--- a/main/mechanics/inst/core/deprecated/area_poly2d.m	Fri Dec 09 14:21:53 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,52 +0,0 @@
-%% Copyright (c) 2011 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
-%%    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 triangle 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); 

--- a/main/mechanics/inst/core/deprecated/center_mass_poly2d.m	Fri Dec 09 14:21:53 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,60 +0,0 @@
-%% Copyright (c) 2011 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
-%%    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
-%% @url{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)],
-

--- a/main/mechanics/inst/core/deprecated/inertia_moment_ncpoly2d.m	Fri Dec 09 14:21:53 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,118 +0,0 @@
-%% Copyright (c) 2011 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
-%%    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{inertia_moment_poly2d, center_mass_poly2d}
-%% @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)
-
-%!test
-%! poly = [0 0; 1 0; 1 0.25; 0.25 0.25; 0.25 0.75; 1 0.75; 1 1; 0 1];
-%! 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);
-%! I_shouldbe = I1 + m1*sumsq(c1) + I2 + m2*sumsq(c2) + I3 + m3*sumsq(c3);
-%! assert(I,I_shouldbe)
-

--- a/main/mechanics/inst/core/deprecated/inertia_moment_poly2d.m	Fri Dec 09 14:21:53 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,69 +0,0 @@
-%% Copyright (c) 2011 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
-%%    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 optional argument @var{offset} is an origin translation vector. All vertex 
-%% are transformed to the reference frame with origin at @var{offset}. 
-%%
-%% 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))}.
-%% or call the function using the offset:
-%% @code{inertia_moment_poly2d (@var{p}, @var{m}, center_mass_poly2d(@var{p}))}
-%%
-%% @seealso{inertia_moment_ncpoly2d, center_mass_poly2d}
-%% @end deftypefn
-
-function I = inertia_moment_poly2d(poly,mass,offset=[])
-
-  numVerts = size(poly,1);
-  
-  if !isempty (offset)
-    V = bsxfun(@minus, poly, offset);
-    Vnext = bsxfun(@minus, poly([2:numVerts 1],:),offset);
-  else
-    V = poly; 
-    Vnext = poly([2:numVerts 1],:);
-  end
-  
-  %% 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)
-

--- a/main/mechanics/inst/core/deprecated/second_moment_poly2d.m	Fri Dec 09 14:21:53 2011 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,70 +0,0 @@
-%% Copyright (c) 2011 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
-%%    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_shape2d (@var{p})
-%% @deftypefnx{Function File} @var{J} = second_moment_shape2d (@var{p}),@var{type}, @var{matrix})
-%% Calculates the second moment of area of a 2D shape. 
-%%
-%% The polygon is described in @var{p}, where each row is a different vertex as seen
-%% from the center of mass of the shape (see @code{center_mass_shape2d}).
-%%
-%% The output @var{J} contains Ix, Ixy and Iy, in that order. It is assumed to be
-%% oriented counter clockwise, otherwise multiply output by -1.
-%%
-%% If @var{matrix} is @code{true} then @var{J} is the symmetric second moment of area
-%% matrix, instead of the vector @code{vech(J)}.
-%% @var{type} indicates how is the shape described. So far the only case handled
-%% is when @var{shape} is a 2D polygon, where each row of @var{shape} is a vertex.
-%%
-%% @seealso{inertia_moment_shape2d, center_mass_shape2d}
-%% @end deftypefn
-
-function J = second_moment_poly2d(shape, typep='polygon', matrix=false)
-
-  if strcmpi (typep, 'polygon')
-
-    [N dim] = size (shape);
-    nxt = [2:N 1];
-    px = shape(:,1);
-    px_nxt = shape(nxt,1);
-    py = shape(:,2);
-    py_nxt = shape(nxt,2);
-    
-    cr_prod = px.*py_nxt - px_nxt.*py;
-
-    J = zeros (3, 1);
-    J(1) = sum ( (py.^2 + py.*py_nxt + py_nxt.^2) .* cr_prod); % Jx
-    J(3) = sum ( (px.^2 + px.*px_nxt + px_nxt.^2) .* cr_prod); % Jy
-    J(2) = 0.5 * sum ( (px.*py_nxt + 2*(px.*py + px_nxt.*py_nxt) + px_nxt.*py) .* cr_prod);
-    J = J/12;
-
-  elseif strcmpi (typep, 'polyline')
-
-    error('second_moment_poly2d:Devel','Polyline, not implemented yet.');
-    #TODO
-  elseif strcmpi (typep, 'cbezier')
-
-    error('second_moment_poly2d:Devel', 'Cubic bezier, not implemented yet');
-    #TODO
-
-  end
-
-  if matrix
-    J = vech2mat (J);
-  end
-
-end
-