gmmake_torus.m

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function t = gmmake_torus(inner_rad, outer_rad, subdiv)
% gmmake_torus: Make a quadratic Bezier approximation to a torus
%  t = gmmake_torus(inner_rad, outer_rad, subdiv)
% inner_rad is the radius of the 'hole'.
% outer_rad is the radius of the entire torus.
% The cross-sectional radius is thus .5*(outer_rad-inner_rad).
% subdiv is the number of bezier subdivisions in each direction.


if outer_rad <= inner_rad | inner_rad <= 0
  error('Outer radius must exceed inner radius and both must be positive')
end
if subdiv < 3
  error('Number of subdivisions must be at least 3')
end

global GM_BREP_TYPE_CODE;
t = zba({GM_BREP_TYPE_CODE; ...
         3; ...
         3; ...
         {}; ... 
         zeros(3, 4 * subdiv^2); ...
         {}; ...
         {}; ...
         {'torus_surf'; {}; {}; {}; cell(3,subdiv^2)}; ...
         {'torus'; {}; {'torus_surf'}; {}; {}}});


tan1 = tan(pi / subdiv);
mult = sqrt(1 + tan1^2);
rad1 = .5 * (inner_rad + outer_rad);
rad2 = .5 * (outer_rad - inner_rad);
for j = 0 : 2 * subdiv - 1
  cos1 = cos(j * pi / subdiv);
  sin1 = sin(j * pi / subdiv);
  for k = 0 : 2 * subdiv - 1
    cos2 = rad2 * cos(k * pi / subdiv);
    sin2 = rad2 * sin(k * pi / subdiv);
    x = 0;
    if rem(j,2) == 0 & rem(k,2) == 0
      y = rad1 + cos2;
      z = sin2;
    elseif rem(j,2) == 0 & rem(k,2) == 1
      y = rad1 + mult*cos2;
      z = mult * sin2;
    elseif rem(j,2) == 1 & rem(k,2) == 0
      y = (rad1 + cos2) * mult;
      z = sin2;
    else
      y = rad1 * mult + cos2 * mult^2;
      z = mult * sin2;
    end
    t{4}(:,j * 2 * subdiv + k) = [cos1*x+sin1*y; -sin1*x+cos1*y; z];
  end
end

for j = 0 : subdiv - 1
  j1 = rem(j + 1, subdiv);
  for k = 0 : subdiv - 1 
    k1 = rem(k + 1, subdiv);
    idx = j * subdiv + k;
    t{7}{4,0}{0,idx} = 'bezier_quad';
    t{7}{4,0}{1,idx} = [2,2];
    t{7}{4,0}{2,idx} = [...
     j*subdiv*4 + k*2;...
     (2*j+1)*subdiv*2 + k*2; ...
     j1*subdiv*4 + k*2; ...
     j*subdiv*4 + k*2+1;...
     (2*j+1)*subdiv*2 + k*2+1; ...
     j1*subdiv*4 + k*2+1; ...
     j*subdiv*4 + k1*2;...
     (2*j+1)*subdiv*2 + k1*2; ...
     j1*subdiv*4 + k1*2]; 
  end
end
		

		
% ------------------------------------------------------------------
% Copyright (c) 1999 by Cornell University.  All rights reserved.
% See the accompanying file 'Copyright' for authorship information,
% the terms of the license governing this software, and disclaimers
% concerning this software.
% ------------------------------------------------------------------
% This file is part of the QMG software.  
% Version 2.0 of QMG, release date September 3, 1999
% ------------------------------------------------------------------