function a = tmat_init ( )
%*****************************************************************************80
%
%% tmat_init() initializes the geometric transformation matrix.
%
% Discussion:
%
% The geometric transformation matrix can be thought of as a 4 by 4
% matrix "A" having components:
%
% r11 r12 r13 t1
% r21 r22 r23 t2
% r31 r32 r33 t3
% 0 0 0 1
%
% This matrix encodes the rotations, scalings and translations that
% are applied to graphical objects.
%
% A point P = (x,y,z) is rewritten in "homogeneous coordinates" as
% PH = (x,y,z,1). Then to apply the transformations encoded in A to
% the point P, we simply compute A * PH.
%
% Individual transformations, such as a scaling, can be represented
% by simple versions of the transformation matrix. If the matrix
% A represents the current set of transformations, and we wish to
% apply a new transformation B, then the original points are
% transformed twice: B * ( A * PH ). The new transformation B can
% be combined with the original one A, to give a single matrix C that
% encodes both transformations: C = B * A.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 23 May 2005
%
% Author:
%
% John Burkardt
%
% Reference:
%
% Foley, van Dam, Feiner, Hughes,
% Computer Graphics, Principles and Practice,
% Addison Wesley, Second Edition, 1990.
%
% Output:
%
% real A(4,4), the geometric transformation matrix.
%
a(1:4,1:4) = 0.0;
for i = 1 : 4
a(i,i) = 1.0;
end
return
end