/usr/share/octave/packages/geometry-1.7.0/geom2d/beltproblem.m is in octave-geometry 1.7.0-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 | ## Copyright (C) 2004-2011 David Legland <david.legland@grignon.inra.fr>
## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
## -*- texinfo -*-
## @deftypefn {Function File} {[@var{tangent},@var{inner}] = } beltproblem (@var{c}, @var{r})
## Finds the four lines tangent to two circles with given centers and radii.
##
## The function solves the belt problem in 2D for circles with center @var{c} and
## radii @var{r}.
##
## @strong{INPUT}
## @table @var
## @item c
## 2-by-2 matrix containig coordinates of the centers of the circles; one row per circle.
## @item r
## 2-by-1 vector with the radii of the circles.
##@end table
##
## @strong{OUPUT}
## @table @var
## @item tangent
## 4-by-4 matrix with the points of tangency. Each row describes a segment(edge).
## @item inner
## 4-by-2 vector with the point of intersection of the inner tangents (crossed belts)
## with the segment that joins the centers of the two circles. If
## the i-th edge is not an inner tangent then @code{inner(i,:)=[NaN,NaN]}.
## @end table
##
## Example:
##
## @example
## c = [0 0;1 3];
## r = [1 0.5];
## [T inner] = beltproblem(c,r)
## @result{} T =
## -0.68516 0.72839 1.34258 2.63581
## 0.98516 0.17161 0.50742 2.91419
## 0.98675 -0.16225 1.49338 2.91888
## -0.88675 0.46225 0.55663 3.23112
##
## @result{} inner =
## 0.66667 2.00000
## 0.66667 2.00000
## NaN NaN
## NaN NaN
##
## @end example
##
## @seealso{edges2d}
## @end deftypefn
function [edgeTan inner] = beltproblem(c,r)
x0 = [c(1,1) c(1,2) c(2,1) c(2,2)];
r0 = r([1 1 2 2]);
middleEdge = createEdge(c(1,:),c(2,:));
ind0 = [1 0 1 0; 0 1 1 0; 1 1 1 0; -1 0 1 0; 0 -1 1 0; -1 -1 1 0;...
1 0 0 1; 0 1 0 1; 1 1 0 1; -1 0 0 1; 0 -1 0 1; -1 -1 0 1;...
1 0 1 1; 0 1 1 1; 1 1 1 1; -1 0 1 1; 0 -1 1 1; -1 -1 1 1;...
1 0 -1 0; 0 1 -1 0; 1 1 -1 0; -1 0 -1 0; 0 -1 -1 0; -1 -1 -1 0;...
1 0 0 -1; 0 1 0 -1; 1 1 0 -1; -1 0 0 -1; 0 -1 0 -1; -1 -1 0 -1;...
1 0 -1 -1; 0 1 -1 -1; 1 1 -1 -1; -1 0 -1 -1; 0 -1 -1 -1; -1 -1 -1 -1];
nInit = size(ind0,1);
ir = randperm(nInit);
edgeTan = zeros(4,4);
inner = zeros(4,2);
nSol = 0;
i=1;
## Solve for 2 different lines
while nSol<4 && i<nInit
ind = find(ind0(ir(i),:)~=0);
x = x0;
x(ind)=x(ind)+r0(ind);
[sol f0 nev]= fsolve(@(x)belt(x,c,r),x);
if nev~=1
perror('fsolve',nev)
end
for j=1:4
notequal(j) = all(abs(edgeTan(j,:)-sol) > 1e-6);
end
if all(notequal)
nSol = nSol+1;
edgeTan(nSol,:) = createEdge(sol(1:2),sol(3:4));
# Find innerTangent
inner(nSol,:) = intersectEdges(middleEdge,edgeTan(nSol,:));
end
i = i+1;
end
endfunction
function res = belt(x,c,r)
res = zeros(4,1);
res(1,1) = (x(3:4) - c(2,1:2))*(x(3:4) - x(1:2))';
res(2,1) = (x(1:2) - c(1,1:2))*(x(3:4) - x(1:2))';
res(3,1) = sumsq(x(1:2) - c(1,1:2)) - r(1)^2;
res(4,1) = sumsq(x(3:4) - c(2,1:2)) - r(2)^2;
end
%!demo
%! c = [0 0;1 3];
%! r = [1 0.5];
%! [T inner] = beltproblem(c,r)
%!
%! figure(1)
%! clf
%! h = drawEdge(T);
%! set(h(find(~isnan(inner(:,1)))),'color','r');
%! set(h,'linewidth',2);
%! hold on
%! drawCircle([c(1,:) r(1); c(2,:) r(2)],'linewidth',2);
%! axis tight
%! axis equal
%!
%! # -------------------------------------------------------------------
%! # The circles with the tangents edges are plotted. The solution with
%! # crossed belts (inner tangets) is shown in red.
|