vb_linear_interpolate3

 Linear interpolation matrix of three neighbor point values
  according to distance from interpolation point
    W = vb_linear_interpolate3(dd)
 --- Input
 dd(n,1:3) : n-th distance from interpolation point to three neighbor points
 --- Output
  W(n,1:3) : n-th interpolation coefficient
 --- Interpolation using 'W'
  y(n,1:3) = Three data values corresponding to the distance dd(n,1:3)
  y_interp(n) = sum( W(n,1:3) .* y(n,1:3) , 2)
  y_interp = sum( W .* y , 2)

 --- Interpolation
 Linear interpolation of three channel points for one vertex
 Interpolation point is correspond to origin [0,0]
 Three data points with distance d(i) are mapped to [x,y] as
  [x(i),y(i)] = [ex(i) , ey(i)] * d(i) , i=1:3
 Linear function in [x,y] space
  f(x,y) = a*x + b*y + c;
  D = [ex.*d ; ey.*d ; ones(1,3)] : transfer matrix of three points
  f(i) = [a, b, c] * D(:,i)  , i=1:3
  [a, b, c] = f * inv(D)
  f(0,0) = c = f * inv(D) * [0; 0; 1]
         = f * ( D \ [0; 0; 1])

  M. Sato  2008-8-1

 Copyright (C) 2011, ATR All Rights Reserved.
 License : New BSD License(see VBMEG_LICENSE.txt)

0001 function    W = vb_linear_interpolate3(dd)
0002 % Linear interpolation matrix of three neighbor point values
0003 %  according to distance from interpolation point
0004 %    W = vb_linear_interpolate3(dd)
0005 % --- Input
0006 % dd(n,1:3) : n-th distance from interpolation point to three neighbor points
0007 % --- Output
0008 %  W(n,1:3) : n-th interpolation coefficient
0009 % --- Interpolation using 'W'
0010 %  y(n,1:3) = Three data values corresponding to the distance dd(n,1:3)
0011 %  y_interp(n) = sum( W(n,1:3) .* y(n,1:3) , 2)
0012 %  y_interp = sum( W .* y , 2)
0013 %
0014 % --- Interpolation
0015 % Linear interpolation of three channel points for one vertex
0016 % Interpolation point is correspond to origin [0,0]
0017 % Three data points with distance d(i) are mapped to [x,y] as
0018 %  [x(i),y(i)] = [ex(i) , ey(i)] * d(i) , i=1:3
0019 % Linear function in [x,y] space
0020 %  f(x,y) = a*x + b*y + c;
0021 %  D = [ex.*d ; ey.*d ; ones(1,3)] : transfer matrix of three points
0022 %  f(i) = [a, b, c] * D(:,i)  , i=1:3
0023 %  [a, b, c] = f * inv(D)
0024 %  f(0,0) = c = f * inv(D) * [0; 0; 1]
0025 %         = f * ( D \ [0; 0; 1])
0026 %
0027 %  M. Sato  2008-8-1
0028 %
0029 % Copyright (C) 2011, ATR All Rights Reserved.
0030 % License : New BSD License(see VBMEG_LICENSE.txt)
0031 
0032 NP = size(dd,1);
0033 W  = zeros(NP,3);
0034 
0035 % Three unit vector for three points
0036 theta = [0, 2*pi/3, 4*pi/3];
0037 ex = cos(theta); 
0038 ey = sin(theta);
0039 ez = ones(1,3);
0040 
0041 % Linear interpolation of three channel points for one vertex
0042 for n=1:NP
0043     d = dd(n,1:3);
0044     D = [ex.*d ; ey.*d ; ez];
0045     C = D \ [0; 0; 1];
0046     W(n,:) = C';
0047 end