Thread: [Octave-cvsupdate] SF.net SVN: octave:[8607] trunk/octave-forge/main (Page 2)

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Revision: 8607
          http://octave.svn.sourceforge.net/octave/?rev=8607&view=rev
Author:   jpicarbajal
Date:     2011-09-26 21:15:30 +0000 (Mon, 26 Sep 2011)
Log Message:
-----------
mechanics-1.0.0. First commit: Adding functions

Added Paths:
-----------
    trunk/octave-forge/main/mechanics/
    trunk/octave-forge/main/mechanics/COPYING
    trunk/octave-forge/main/mechanics/DESCRIPTION
    trunk/octave-forge/main/mechanics/INDEX
    trunk/octave-forge/main/mechanics/doc/
    trunk/octave-forge/main/mechanics/inst/
    trunk/octave-forge/main/mechanics/inst/area_poly2d.m
    trunk/octave-forge/main/mechanics/inst/center_mass_poly2d.m
    trunk/octave-forge/main/mechanics/inst/inertia_moment_ncpoly2d.m
    trunk/octave-forge/main/mechanics/inst/inertia_moment_poly2d.m
    trunk/octave-forge/main/mechanics/inst/private/
    trunk/octave-forge/main/mechanics/inst/second_moment_poly2d.m

Added: trunk/octave-forge/main/mechanics/COPYING
===================================================================

--- trunk/octave-forge/main/mechanics/COPYING	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/COPYING	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,674 @@
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+address new problems or concerns.
+
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+Program specifies that a certain numbered version of the GNU General
+Public License "or any later version" applies to it, you have the
+option of following the terms and conditions either of that numbered
+version or of any later version published by the Free Software
+Foundation.  If the Program does not specify a version number of the
+GNU General Public License, you may choose any version ever published
+by the Free Software Foundation.
+
+  If the Program specifies that a proxy can decide which future
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+public statement of acceptance of a version permanently authorizes you
+to choose that version for the Program.
+
+  Later license versions may give you additional or different
+permissions.  However, no additional obligations are imposed on any
+author or copyright holder as a result of your choosing to follow a
+later version.
+
+  15. Disclaimer of Warranty.
+
+  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
+APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
+HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
+OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
+THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
+PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
+IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
+ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
+
+  16. Limitation of Liability.
+
+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
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+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
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+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    <one line to give the program's name and a brief idea of what it does.>
+    Copyright (C) <year>  <name of author>
+
+    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/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    <program>  Copyright (C) <year>  <name of author>
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

Added: trunk/octave-forge/main/mechanics/DESCRIPTION
===================================================================
--- trunk/octave-forge/main/mechanics/DESCRIPTION	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/DESCRIPTION	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,11 @@
+Name: Mechanics
+Version: 1.0.0
+Date: Monday, September 26 2011
+Author: Juan Pablo Carbajal <car...@if...>
+Maintainer: Juan Pablo Carbajal <car...@if...>
+Title: Classical Mechanics
+Description: Library with functions useful for numerical computation in classical mechanics.
+Depends: octave (>= 3.4.0)
+Autoload: no
+License: GPL version 3 or later
+Url: http://octave.sf.net

Added: trunk/octave-forge/main/mechanics/INDEX
===================================================================
--- trunk/octave-forge/main/mechanics/INDEX	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/INDEX	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,8 @@
+mechanics >> Classical Mechanics
+1D Mechanics
+2D Mechanics
+ area_poly2d
+ center_mass_poly2d
+ inertia_moment_poly2d
+ inertia_moment_ncpoly2d
+ second_moment_poly2d

Added: trunk/octave-forge/main/mechanics/inst/area_poly2d.m
===================================================================
--- trunk/octave-forge/main/mechanics/inst/area_poly2d.m	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/inst/area_poly2d.m	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,52 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%% 
+%%    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
+%%    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{A} = area_poly2d (@var{p})
+%% Calculates the Area of a 2D polygon.
+%%
+%% The polygon is described in @var{p}, where each row is a different vertex.
+%% The algorithm was adapted from P. Bourke web page
+%% @uref{http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/}
+%%
+%% @seealso{inertia_moment_poly2d, center_mass_poly2d}
+%% @end deftypefn
+
+function A = area_poly2d(poly)
+
+  N = size(poly,1);
+  nxt = [2:N 1];
+  px = poly(:,1);
+  px_nxt = poly(nxt,1);
+  py = poly(:,2);
+  py_nxt = poly(nxt,2);
+
+  A = sum(px.*py_nxt - px_nxt.*py)/2;
+  
+end
+
+%!demo
+%! % A parametrized arbitrary triagle and its area
+%!
+%!  triangle = @(a,b,h) [0 0; b 0; a h];
+%!  h = linspace(0.1,1,10);
+%!  b = pi;
+%!  for i=1:length(h);
+%!    P = triangle(0.1,b,h(i));
+%!    area(i) = area_poly2d(P);
+%!  end
+%!
+%! % The area of the triangle is b*h/2
+%!  plot(h,area,'o',h,b*h/2); 

Added: trunk/octave-forge/main/mechanics/inst/center_mass_poly2d.m
===================================================================
--- trunk/octave-forge/main/mechanics/inst/center_mass_poly2d.m	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/inst/center_mass_poly2d.m	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,60 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%% 
+%%    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
+%%    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{cm} = center_mass_poly2d (@var{p})
+%% Calculates the center of mass a 2D polygon.
+%%
+%% The polygon is described in @var{p}, where each row is a different vertex.
+%% The algorithm was adapted from P. Bourke web page
+%% @uref{http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/}
+%%
+%% @seealso{inertia_moment_poly2d, area_poly2d}
+%% @end deftypefn
+
+function cm = center_mass_poly2d(poly)
+
+  N = size(poly,1);
+  nxt = [2:N 1];
+  px = poly(:,1);
+  px_nxt = poly(nxt,1);
+  py = poly(:,2);
+  py_nxt = poly(nxt,2);
+  
+  cm = zeros(1,2);
+  cr_prod = (px.*py_nxt - px_nxt.*py);
+  
+  % Area
+  A = sum(cr_prod)/2;
+
+  % Center of mass  
+  cm(1) = sum( (px+px_nxt) .* cr_prod );
+  cm(2) = sum( (py+py_nxt) .* cr_prod );
+  cm = cm/(6*A);
+   
+end
+
+%!demo
+%! % The center of mass of this two triangles is the same
+%! % since both describe the same figure.
+%!
+%!  P = [0 0; 1 0; 0 1]; 
+%!  P2=[0 0; 0.1 0; 0.2 0; 0.25 0; 1 0; 0 1];
+%!  [center_mass_poly2d(P) center_mass_poly2d(P2)],
+%!
+%! % The centroid does not give the right answer
+%! 
+%!  [mean(P) mean(P2)],
+

Added: trunk/octave-forge/main/mechanics/inst/inertia_moment_ncpoly2d.m
===================================================================
--- trunk/octave-forge/main/mechanics/inst/inertia_moment_ncpoly2d.m	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/inst/inertia_moment_ncpoly2d.m	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,102 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%% 
+%%    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
+%%    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{I} = inertia_moment_ncpoly2d (@var{p}, @var{m})
+%% Calculates the moment of inertia of a simple 2D polygon.
+%%
+%% The polygon is described in @var{p}, where each row is a different vertex.
+%% @var{m} is the total mass of the polygon, assumed uniformly distributed.
+%% The polygon is triangulated using delaunay algorithm and then the 
+%% Superposition Principle and the Parallel axis theorem are applied to each
+%% triangle.
+%%
+%% The position of the vertices is assumed to be given from the center of mass 
+%% of the polygon.
+%% To change a general polygon to this description you can use:
+%% @code{P = P - repmat(center_mass_poly2d(P),size(P,1))}.
+%%
+%% @seealso{}
+%% @end deftypefn
+
+function I = inertia_moment_ncpoly2d (poly, M)
+  %% Get total area
+  A = area_poly2d (poly);
+
+  %% triangulate
+  T = delaunay (poly(:,1), poly(:,2));
+  nT = size(T,1);
+  
+% debug
+% triplot(T,poly(:,1),poly(:,2),'color',[0.8 0.8 0.8])
+% hold on
+% drawPolygon(poly,'k'); 
+% hold off;
+
+  I = 0;
+  for it = 1:nT
+    P = poly (T(it,:), :);
+    %% get centers of mass
+    cm =  center_mass_poly2d (P);
+    
+    % Check if triangle CoM is inside polygon
+    if ~inpolygon (cm(1), cm(2), poly(:,1), poly(:,2))
+      continue
+    end
+    
+    %% get the mass as fraction of total area
+    a = area_poly2d (P);
+    if a < 0
+      aux = P(1,:);
+      P(1,:) = P(2,:);
+      P(2,:) = aux;
+      a = -a;
+    end
+    m = M*a/A;
+
+% debug
+% patch(P(:,1),P(:,2),'facecolor','b','edgecolor','none');
+% pause
+
+
+
+    %% get moment of inertia
+    mo = inertia_moment_poly2d (P, m, cm);
+
+    %% Assemble: Superposition + parallel axis
+    I += mo + m * sumsq (cm);
+  end
+
+end
+
+%!demo
+%! % C shape polygon
+%!  poly = [0 0; 1 0; 1 0.25; 0.25 0.25; 0.25 0.75; 1 0.75; 1 1; 0 1];
+%! 
+%! % Take to center of mass
+%!  poly = poly - repmat(center_mass_poly2d(poly),size(poly,1),1);
+%!  A = area_poly2d(poly);
+%!
+%!  I = inertia_moment_ncpoly2d(poly,1)
+%!
+%!  % It should give (breaking C in rectangles)
+%!  r1 = [poly(1:3,:); poly(1,1) poly(3,2)]; a1 = area_poly2d(r1); m1 = abs(a1/A); 
+%!  c1 = center_mass_poly2d(r1); I1 = inertia_moment_poly2d(r1,m1,c1);
+%!  r2 = [r1(4,:); poly(4:5,:); poly(1,1) poly(5,2)]; a2 = area_poly2d(r2); m2 = abs(a2/A); 
+%!  c2 = center_mass_poly2d(r2); I2 = inertia_moment_poly2d(r2,m2,c2);
+%!  r3 = [poly(5:8,:); r2(4,:)]; a3 = area_poly2d(r3); m3 = abs(a3/A); 
+%!  c3 = center_mass_poly2d(r3); I3 = inertia_moment_poly2d(r3,m3,c3);
+%! 
+%! I1 + m1*sumsq(c1) + I2 + m2*sumsq(c2) + I3 + m3*sumsq(c3)

Added: trunk/octave-forge/main/mechanics/inst/inertia_moment_poly2d.m
===================================================================
--- trunk/octave-forge/main/mechanics/inst/inertia_moment_poly2d.m	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/inst/inertia_moment_poly2d.m	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,63 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%% 
+%%    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
+%%    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{I} = inertia_moment_poly2d (@var{p}, @var{m}, @var{offset})
+%% Calculates the moment of inertia of a 2D star-shaped polygon.
+%%
+%% The polygon is described in @var{p}, where each row is a different vertex.
+%% @var{m} is the total mass of the polygon, assumed uniformly distributed.
+%% The optinal argument @var{offset} is an origin translation vector. All vertex 
+%% are transformed to the reference frame with origin at @var{offset} respect to
+%% the center of mass.
+%%
+%% This expression assumes that the polygon is star-shaped. The position of the
+%% vertices is assumed to be given from the center of mass of the polygon.
+%% To change a general polygon to this description you can use:
+%% @code{P = P - repmat(center_mass_poly2d(P),size(P,1))}.
+%%
+%% @seealso{}
+%% @end deftypefn
+
+function I = inertia_moment_poly2d(poly,mass,offset=[0 0])
+  numVerts = size(poly,1);
+  R = repmat(offset,numVerts,1);
+  
+  V = poly - R;
+  Vnext = poly([2:numVerts 1],:) - R;
+  
+  %% Area of the parallelograms
+  A = sqrt(sumsq(cross([Vnext zeros(numVerts,1)],[V zeros(numVerts,1)],2),2));
+  %% Distance between points
+  B = dot(V,V,2) + dot(V,Vnext,2) + dot(Vnext,Vnext,2);
+  
+  C = sum(A.*B);
+  
+  I = mass*C/(6*sum(A));
+end
+
+%!demo
+%! 
+%! % The same triangle respect to one of its vertices described with two polygons
+%!  P = [0 0; 1 0; 0 1]; 
+%!  P2=[0 0; 0.1 0; 0.2 0; 0.25 0; 1 0; 0 1];
+%!
+%! % Now described from the center of mass of the triangle
+%! Pc = P - repmat(center_mass_poly2d(P), 3, 1);
+%! inertia_moment_poly2d(Pc,1)
+%!
+%! Pc = P2 -repmat(center_mass_poly2d(P2), size(P2,1), 1);
+%! inertia_moment_poly2d(Pc,1)
+

Added: trunk/octave-forge/main/mechanics/inst/second_moment_poly2d.m
===================================================================
--- trunk/octave-forge/main/mechanics/inst/second_moment_poly2d.m	                        (rev 0)
+++ trunk/octave-forge/main/mechanics/inst/second_moment_poly2d.m	2011-09-26 21:15:30 UTC (rev 8607)
@@ -0,0 +1,48 @@
+%% Copyright (c) 2011 Juan Pablo Carbajal <car...@if...>
+%% 
+%%    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
+%%    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{J} = second_moment_poly2d (@var{p})
+%% Calculates the second moment of area of a 2D polygon.
+%%
+%% The polygon is described in @var{p}, where each row is a different vertex.
+%% The output @var{J} contains Ix, Iy and Ixy, in that order.
+%%
+%% The algorithm was adapted from P. Bourke web page
+%% @uref{http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/}
+%%
+%% @seealso{inertia_moment_poly2d, center_mass_poly2d}
+%% @end deftypefn
+
+function J = second_moment_poly2d(poly)
+
+  N = size(poly,1);
+  nxt = [2:N 1];
+  px = poly(:,1);
+  px_nxt = poly(nxt,1);
+  py = poly(:,2);
+  py_nxt = poly(nxt,2);
+  
+  cm = zeros(1,2);
+  cr_prod = (px.*py_nxt - px_nxt.*py);
+
+  J = zeros(1,3);
+  J(1) = sum((py.^2 + py.*py_nxt + py_nxt.^2).*cr_prod);
+  J(2) = sum((px.^2 + px.*px_nxt + py_nxt.^2).*cr_prod);
+  J(3) = 0.5*sum((px.*py_nxt + 2*px.*py + px_nxt.*py_nxt + px_nxt.*py).*cr_prod);
+  J = J/12;
+  
+end
+

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Thread: [Octave-cvsupdate] SF.net SVN: octave:[8607] trunk/octave-forge/main (Page 2)

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