#!/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 from inkex.localization import inkex_gettext as _ 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()