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|
#
# Copyright (c) 2003, 2004 Art Haas
#
# This file is part of PythonCAD.
#
# PythonCAD 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.
#
# PythonCAD 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 PythonCAD; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
#
# functions for handling tangent circles on multiple objects
#
import math
from PythonCAD.Generic import hcline
from PythonCAD.Generic import vcline
from PythonCAD.Generic import acline
from PythonCAD.Generic import cline
from PythonCAD.Generic import ccircle
#
# common constants
#
_dtr = math.pi/180.0
_piover2 = math.pi/2.0
#
# find the projection point of point (x, y) on a line
# from (x1, y1) to (x2, y2)
#
def _get_two_point_projection(x1, y1, x2, y2, x, y):
_sqlen = pow((x2 - x1), 2) + pow((y2 - y1), 2)
_rn = ((x - x1) * (x2 - x1)) + ((y - y1) * (y2 - y1))
_r = _rn/_sqlen
_px = x1 + _r * (x2 - x1)
_py = y1 + _r * (y2 - y1)
return _px, _py
#
# find the projection point of point (x, y) on a line
# defined by an angle and y intercept
#
def _get_angled_projection(angle, yint, x, y):
_x1 = 0.0
_y1 = yint
_x2 = _x1 + math.cos(angle)
_y2 = _y1 + math.sin(angle)
return _get_two_point_projection(_x1, _y1, _x2, _y2, x, y)
def _two_line_tangent(x1, y1, x2, y2, x3, y3, x4, y4, x, y):
#
# this function calculates the apprpriate tangent circle
# for two lines (x1, y1)->(x2, y2) and (x3, y3)->(x4, y4)
# using a point (x, y) to determine which tangent circle
# should be defined
#
# test if lines are parallel
#
_cx = _cy = _radius = None
_denom = ((x2 - x1) * (y4 - y3)) - ((y2 - y1) * (x4 - x3))
# print "denom: %g" % _denom
if abs(_denom) < 1e-10:
# print "parallel ..."
if abs(x2 - x1) < 1e-10: # both vertical
if x < min(x1, x3) or x > max(x1, x3):
return None
_cx = (x3 + x1)/2.0
_cy = y
_radius = abs(x3 - x1)/2.0
elif abs(y2 - y1) < 1e-10: # both horizontal
if y < min(y1, y3) or y > max(y1, y3):
return None
_cx = x
_cy = (y3 + y1)/2.0
_radius = abs(y3 - y1)/2.0
else: # both at equal angles
_ax1, _ay1 = _get_two_point_projection(x1, y1, x2, y2, x, y)
# print "ax1: %g; ay1: %g" % (_ax1, _ay1)
_ax2, _ay2 = _get_two_point_projection(x3, y3, x4, y4, x, y)
# print "ax2: %g; ay2: %g" % (_ax2, _ay2)
if (x < min(_ax1, _ax2) or
x > max(_ax1, _ax2) or
y < min(_ay1, _ay2) or
y > max(_ay1, _ay2)):
return None
_cx = (_ax1 + _ax2)/2.0
_cy = (_ay1 + _ay2)/2.0
_radius = math.hypot((_ax1 - _cx), (_ay1 - _cy))
return _cx, _cy, _radius
#
# the lines are not parallel, so we have to test for the
# different combinations of horizontal/vertical/sloped lines ...
#
if abs(y2 - y1) < 1e-10: # horizontal line 1
# print "horizontal line 1 ..."
if abs(y4 - y3) < 1e-10: # this should be handled above ...
# print "horizontal line 2 ..."
if y < min(y1, y3) or y > max(y1, y3):
return None
_cx = x
_cy = (y1 + y3)/2.0
_radius = abs(_cy - y1)
elif abs(x4 - x3) < 1e-10: # vertical line 2
# print "vertical line 2 ..."
_a1 = math.pi/4.0
_a2 = -_a1
else:
_angle = math.atan2((y4 - y3), (x4 - x3))
_a1 = _angle/2.0
if _a1 > 0.0:
_a2 = _a1 - _piover2
else:
_a2 = _a1 + _piover2
elif abs(x2 - x1) < 1e-10: # vertical line 1
# print "vertical line 1 ..."
if abs(y4 - y3) < 1e-10: # horizontal line2
# print "horizontal line 2 ..."
_a1 = math.pi/4.0
_a2 = -_a1
elif abs(x4 - x3) < 1e-10: # this should be handled above ...
if x < min(x1, x3) or x > max(x1, x3):
return None
_cx = (x1 + x3)/2.0
_cy = y
_radius = abs(_cx - x1)
else:
_angle = math.atan2((y4 - y3), (x4 - x3))
if _angle > 0.0:
_a1 = (_angle + _piover2)/2.0
_a2 = _a1 - _piover2
else:
_a1 = (_angle - _piover2)/2.0
_a2 = _a1 + _piover2
else:
_angle1 = math.atan2((y2 - y1), (x2 - x1))
if abs(y4 - y3) < 1e-10: # horizontal line2
_a1 = _angle1/2.0
if _a1 > 0.0:
_a2 = _a1 - _piover2
else:
_a2 = _a1 + _piover2
elif abs(x4 - x3) < 1e-10: # vertical line2
if _angle1 > 0.0:
_a1 = (_angle1 + _piover2)/2.0
_a2 = _a1 - _piover2
else:
_a1 = (_angle1 - _piover2)/2.0
_a2 = _a1 + _piover2
else:
_angle2 = math.atan2((y4 - y3), (x4 - x3))
_a1 = (_angle1 + _angle2)/2.0
if _a1 > 0.0:
_a2 = _a1 - _piover2
else:
_a2 = _a1 + _piover2
if _cx is not None and _cy is not None and _radius is not None:
return _cx, _cy, _radius
#
# handle the general case of two lines at arbitrary angles
#
# print "arbitrary angles ..."
# print "a1: %g" % (_a1/_dtr)
# print "a2: %g" % (_a2/_dtr)
_rn = ((y1 - y3) * (x4 - x3)) - ((x1 - x3) * (y4 - y3))
# print "rn: %g" % _rn
_r = _rn/_denom
# print "r: %g" % _r
_ix = x1 + _r * (x2 - x1)
_iy = y1 + _r * (y2 - y1)
# print "ix: %g; iy: %g" % (_ix, _iy)
_m1 = math.tan(_a1)
_b1 = _iy - (_m1 * _ix)
# print "line1: m: %g; b: %g" % (_m1, _b1)
_m2 = math.tan(_a2)
_b2 = _iy - (_m2 * _ix)
# print "line2: m: %g; b: %g" % (_m2, _b2)
_px1, _py1 = _get_angled_projection(_a1, _b1, x, y)
# print "px1: %g; py1: %g" % (_px1, _py1)
_sep1 = math.hypot((_px1 - x), (_py1 - y))
_px2, _py2 = _get_angled_projection(_a2, _b2, x, y)
# print "px2: %g; py2: %g" % (_px2, _py2)
_sep2 = math.hypot((_px2 - x), (_py2 - y))
if _sep1 < _sep2:
_cx = _px1
_cy = _py1
else:
_cx = _px2
_cy = _py2
_px, _py = _get_two_point_projection(x1, y1, x2, y2, _cx, _cy)
_radius = math.hypot((_px - _cx), (_py - _cy))
return _cx, _cy, _radius
#
# horizontal construction line tangents
#
def _hcl_hcl_tangent(hcla, hclb, x, y):
_hx1, _hy1 = hcla.getLocation().getCoords()
_hx2, _hy2 = hclb.getLocation().getCoords()
if y < min(_hy1, _hy2) or y > max(_hy1, _hy2):
return None
_cx = x
_cy = (_hy1 + _hy2)/2.0
_radius = abs(_cy - _hy1)
return _cx, _cy, _radius
def _hcl_vcl_tangent(hcl, vcl, x, y):
_hx, _hy = hcl.getLocation().getCoords()
_hx2 = _hx + 1.0
_vx, _vy = vcl.getLocation().getCoords()
_vy2 = _vy + 1.0
return _two_line_tangent(_hx, _hy, _hx2, _hy, _vx, _vy, _vx, _vy2, x, y)
def _hcl_acl_tangent(hcl, acl, x, y):
_hx, _hy = hcl.getLocation().getCoords()
_hx2 = _hx + 1.0
_ax, _ay = acl.getLocation().getCoords()
_angle = acl.getAngle() * _dtr
_ax2 = _ax + math.cos(_angle)
_ay2 = _ay + math.sin(_angle)
return _two_line_tangent(_hx, _hy, _hx2, _hy, _ax, _ay, _ax2, _ay2, x, y)
def _hcl_cl_tangent(hcl, cl, x, y):
_hx, _hy = hcl.getLocation().getCoords()
_hx2 = _hx + 1.0
_p1, _p2 = cl.getKeypoints()
_x1, _y1 = _p1.getCoords()
_x2, _y2 = _p2.getCoords()
return _two_line_tangent(_hx, _hy, _hx2, _hy, _x1, _y1, _x2, _y2, x, y)
#
# the HCLine-CCircle tangent circle problem has been generalized
# to solve the {VCLine/ACLine/CLine}-CCircle tangent calculation
#
def _gen_cline_ccircle_tangent(radius, hy, x):
#
# center of ccircle : (0,0)
# radius of ccircle : r
# distance between ccircle and hcl: hy
# x-coordinate of mouse: x
#
# center of tangent circle : (px, py)
#
# projection point on hcl: (px, hy)
#
# Projection point outside the radius of the circle gives:
#
# math.hypot((px - cx), (py - cy)) == math.hypot((px - px), (py - hy)) + r
#
# Projection point inside the radius of the circle gives:
#
# math.hypot((px - cx), (py - cy)) + rt = r
#
# rt == radius of tangent circle
#
# Distance from projection point to tangent circle center
#
# math.hypot((px - px), (py - hy)) = rt
#
# lots of algebra reduces to the following two cases
#
_cx = x
if hy > 0.0:
_num = pow(x, 2) - pow(hy, 2) - (2.0 * hy * radius) - pow(radius, 2)
_den = (-2.0 * hy) - (2.0 * radius)
else:
_num = pow(x, 2) - pow(hy, 2) + (2.0 * hy * radius) - pow(radius, 2)
_den = (2.0 * radius) - (2.0 * hy)
# print "num: %g" % _num
# print "den: %g" % _den
_cy = _num/_den
_radius = abs(_cy - hy)
return _cx, _cy, _radius
def _hcl_cc_tangent(hcl, cc, x, y):
_hx, _hy = hcl.getLocation().getCoords()
# print "hy: %g" % _hy
_ccx, _ccy = cc.getCenter().getCoords()
_rad = cc.getRadius()
#
# transform the coords into system where circle center is (0,0)
#
_sep = _hy - _ccy
_xproj = x - _ccx
_tcx, _tcy, _tcrad = _gen_cline_ccircle_tangent(_rad, _sep, _xproj)
#
# transform result back into real coordinates
#
_cx = _tcx + _ccx
_cy = _tcy + _ccy
return _cx, _cy, _tcrad
#
# vertical construction line
#
def _vcl_vcl_tangent(vcl1, vcl2, x, y):
_vx1, _vy1 = vcl1.getLocation().getCoords()
_vx2, _vy2 = vcl2.getLocation().getCoords()
if x < min(_vx1, _vx2) or x > max(_vx1, _vx2):
return None
_cx = (_vx1 + _vx2)/2.0
_cy = y
_radius = abs(_cx - _vx1)
return _cx, _cy, _radius
def _vcl_acl_tangent(vcl, acl, x, y):
_vx, _vy = vcl.getLocation().getCoords()
_vy2 = _vy + 1.0
_ax, _ay = acl.getLocation().getCoords()
_angle = acl.getAngle() * _dtr
_ax2 = _ax + math.cos(_angle)
_ay2 = _ay + math.sin(_angle)
return _two_line_tangent(_vx, _vy, _vx, _vy2, _ax, _ay, _ax2, _ay2, x, y)
def _vcl_cl_tangent(hcl, cl, x, y):
_vx, _vy = hcl.getLocation().getCoords()
_vy2 = _vy + 1.0
_p1, _p2 = cl.getKeypoints()
_x1, _y1 = _p1.getCoords()
_x2, _y2 = _p2.getCoords()
return _two_line_tangent(_vx, _vy, _vx, _vy2, _x1, _y1, _x2, _y2, x, y)
def _vcl_cc_tangent(vcl, cc, x, y):
_vx, _vy = vcl.getLocation().getCoords()
# print "vx: %g" % _vx
_ccx, _ccy = cc.getCenter().getCoords()
_rad = cc.getRadius()
#
# transform the coords into system where circle center is (0,0) and
# rotate 90 degrees
#
_sep = _vx - _ccx
_xproj = y - _ccy
_tcx, _tcy, _tcrad = _gen_cline_ccircle_tangent(_rad, _sep, _xproj)
#
# transform result back into real coordinates
#
_cx = _tcy + _ccx
_cy = _tcx + _ccy
return _cx, _cy, _tcrad
#
# angular construction line
#
def _acl_acl_tangent(acl1, acl2, x, y):
_ax1, _ay1 = acl1.getLocation().getCoords()
_angle1 = acl1.getAngle() * _dtr
_ax2 = _ax1 + math.cos(_angle1)
_ay2 = _ay1 + math.sin(_angle1)
_ax3, _ay3 = acl2.getLocation().getCoords()
_angle2 = acl2.getAngle() * _dtr
_ax4 = _ax3 + math.cos(_angle2)
_ay4 = _ay3 + math.sin(_angle2)
return _two_line_tangent(_ax1, _ay1, _ax2, _ay2, _ax3, _ay3, _ax4, _ay4,
x, y)
def _acl_cl_tangent(acl, cl, x, y):
_ax1, _ay1 = acl.getLocation().getCoords()
_angle = acl.getAngle() * _dtr
_ax2 = _ax1 + math.cos(_angle)
_ay2 = _ay1 + math.sin(_angle)
_p1, _p2 = cl.getKeypoints()
_x1, _y1 = _p1.getCoords()
_x2, _y2 = _p2.getCoords()
return _two_line_tangent(_ax1, _ay1, _ax2, _ay2, _x1, _y1, _x2, _y2, x, y)
def _acl_cc_tangent(acl, cc, x, y):
_ax, _ay = acl.getLocation().getCoords()
# print "ax: %g; ay: %g" % (_ax, _ay)
_angle = acl.getAngle()
_ccx, _ccy = cc.getCenter().getCoords()
_rad = cc.getRadius()
#
# transform the coords into the system where the circle center is (0,0)
# and rotate so the ACLine is horizontal
#
_apx, _apy = acl.getProjection(_ccx, _ccy)
_sep = math.hypot((_apx - _ccx), (_apy - _ccy))
if abs(_angle) < 1e-10: # horizontal
_sine = 0.0
if _apy > _ccy: # system rotated 0.0
_cosine = 1.0
else: # system rotated 180.0
_cosine = -1.0
elif abs(abs(_angle) - 90.0) < 1e-10: # vertical
_cosine = 0.0
if _apx > _ccx: # system rotated 90.0
_sine = 1.0
else: # system rotated -90.0
_sine = -1.0
else:
_angle = _piover2 - math.atan2((_apy - _ccy), (_apx - _ccx))
_sine = math.sin(_angle)
_cosine = math.cos(_angle)
#
# transform (x, y)
#
_tx1 = x - _ccx
_ty1 = y - _ccy
#
# transform by rotating through _negative_ angle to
# map to horizontal line
#
_tx = (_tx1 * _cosine) - (_ty1 * _sine)
_ty = (_tx1 * _sine) + (_ty1 * _cosine)
_tcx, _tcy, _tcrad = _gen_cline_ccircle_tangent(_rad, _sep, _tx)
#
# transform result back into real coordinates
#
_cx = ((_tcx * _cosine) + (_tcy * _sine)) + _ccx
_cy = (-(_tcx * _sine) + (_tcy * _cosine)) + _ccy
return _cx, _cy, _tcrad
#
# two-point construction line
#
def _cl_cl_tangent(cl1, cl2, x, y):
_p1, _p2 = cl1.getKeypoints()
_x1, _y1 = _p1.getCoords()
_x2, _y2 = _p2.getCoords()
_p3, _p4 = cl2.getKeypoints()
_x3, _y3 = _p3.getCoords()
_x4, _y4 = _p4.getCoords()
return _two_line_tangent(_x1, _y1, _x2, _y2, _x3, _y3, _x4, _y4, x, y)
def _cl_cc_tangent(cl, cc, x, y):
_p1, _p2 = cl.getKeypoints()
_x1, _y1 = _p1.getCoords()
# print "x1: %g; y1: %g" % (_x1, _y1)
_x2, _y2 = _p2.getCoords()
# print "x2: %g; y2: %g" % (_x2, _y2)
_ccx, _ccy = cc.getCenter().getCoords()
# print "ccx: %g; ccy: %g" % (_ccx, _ccy)
_rad = cc.getRadius()
#
# transform the coords into the system where the circle center is (0,0)
# and rotate so the CLine is horizontal
#
_apx, _apy = cl.getProjection(_ccx, _ccy)
# print "apx: %g; apy: %g" % (_apx, _apy)
_sep = math.hypot((_apx - _ccx), (_apy - _ccy))
# print "sep: %g" % _sep
#
# use the line (ccx, ccy) to (apx, apy) to determine the
# angular rotation
#
if abs(_apx - _ccx) < 1e-10: # cline is horizontal
_sine = 0.0
if _apy > _ccy: # system rotated 0.0
_cosine = 1.0
else: # system rotated 180.0
_cosine = -1.0
elif abs(_apy - _ccy) < 1e-10: # cline is vertical; system rotated -90.0
_cosine = 0.0
if _apx > _ccx: # system rotated 90.0
_sine = 1.0
else: # system rotated -90.0
_sine = -1.0
else:
_angle = _piover2 - math.atan2((_apy - _ccy), (_apx - _ccx))
# print "angle: %g" % _angle
_sine = math.sin(_angle)
_cosine = math.cos(_angle)
# print "sin(angle): %g" % _sine
# print "cos(angle): %g" % _cosine
#
# transform (x, y) into
_tx1 = x - _ccx
_ty1 = y - _ccy
# print "tx1: %g; ty1: %g" % (_tx1, _ty1)
#
# transform by rotating through angle to
# map to horizontal line
#
_tx = (_tx1 * _cosine) - (_ty1 * _sine)
_ty = (_tx1 * _sine) + (_ty1 * _cosine)
# print "tx: %g; ty: %g" % (_tx, _ty)
_tcx, _tcy, _tcrad = _gen_cline_ccircle_tangent(_rad, _sep, _tx)
#
# transform result back into real coordinates
#
# print "tcx: %g: tcy: %g" % (_tcx, _tcy)
_cx = ((_tcx * _cosine) + (_tcy * _sine)) + _ccx
_cy = (-(_tcx * _sine) + (_tcy * _cosine)) + _ccy
# print "cx: %g; cy %g" % (_cx, _cy)
return _cx, _cy, _tcrad
def calc_tangent_circle(obja, objb, x, y):
_x = x
if not isinstance(_x, float):
_x = float(x)
_y = y
if not isinstance(_y, float):
_y = float(y)
_tandata = None
if isinstance(obja, hcline.HCLine):
if isinstance(objb, hcline.HCLine):
_tandata = _hcl_hcl_tangent(obja, objb, _x, _y)
elif isinstance(objb, vcline.VCLine):
_tandata = _hcl_vcl_tangent(obja, objb, _x, _y)
elif isinstance(objb, acline.ACLine):
_tandata = _hcl_acl_tangent(obja, objb, _x, _y)
elif isinstance(objb, cline.CLine):
_tandata = _hcl_cl_tangent(obja, objb, _x, _y)
elif isinstance(objb, ccircle.CCircle):
_tandata = _hcl_cc_tangent(obja, objb, _x, _y)
elif isinstance(obja, vcline.VCLine):
if isinstance(objb, hcline.HCLine):
_tandata = _hcl_vcl_tangent(objb, obja, _x, _y)
elif isinstance(objb, vcline.VCLine):
_tandata = _vcl_vcl_tangent(obja, objb, _x, _y)
elif isinstance(objb, acline.ACLine):
_tandata = _vcl_acl_tangent(obja, objb, _x, _y)
elif isinstance(objb, cline.CLine):
_tandata = _vcl_cl_tangent(obja, objb, _x, _y)
elif isinstance(objb, ccircle.CCircle):
_tandata = _vcl_cc_tangent(obja, objb, _x, _y)
elif isinstance(obja, acline.ACLine):
if isinstance(objb, hcline.HCLine):
_tandata = _hcl_acl_tangent(objb, obja, _x, _y)
elif isinstance(objb, vcline.VCLine):
_tandata = _vcl_acl_tangent(objb, obja, _x, _y)
elif isinstance(objb, acline.ACLine):
_tandata = _acl_acl_tangent(obja, objb, _x, _y)
elif isinstance(objb, cline.CLine):
_tandata = _acl_cl_tangent(obja, objb, _x, _y)
elif isinstance(objb, ccircle.CCircle):
_tandata = _acl_cc_tangent(obja, objb, _x, _y)
elif isinstance(obja, cline.CLine):
if isinstance(objb, hcline.HCLine):
_tandata = _hcl_cl_tangent(objb, obja, _x, _y)
elif isinstance(objb, vcline.VCLine):
_tandata = _vcl_cl_tangent(objb, obja, _x, _y)
elif isinstance(objb, acline.ACLine):
_tandata = _acl_cl_tangent(objb, obja, _x, _y)
elif isinstance(objb, cline.CLine):
_tandata = _cl_cl_tangent(obja, objb, _x, _y)
elif isinstance(objb, ccircle.CCircle):
_cl_cc_tangent(obja, objb, _x, _y)
elif isinstance(obja, ccircle.CCircle):
if isinstance(objb, hcline.HCLine):
_tandata = _hcl_cc_tangent(objb, obja, _x, _y)
elif isinstance(objb, vcline.VCLine):
_tandata = _vcl_cc_tangent(objb, obja, _x, _y)
elif isinstance(objb, acline.ACLine):
_tandata = _acl_cc_tangent(objb, obja, _x, _y)
elif isinstance(objb, cline.CLine):
_tandata = _cl_cc_tangent(objb, obja, _x, _y)
else:
pass # CCircle/CCircle tangent circles to do later ...
return _tandata
#
# calculate the possible tangent lines between two circles
#
def _calc_values(ax, ay, bx, by, cx, cy):
"""This function was used for debugging"""
_den = pow((bx - ax), 2) + pow((by - ay), 2)
_num = ((cx - ax) * (bx - ax)) + ((cy - ay) * (by - ay))
_r = _num/_den
# print "r: %g" % _r
_num = ((ay - cy) * (bx - ax)) - ((ax - cx) * (by - ay))
_s = _num/_den
# print "s: %g" % _s
_sep = abs(_s) * math.sqrt(_den)
# print "sep: %g" % _sep
# return _r, _s, _sep
def _calc_tangent_triangle(r1, r2, sep, ip):
_sine = r1/abs(ip)
# print "sin: %g" % _sine
_angle = math.asin(_sine)
# print "angle: %g" % (_angle * (180.0/math.pi))
_tan = math.tan(_angle)
# print "tan(angle): %g" % _tan
_cosine = math.cos(_angle)
# print "cos(angle): %g" % _cosine
_tanlen = r1/_tan
# print "tanlen: %g" % _tanlen
if ip < 0.0: # r1 < r2 and intersection point left of r1
assert abs(ip) > r1, "Expected ip beyond radius: %g < %g" % (ip, r1)
_tx1 = ip + (_tanlen * _cosine)
else:
_tx1 = ip - (_tanlen * _cosine)
# print "tx1: %g" % _tx1
_ty1 = _tanlen * _sine
# print "ty1: %g" % _ty1
_dist = math.hypot(_tx1, _ty1)
# print "dist: %g" % _dist
assert abs(_dist - r1) < 1e-10, "Invalid tangent point for circle 1"
_tanlen = r2/_tan
# print "tanlen: %g" % _tanlen
if ip < 0.0: # see above
_tx2 = ip + (_tanlen * _cosine)
_ty2 = _tanlen * _sine
elif ip > (sep + r2): # only possible if r1 > r2
_tx2 = ip - (_tanlen * _cosine)
_ty2 = _tanlen * _sine
else:
_tx2 = ip + (_tanlen * _cosine)
_ty2 = -1.0 * _tanlen * _sine
# print "tx2: %g" % _tx2
# print "ty2: %g" % _ty2
_dist = math.hypot((_tx2 - sep), _ty2)
# print "dist: %g" % _dist
assert abs(_dist - r2) < 1e-10, "Invalid tangent point for circle 2"
return _tx1, _ty1, _tx2, _ty2
def calc_two_circle_tangents(r1, r2, sep):
# print "in calc_two_circle_tangents() ..."
_r1 = r1
if not isinstance(_r1, float):
_r1 = float(r1)
if not _r1 > 0.0:
raise ValueError, "Invalid radius: %g" % _r1
_r2 = r2
if not isinstance(_r2, float):
_r2 = float(r2)
if not _r2 > 0.0:
raise ValueError, "Invalid radius: %g" % _r2
_sep = sep
if not isinstance(_sep, float):
_sep = float(sep)
_tangents = []
if (abs(_sep) + min(_r1, _r2)) > max(_r1, _r2): # small circle not within larger
if abs(_r1 - _r2) < 1e-10:
# print "same radii ..."
_tangents.append((0.0, _r1, _sep, _r2))
_tangents.append((0.0, -_r1, _sep, -_r2))
if abs(_sep) > _r1 + _r2:
_mid = _sep/2.0
_angle = math.asin(_r1/_mid)
_tanlen = _r1/math.tan(_angle)
_xt = _tanlen * math.cos(_angle)
_yt = _tanlen * math.sin(_angle)
_tx1 = _mid - _xt
_ty1 = _yt
_tx2 = _mid + _xt
_ty2 = -_yt
_tangents.append((_tx1, _ty1, _tx2, _ty2))
# _calc_values(_tx1, _ty1, _tx2, _ty2, 0.0, 0.0)
# _calc_values(_tx1, _ty1, _tx2, _ty2, _sep, 0.0)
_tangents.append((_tx1, -_ty1, _tx2, -_ty2))
# _calc_values(_tx1, -_ty1, _tx2, -_ty2, 0.0, 0.0)
# _calc_values(_tx1, -_ty1, _tx2, -_ty2, _sep, 0.0)
else:
_alpha = pow((_r1/_r2), 2)
# print "alpha: %g" % _alpha
_a = (1.0 - _alpha)
# print "a: %g" % _a
_b = (2.0 * _alpha * _sep)
# print "b: %g" % _b
_c = (-1.0 * _alpha * pow(_sep, 2))
# print "c: %g" % _c
_det = pow(_b, 2) - (4.0 * _a * _c)
# print "det: %g" % _det
if _det > 0.0: # can this ever be negative?
# print "r1: %g" % _r1
# print "r2: %g" % _r2
# print "sep: %g" % _sep
_denom = 2.0 * _a
_det_sqrt = math.sqrt(_det)
_num = (-1.0 * _b) + _det_sqrt
_offset = _num/_denom
# print "offset: %g" % _offset
if (_r1 > _r2):
# print "r1 > r2"
if ((_offset > (_sep + _r2)) or
((_offset > _r1) and (_offset < (_sep - _r2)))):
_tpts = _calc_tangent_triangle(_r1, _r2, _sep, _offset)
_tangents.append(_tpts)
_tx1, _ty1, _tx2, _ty2 = _tpts
# _calc_values(_tx1, _ty1, _tx2, _ty2, 0.0, 0.0)
# _calc_values(_tx1, _ty1, _tx2, _ty2, _sep, 0.0)
# _calc_values(_tx2, _ty2, _tx1, _ty1, _sep, 0.0)
# _calc_values(_tx2, _ty2, _tx1, _ty1, 0.0, 0.0)
_tpts = (_tx1, - _ty1, _tx2, -_ty2)
_tangents.append(_tpts)
# _calc_values(_tx1, -_ty1, _tx2,-_ty2, 0.0, 0.0)
# _calc_values(_tx1, -_ty1, _tx2, -_ty2, _sep, 0.0)
# _calc_values(_tx2, -_ty2, _tx1, -_ty1, _sep, 0.0)
# _calc_values(_tx2, -_ty2, _tx1, -_ty1, 0.0, 0.0)
else: # _r1 < _r2
# print "r1 < r2"
if ((_offset < -_r1) or
((_offset > _r1) and (_offset < (_sep - _r2)))):
_tpts = _calc_tangent_triangle(_r1, _r2, _sep, _offset)
_tangents.append(_tpts)
_tx1, _ty1, _tx2, _ty2 = _tpts
# _calc_values(_tx1, _ty1, _tx2, _ty2, 0.0, 0.0)
# _calc_values(_tx1, _ty1, _tx2, _ty2, _sep, 0.0)
# _calc_values(_tx2, _ty2, _tx1, _ty1, _sep, 0.0)
# _calc_values(_tx2, _ty2, _tx1, _ty1, 0.0, 0.0)
_tpts = (_tx1, - _ty1, _tx2, -_ty2)
_tangents.append(_tpts)
# _calc_values(_tx1, -_ty1, _tx2,-_ty2, 0.0, 0.0)
# _calc_values(_tx1, -_ty1, _tx2, -_ty2, _sep, 0.0)
# _calc_values(_tx2, -_ty2, _tx1, -_ty1, _sep, 0.0)
# _calc_values(_tx2, -_ty2, _tx1, -_ty1, 0.0, 0.0)
_num = (-1.0 * _b) - _det_sqrt
_offset = _num/_denom
# print "offset: %g" % _offset
if (_r1 > _r2):
# print "r1 > r2"
if ((_offset > (_sep + _r2)) or
((_offset > _r1) and (_offset < (_sep - _r2)))):
_tpts = _calc_tangent_triangle(_r1, _r2, _sep, _offset)
_tangents.append(_tpts)
_tx1, _ty1, _tx2, _ty2 = _tpts
_tpts = (_tx1, - _ty1, _tx2, -_ty2)
_tangents.append(_tpts)
else: # _r1 < _r2
# print "r1 < r2"
if ((_offset < -_r1) or
((_offset > _r1) and (_offset < (_sep - _r2)))):
_tpts = _calc_tangent_triangle(_r1, _r2, _sep, _offset)
_tangents.append(_tpts)
_tx1, _ty1, _tx2, _ty2 = _tpts
# _calc_values(_tx1, _ty1, _tx2, _ty2, 0.0, 0.0)
# _calc_values(_tx1, _ty1, _tx2, _ty2, _sep, 0.0)
# _calc_values(_tx2, _ty2, _tx1, _ty1, _sep, 0.0)
# _calc_values(_tx2, _ty2, _tx1, _ty1, 0.0, 0.0)
_tpts = (_tx1, - _ty1, _tx2, -_ty2)
_tangents.append(_tpts)
# _calc_values(_tx1, -_ty1, _tx2,-_ty2, 0.0, 0.0)
# _calc_values(_tx1, -_ty1, _tx2, -_ty2, _sep, 0.0)
# _calc_values(_tx2, -_ty2, _tx1, -_ty1, _sep, 0.0)
# _calc_values(_tx2, -_ty2, _tx1, -_ty1, 0.0, 0.0)
return _tangents
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