對于2D/3D空間的元素坐标計算 (Matlab)

給定3個不共線的點的坐标，指明行數和列數，就可以計算出這個平行四邊形内所有元素的坐标。主要利用平行四邊形法則和定比分點公式，輸出可以是3維數組或者2維數組。

function location = position(ini,m,n)



% ------------------------------------

% This program is used to calculate the position of 

% every matrix element in a 3D or 2D plane

% 

%     A      m      B

%      *   *   *   *

%  n   *   *   *   *

%      *   *   *   *

%      *   *   *   *

%     C             D

% 

% Input:

% ini: the initial 3 points of the plane, A B C, row vectors.

%      ini must be a 3*3 or 3*2 matrix, for example:[0,0,0; 0,4,4; 4,0,0];

% m: the column of the matrix, say, m=5;

% n: the row of the matrix, say, n=5;

% 

% Output:

% pos: 3D vectors. Each slice contains the positions of the row points. 

% location: 2D vectors, stored by row.

% ------------------------------------





%% Validation

%Validate the form of ini

form = size(in