/usr/share/octave/packages/geometry-1.7.0/geom2d/cbezier2poly.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{pp} =} cbezier2poly (@var{points})
## @deftypefnx {Function File} {[@var{x} @var{y}] =} cbezier2poly (@var{points},@var{t})
## Returns the polynomial representation of the cubic Bezier defined by the control points @var{points}.
##
## With only one input argument, calculates the polynomial @var{pp} of the cubic
## Bezier curve defined by the 4 control points stored in @var{points}. The first
## point is the inital point of the curve. The segment joining the first point
## with the second point (first center) defines the tangent of the curve at the initial point.
## The segment that joints the third point (second center) with the fourth defines the tanget at
## the end-point of the curve, which is defined in the fourth point.
## @var{points} is either a 4-by-2 array (vertical concatenation of point
## coordinates), or a 1-by-8 array (horizotnal concatenation of point
## coordinates). @var{pp} is a 2-by-3 array, 1st row is the polynomial for the
## x-coordinate and the 2nd row for the y-coordinate. Each row can be evaluated
## with @code{polyval}. The polynomial @var{pp}(t) is defined for t in [0,1].
##
## When called with a second input argument @var{t}, it returns the coordinates
## @var{x} and @var{y} corresponding to the polynomial evaluated at @var{t} in
## [0,1].
##
## @seealso{drawBezierCurve, polyval}
## @end deftypefn
function varargout = cbezier2poly (points, ti=[])
# rename points
if size(points, 2)==2
# case of points given as a 4-by-2 array
p1 = points(1,:);
c1 = points(2,:);
c2 = points(3,:);
p2 = points(4,:);
elseif size(points,2) == 8
# case of points given as a 1-by-8 array, [X1 Y1 CX1 CX2..]
p1 = points(1:2);
c1 = points(3:4);
c2 = points(5:6);
p2 = points(7:8);
else
print_usage ;
end
# compute coefficients of Bezier Polynomial
pp = zeros(2,4);
pp(:,4) = [p1(1); ...
p1(2)];
pp(:,3) = [3 * c1(1) - 3 * p1(1); ...
3 * c1(2) - 3 * p1(2)];
pp(:,2) = [3 * p1(1) - 6 * c1(1) + 3 * c2(1); ...
3 * p1(2) - 6 * c1(2) + 3 * c2(2)];
pp(:,1) = [p2(1) - 3 * c2(1) + 3 * c1(1) - p1(1); ...
p2(2) - 3 * c2(2) + 3 * c1(2) - p1(2)];
if isempty (ti)
varargout{1} = pp;
else
varargout{1} = polyval (pp(1,:), ti);
varargout{2} = polyval (pp(2,:), ti);
end
endfunction
%!demo
%! points = [45.714286 483.79075; ...
%! 241.65656 110.40445; ...
%! 80.185847 741.77381; ...
%! 537.14286 480.93361];
%!
%! pp = cbezier2poly(points);
%! t = linspace(0,1,64);
%! x = polyval(pp(1,:),t);
%! y = polyval(pp(2,:),t);
%! plot (x,y,'b-',points([1 4],1),points([1 4],2),'s',...
%! points([2 3],1),points([2 3],2),'o');
%! line(points([2 1],1),points([2 1],2),'color','r');
%! line(points([3 4],1),points([3 4],2),'color','r');
%!demo
%! points = [0 0; ...
%! 1 1; ...
%! 1 1; ...
%! 2 0];
%!
%! t = linspace(0,1,64);
%! [x y] = cbezier2poly(points,t);
%! plot (x,y,'b-',points([1 4],1),points([1 4],2),'s',...
%! points([2 3],1),points([2 3],2),'o');
%! line(points([2 1],1),points([2 1],2),'color','r');
%! line(points([3 4],1),points([3 4],2),'color','r');
%!test
%! points = [0 0; ...
%! 1 1; ...
%! 1 1; ...
%! 2 0];
%! t = linspace(0,1,64);
%!
%! [x y] = cbezier2poly(points,t);
%! pp = cbezier2poly(points);
%! x2 = polyval(pp(1,:),t);
%! y2 = polyval(pp(2,:),t);
%! assert(x,x2);
%! assert(y,y2);
%!test
%! points = [0 0; ...
%! 1 1; ...
%! 1 1; ...
%! 2 0];
%! t = linspace(0,1,64);
%!
%! p = reshape(points,1,8);
%! [x y] = cbezier2poly(p,t);
%! pp = cbezier2poly(p);
%! x2 = polyval(pp(1,:),t);
%! y2 = polyval(pp(2,:),t);
%! assert(x,x2);
%! assert(y,y2);
|