1#!/usr/local/bin/python3.8 2# coding=utf-8 3# 4# Copyright (C) 2009 John Beard john.j.beard@gmail.com 5# 6# This program is free software; you can redistribute it and/or modify 7# it under the terms of the GNU General Public License as published by 8# the Free Software Foundation; either version 2 of the License, or 9# (at your option) any later version. 10# 11# This program is distributed in the hope that it will be useful, 12# but WITHOUT ANY WARRANTY; without even the implied warranty of 13# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14# GNU General Public License for more details. 15# 16# You should have received a copy of the GNU General Public License 17# along with this program; if not, write to the Free Software 18# Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. 19# 20""" 21This extension renders a wireframe sphere constructed from lines of latitude 22and lines of longitude. 23 24The number of lines of latitude and longitude is independently variable. Lines 25of latitude and longtude are in separate subgroups. The whole figure is also in 26its own group. 27 28The whole sphere can be tilted towards or away from the veiwer by a given 29number of degrees. If the whole sphere is then rotated normally in Inkscape, 30any position can be achieved. 31 32There is an option to hide the lines at the back of the sphere, as if the 33sphere were opaque. 34""" 35# FIXME: Lines of latitude only have an approximation of the function needed 36# to hide the back portion. If you can derive the proper equation, 37# please add it in. 38# Line of longitude have the exact method already. 39# Workaround: Use the Inkscape ellipse tool to edit the start and end 40# points of the lines of latitude to end at the horizon circle. 41# 42# TODO: Add support for odd numbers of lines of longitude. This means breaking 43# the line at the poles, and having two half ellipses for each line. 44# The angles at which the ellipse arcs pass the poles are not constant and 45# need to be derived before this can be implemented. 46# TODO: Add support for prolate and oblate spheroids 47# 48# 0.10 2009-10-25 First version. Basic spheres supported. 49# Hidden lines of latitude still not properly calculated. 50# Prolate and oblate spheroids not considered. 51 52from math import acos, atan, cos, pi, sin, tan 53 54import inkex 55 56# add a tiny value to the ellipse radii, so that if we get a 57# zero radius, the ellipse still shows up as a line 58EPSILON = 0.001 59 60 61class WireframeSphere(inkex.GenerateExtension): 62 """Writeframe extension, generate a wireframe""" 63 container_label = 'WireframeSphere' 64 65 def container_transform(self): 66 transform = super(WireframeSphere, self).container_transform() 67 if self.options.TILT < 0: 68 transform *= inkex.Transform(scale=(1, -1)) 69 return transform 70 71 def add_arguments(self, pars): 72 pars.add_argument("--num_lat", type=int, dest="NUM_LAT", default=19) 73 pars.add_argument("--num_long", type=int, dest="NUM_LONG", default=24) 74 pars.add_argument("--radius", type=float, dest="RADIUS", default=100.0) 75 pars.add_argument("--tilt", type=float, dest="TILT", default=35.0) 76 pars.add_argument("--rotation", type=float, dest="ROT_OFFSET", default=4) 77 pars.add_argument("--hide_back", type=inkex.Boolean, dest="HIDE_BACK", default=False) 78 79 def generate(self): 80 opt = self.options 81 82 # PARAMETER PROCESSING 83 if opt.NUM_LONG % 2 != 0: # lines of longitude are odd : abort 84 inkex.errormsg('Please enter an even number of lines of longitude.') 85 return 86 87 radius = self.svg.unittouu(str(opt.RADIUS) + 'px') 88 tilt = abs(opt.TILT) * (pi / 180) # Convert to radians 89 rotate = opt.ROT_OFFSET * pi / 180 # Convert to radians 90 91 # only process longitudes if we actually want some 92 if opt.NUM_LONG > 0: 93 # Yieled elements are added to generated container 94 yield self.longitude_lines(opt.NUM_LONG, tilt, radius, rotate) 95 96 if opt.NUM_LAT > 0: 97 # Yieled elements are added to generated container 98 # Account for the fact that we loop over N-1 elements 99 yield self.latitude_lines(opt.NUM_LAT + 1, tilt, radius) 100 101 # THE HORIZON CIRCLE - circle, centred on the sphere centre 102 yield self.draw_ellipse((radius, radius), (0, 0)) 103 104 def longitude_lines(self, number, tilt, radius, rotate): 105 """Add lines of latitude as a group""" 106 # GROUP FOR THE LINES OF LONGITUDE 107 grp_long = inkex.Group() 108 grp_long.set('inkscape:label', 'Lines of Longitude') 109 110 # angle between neighbouring lines of longitude in degrees 111 #delta_long = 360.0 / number 112 113 for i in range(0, number // 2): 114 # The longitude of this particular line in radians 115 long_angle = rotate + (i * (360.0 / number)) * (pi / 180.0) 116 if long_angle > pi: 117 long_angle -= 2 * pi 118 # the rise is scaled by the sine of the tilt 119 # length = sqrt(width*width+height*height) #by pythagorean theorem 120 # inverse = sin(acos(length/so.RADIUS)) 121 inverse = abs(sin(long_angle)) * cos(tilt) 122 123 rads = (radius * inverse + EPSILON, radius) 124 125 # The rotation of the ellipse to get it to pass through the pole (degs) 126 rotation = atan( 127 (radius * sin(long_angle) * sin(tilt)) / 128 (radius * cos(long_angle)) 129 ) * (180.0 / pi) 130 131 # remove the hidden side of the ellipses if required 132 # this is always exactly half the ellipse, but we need to find out which half 133 start_end = (0, 2 * pi) # Default start and end angles -> full ellipse 134 if self.options.HIDE_BACK: 135 if long_angle <= pi / 2: # cut out the half ellispse that is hidden 136 start_end = (pi / 2, 3 * pi / 2) 137 else: 138 start_end = (3 * pi / 2, pi / 2) 139 140 # finally, draw the line of longitude 141 # the centre is always at the centre of the sphere 142 elem = grp_long.add(self.draw_ellipse(rads, (0, 0), start_end)) 143 # the rotation will be applied about the group centre (the centre of the sphere) 144 elem.transform = inkex.Transform(rotate=(rotation,)) 145 return grp_long 146 147 def latitude_lines(self, number, tilt, radius): 148 """Add lines of latitude as a group""" 149 # GROUP FOR THE LINES OF LATITUDE 150 grp_lat = inkex.Group() 151 grp_lat.set('inkscape:label', 'Lines of Latitude') 152 153 # Angle between the line of latitude (subtended at the centre) 154 delta_lat = 180.0 / number 155 156 for i in range(1, number): 157 # The angle of this line of latitude (from a pole) 158 lat_angle = ((delta_lat * i) * (pi / 180)) 159 160 # The width of the LoLat (no change due to projection) 161 # The projected height of the line of latitude 162 rads = ( 163 radius * sin(lat_angle), # major 164 (radius * sin(lat_angle) * sin(tilt)) + EPSILON, # minor 165 ) 166 167 # The x position is the sphere center, The projected y position of the LoLat 168 pos = (0, radius * cos(lat_angle) * cos(tilt)) 169 170 if self.options.HIDE_BACK: 171 if lat_angle > tilt: # this LoLat is partially or fully visible 172 if lat_angle > pi - tilt: # this LoLat is fully visible 173 grp_lat.add(self.draw_ellipse(rads, pos)) 174 else: # this LoLat is partially visible 175 proportion = -(acos(tan(lat_angle - pi / 2) \ 176 / tan(pi / 2 - tilt))) / pi + 1 177 # make the start and end angles (mirror image around pi/2) 178 start_end = (pi / 2 - proportion * pi, pi / 2 + proportion * pi) 179 grp_lat.add(self.draw_ellipse(rads, pos, start_end)) 180 181 else: # just draw the full lines of latitude 182 grp_lat.add(self.draw_ellipse(rads, pos)) 183 return grp_lat 184 185 def draw_ellipse(self, r_xy, c_xy, start_end=(0, 2 * pi)): 186 """Creates an elipse with all the required sodipodi attributes""" 187 path = inkex.PathElement() 188 path.update(**{ 189 'style': {'stroke': '#000000', 190 'stroke-width': str(self.svg.unittouu('1px')), 191 'fill': 'none'}, 192 'sodipodi:cx': str(c_xy[0]), 193 'sodipodi:cy': str(c_xy[1]), 194 'sodipodi:rx': str(r_xy[0]), 195 'sodipodi:ry': str(r_xy[1]), 196 'sodipodi:start': str(start_end[0]), 197 'sodipodi:end': str(start_end[1]), 198 'sodipodi:open': 'true', # all ellipse sectors we will draw are open 199 'sodipodi:type': 'arc', 200 'sodipodi:arc-type': 'arc', 201 }) 202 return path 203 204if __name__ == '__main__': 205 WireframeSphere().run() 206