'stroke': '#000000', 'stroke-width': str(width), 'fill': 'none'} + elem = parent.add(inkex.PathElement()) + elem.update(**{ + 'style': style, + 'inkscape:label': name, + 'd': 'M ' + str(point1[X] + offset[X]) + ',' + str(point1[Y] + offset[Y]) + + ' L ' + str(point2[X] + offset[X]) + ',' + str(point2[Y] + offset[Y]) + + ' L ' + str(point3[X] + offset[X]) + ',' + str(point3[Y] + offset[Y]) + + ' L ' + str(point1[X] + offset[X]) + ',' + str(point1[Y] + offset[Y]) + ' z'}) + return elem + + +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 third_side_from_enclosed_angle(s_a, s_b, a_c): # return the side opposite a_c + c_squared = s_a * s_a + s_b * s_b - 2 * s_a * s_b * cos(a_c) + if c_squared > 0: + return sqrt(c_squared) + else: + return 0 # means we have an invalid or degenerate triangle (zero is caught at the drawing stage) + + +def pt_on_circ(radius, angle): # return the x,y coordinate of the polar coordinate + x = radius * cos(angle) + y = radius * sin(angle) + return [x, y] + + +def v_add(point1, point2): # add an offset to coordinates + return [point1[X] + point2[X], point1[Y] + point2[Y]] + + +def is_valid_tri_from_sides(a, b, c): # check whether triangle with sides a,b,c is valid + return (a + b) > c and (a + c) > b and (b + c) > a and a > 0 and b > 0 and c > 0 # two sides must always be greater than the third + # no zero-length sides, no degenerate case + + +def draw_tri_from_3_sides(s_a, s_b, s_c, offset, width, parent): # draw a triangle from three sides (with a given offset + if is_valid_tri_from_sides(s_a, s_b, s_c): + a_b = angle_from_3_sides(s_a, s_c, s_b) + + a = (0, 0) # a is the origin + b = v_add(a, (s_c, 0)) # point B is horizontal from the origin + c = v_add(b, pt_on_circ(s_a, pi - a_b)) # get point c + c[1] = -c[1] + + offx = max(b[0], c[0]) / 2 # b or c could be the furthest right + offy = c[1] / 2 # c is the highest point + offset = (offset[0] - offx, offset[1] - offy) # add the centre of the triangle to the offset + + draw_SVG_tri(a, b, c, offset, width, 'Triangle', parent) + else: + inkex.errormsg('Invalid Triangle Specifications.') + + +class Triangle(inkex.EffectExtension): + def add_arguments(self, pars): + pars.add_argument("--s_a", type=float, default=100.0, help="Side Length a") + pars.add_argument("--s_b", type=float, default=100.0, help="Side Length b") + pars.add_argument("--s_c", type=float, default=100.0, help="Side Length c") + pars.add_argument("--a_a", type=float, default=60.0, help="Angle a") + pars.add_argument("--a_b", type=float, default=30.0, help="Angle b") + pars.add_argument("--a_c", type=float, default=90.0, help="Angle c") + pars.add_argument("--mode", default='3_sides', help="Side Length c") + + def effect(self): + tri = self.svg.get_current_layer() + offset = self.svg.namedview.center + self.options.s_a = self.svg.unittouu(str(self.options.s_a) + 'px') + self.options.s_b = self.svg.unittouu(str(self.options.s_b) + 'px') + self.options.s_c = self.svg.unittouu(str(self.options.s_c) + 'px') + stroke_width = self.svg.unittouu('2px') + + if self.options.mode == '3_sides': + s_a = self.options.s_a + s_b = self.options.s_b + s_c = self.options.s_c + draw_tri_from_3_sides(s_a, s_b, s_c, offset, stroke_width, tri) + + elif self.options.mode == 's_ab_a_c': + s_a = self.options.s_a + s_b = self.options.s_b + a_c = self.options.a_c * pi / 180 # in rad + + s_c = third_side_from_enclosed_angle(s_a, s_b, a_c) + draw_tri_from_3_sides(s_a, s_b, s_c, offset, stroke_width, tri) + + elif self.options.mode == 's_ab_a_a': + s_a = self.options.s_a + s_b = self.options.s_b + a_a = self.options.a_a * pi / 180 # in rad + + if (a_a < pi / 2.0) and (s_a < s_b) and (s_a > s_b * sin(a_a)): # this is an ambiguous case + ambiguous = True # we will give both answers + else: + ambiguous = False + + sin_a_b = s_b * sin(a_a) / s_a + + if (sin_a_b <= 1) and (sin_a_b >= -1): # check the solution is possible + a_b = asin(sin_a_b) # acute solution + a_c = pi - a_a - a_b + error = False + else: + sys.stderr.write('Error:Invalid Triangle Specifications.\n') # signal an error + error = True + + if not error and (a_b < pi) and (a_c < pi): # check that the solution is valid, if so draw acute solution + s_c = third_side_from_enclosed_angle(s_a, s_b, a_c) + draw_tri_from_3_sides(s_a, s_b, s_c, offset, stroke_width, tri) + + if not error and ((a_b > pi) or (a_c > pi) or ambiguous): # we want the obtuse solution + a_b = pi - a_b + a_c = pi - a_a - a_b + s_c = third_side_from_enclosed_angle(s_a, s_b, a_c) + draw_tri_from_3_sides(s_a, s_b, s_c, offset, stroke_width, tri) + + elif self.options.mode == 's_a_a_ab': + s_a = self.options.s_a + a_a = self.options.a_a * pi / 180 # in rad + a_b = self.options.a_b * pi / 180 # in rad + + a_c = pi - a_a - a_b + s_b = s_a * sin(a_b) / sin(a_a) + s_c = s_a * sin(a_c) / sin(a_a) + + draw_tri_from_3_sides(s_a, s_b, s_c, offset, stroke_width, tri) + + elif self.options.mode == 's_c_a_ab': + s_c = self.options.s_c + a_a = self.options.a_a * pi / 180 # in rad + a_b = self.options.a_b * pi / 180 # in rad + + a_c = pi - a_a - a_b + s_a = s_c * sin(a_a) / sin(a_c) + s_b = s_c * sin(a_b) / sin(a_c) + + draw_tri_from_3_sides(s_a, s_b, s_c, offset, stroke_width, tri) + + +if __name__ == '__main__': + Triangle().run() |