/usr/share/octave/packages/geometry-1.7.0/shape2d/curve2polyline.m is in octave-geometry 1.7.0-1build1.
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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 | ## Copyright (C) 2012 Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
##
## 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 3 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, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{polyline} = } curve2polyline (@var{curve})
## @deftypefnx {Function File} {@var{polyline} = } curve2polyline (@dots{},@var{property},@var{value},@dots{})
## Adaptive sampling of a parametric curve.
##
## The @var{curve} is described as a 2-by-N matrix. Rows correspond to the
## polynomial (compatible with @code{polyval}) describing the respective component
## of the curve. The curve must be parametrized in the interval [0,1].
## The vertices of the polyline are accumulated in regions of the curve where
## the curvature is higher.
##
## @strong{Parameters}
## @table @samp
## @item 'Nmax'
## Maximum number of vertices. Not used.
## @item 'Tol'
## Tolerance for the error criteria. Default value @code{1e-4}.
## @item 'MaxIter'
## Maximum number of iterations. Default value @code{10}.
## @item 'Method'
## Not implemented.
## @end table
##
## @seealso{shape2polygon, curveval}
## @end deftypefn
## This function is based on the algorithm described in
## L. H. de Figueiredo (1993). "Adaptive Sampling of Parametric Curves". Graphic Gems III.
## I had to remove the recursion so this version could be improved.
## Thursday, April 12 2012 -- JuanPi
function [polyline t bump]= curve2polyline (curve, varargin)
## TODO make tolerance relative to the "diameter" of the curve.
# --- Parse arguments --- #
parser = inputParser ();
parser.FunctionName = "curve2polyline";
parser = addParamValue (parser,'Nmax', 32, @(x)x>0);
parser = addParamValue (parser,'Tol', 1e-4, @(x)x>0);
parser = addParamValue (parser,'MaxIter', 10, @(x)x>0);
parser = parse(parser,varargin{:});
Nmax = parser.Results.Nmax;
tol = parser.Results.Tol;
MaxIter = parser.Results.MaxIter;
clear parser toldef
# ------ #
t = [0; 1];
tf = 1;
points = 1;
for iter = 1:MaxIter
# Add parameter values where error is still bigger than tol.
t = interleave(t, tf);
nt = length(t);
# Update error
polyline = curveval (curve,t);
bump = bumpyness(polyline);
# Check which intervals must be subdivided
idx = find(bump > tol);
# The position of the bumps mpas into intervals
# 1 -> 1 2
# 2 -> 3 4
# 3 -> 5 6
# and so on
idx = [2*(idx-1)+1; 2*idx](:);
tf = false (nt-1,1);
tf(idx) = true;
if all (!tf)
break;
end
end
endfunction
function f = bumpyness (p)
## Check for co-linearity
## TODO implement various method for this
## -- Area of the triangle close to zero (used currently).
## -- Angle close to pi.
## -- abs(p0-pt) + abs(pt-p1) - abs(p0-p1) almost zero.
## -- Curve's tange at 0,t,1 are almost parallel.
## -- pt is in chord p0 -> p1.
## Do this in isParallel.m and remove this function
PL = p(1:2:end-2,:);
PC = p(2:2:end-1,:);
PR = p(3:2:end,:);
a = PL - PC;
b = PR - PC;
f = (a(:,1).*b(:,2) - a(:,2).*b(:,1)).^2;
endfunction
function tt = interleave (t,varargin)
nt = length(t);
ntt = 2 * nt -1;
tt = zeros(ntt,1);
tt(1:2:ntt) = t;
beta = 0.4 + 0.2*rand(nt-1, 1);
tt(2:2:ntt) = t(1:end-1) + beta.*(t(2:end)-t(1:end-1));
if nargin > 1
tf = true (ntt,1);
tf(2:2:ntt) = varargin{1};
tt(!tf) = [];
end
endfunction
%!demo
%! curve = [0 0 1 0;1 -0.3-1 0.3 0];
%! polyline = curve2polyline(curve,'tol',1e-8);
%!
%! t = linspace(0,1,100)';
%! pc = curveval(curve,t);
%!
%! plot(polyline(:,1),polyline(:,2),'-o',pc(:,1),pc(:,2),'-r')
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