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#!/usr/bin/env python
'''
Copyright (C) 2007 John Beard john.j.beard@gmail.com
##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
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., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
'''
import inkex
import simplestyle, sys
from math import *
def draw_SVG_tri( (x1, y1), (x2, y2), (x3, y3), (ox,oy), width, name, parent):
style = { 'stroke': '#000000', 'stroke-width':str(width), 'fill': 'none' }
tri_attribs = {'style':simplestyle.formatStyle(style),
inkex.addNS('label','inkscape'):name,
'd':'M '+str(x1+ox)+','+str(y1+oy)+
' L '+str(x2+ox)+','+str(y2+oy)+
' L '+str(x3+ox)+','+str(y3+oy)+
' L '+str(x1+ox)+','+str(y1+oy)+' z'}
inkex.etree.SubElement(parent, inkex.addNS('path','svg'), tri_attribs )
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( (x1,y1),(x2,y2) ):#add an offset to coordinates
return [x1+x2, y1+y2]
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, 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, 2, 'Triangle', parent)
else:
sys.stderr.write('Error:Invalid Triangle Specifications.\n')
class Grid_Polar(inkex.Effect):
def __init__(self):
inkex.Effect.__init__(self)
self.OptionParser.add_option("--s_a",
action="store", type="float",
dest="s_a", default=100.0,
help="Side Length a")
self.OptionParser.add_option("--s_b",
action="store", type="float",
dest="s_b", default=100.0,
help="Side Length b")
self.OptionParser.add_option("--s_c",
action="store", type="float",
dest="s_c", default=100.0,
help="Side Length c")
self.OptionParser.add_option("--a_a",
action="store", type="float",
dest="a_a", default=60.0,
help="Angle a")
self.OptionParser.add_option("--a_b",
action="store", type="float",
dest="a_b", default=30.0,
help="Angle b")
self.OptionParser.add_option("--a_c",
action="store", type="float",
dest="a_c", default=90.0,
help="Angle c")
self.OptionParser.add_option("--mode",
action="store", type="string",
dest="mode", default='3_sides',
help="Side Length c")
def effect(self):
tri = self.current_layer
offset = (self.view_center[0],self.view_center[1]) #the offset require to centre the triangle
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, 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, 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 ambigous 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, 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, 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, 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, tri)
if __name__ == '__main__':
e = Grid_Polar()
e.affect()
# vim: expandtab shiftwidth=4 tabstop=8 softtabstop=4 encoding=utf-8 textwidth=99
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