compact_topology_optimization/2d/util_MMC/MMC_init.m

%--------------------------
 % @Author: Jingqiao Hu
 % @Date: 2021-09-27 11:00:42
 % @LastEditTime: 2021-10-06 17:27:12

 % t0 is the initial value, t1 is the max-value of thickness
 %       9         10
 %   ����������������������������������������
 %   |  1\/2  |   3\/4  |
 % 15|   /\   |17  /\   |19
 %   |   11        12   |
 %   ����������������������������������������
 %   |  5\/6  |   7\/8  |
 % 16|   /\   |18  /\   |20
 %   ����������������������������������������
 %       13        14
 % saves [t1,t2,t3, x, y, len, sin(theta)]
%--------------------------
function [MMCs, MMCs_max, MMCs_min] = MMC_init(nelx, nely, lx, t, t_min, t_max, vnum, local_cnum)
    % MMCs = repmat(t, 20, nely, nelx); % 20 components in one coarse-ele
    % MMCs_min = repmat(t0, 20, nely, nelx); 
    % MMCs_max = repmat(t1, 20, nely, nelx); 

    MMCs = zeros(local_cnum, nelx*nely, vnum); % saves [t1,t2,t3, x, y, len, sin(theta)]
    MMCs_max = zeros(local_cnum, nelx*nely, vnum);
    MMCs_min = zeros(local_cnum, nelx*nely, vnum);

    mmc = zeros(local_cnum, vnum);

    % 1-8: xxxx
    mmc(1:2, 4:5) = repmat(lx/4, 2, 2);
    mmc(3:4, 4:5) = repmat([lx/4*3, lx/4], 2, 1);
    mmc(5:6, 4:5) = repmat([lx/4, lx/4*3], 2, 1);
    mmc(7:8, 4:5) = repmat(lx/4*3, 2, 2);

    mmc(1:8, 6) = 0.38; lx/2 * sqrt(2) / 2;

    mmc(1:2:8, 7) = -0.7; 1 / sqrt(2);
    mmc(2:2:8, 7) = 0.7; 1 / sqrt(2);

    if local_cnum > 8
        % 9-20: vertical & horizontal
        mmc(15:16, 4) = 0;
        mmc(17:18, 4) = lx/2;
        mmc(19:20, 4) = lx;
        mmc([15,17,19], 5) = lx/4;
        mmc([16,18,20], 5) = lx/4*3;
        mmc( 9:10, 5) = 0;
        mmc(11:12, 5) = lx/2;
        mmc(13:14, 5) = lx;
        mmc( [9,11,13], 4) = lx/4;
        mmc([10,12,14], 4) = lx/4*3;

        mmc(9:end, 6) = lx/2 / 2;

        mmc( 9:14, 7) = 0;
        mmc(15:20, 7) = 1;        
    end
    
    mmc(:, 1:3) = t;

    mmc_min = repmat([t_min, t_min, t_min, 0, 0, 0.01, -1], local_cnum, 1);
    mmc_max = repmat([t_max, t_max, t_max, lx, lx, lx, 1], local_cnum, 1);
            
    for i = 1:nelx
        for j = 1:nely
            mmc_new = mmc;
            
            % transform to global coordinates:
            mmc_new(:, 4) = mmc(:, 4) + lx * (i-1);
            mmc_new(:, 5) = mmc(:, 5) + lx * (j-1);
            MMCs(:, j+(i-1)*nely, :) = mmc_new;

            % the min & max of position of component must be in this block
            mmc_new = mmc_max;
            mmc_new(:, 4) = mmc_max(:, 4) + lx * (i-1);
            mmc_new(:, 5) = mmc_max(:, 5) + lx * (j-1);
            MMCs_max(:, j+(i-1)*nely, :) = mmc_new;

            mmc_new = mmc_min;
            mmc_new(:, 4) = mmc_min(:, 4) + lx * (i-1);
            mmc_new(:, 5) = mmc_min(:, 5) + lx * (j-1);
            MMCs_min(:, j+(i-1)*nely, :) = mmc_new;
        end
    end

    MMCs = permute(MMCs, [3,1,2]); % [7,20,nelx*nely]
    MMCs_max = permute(MMCs_max, [3,1,2]);
    MMCs_min = permute(MMCs_min, [3,1,2]);

    MMCs = reshape(MMCs, vnum, []); % [7, 20*nele], note the order is local
    MMCs_max = reshape(MMCs_max, vnum, []);
    MMCs_min = reshape(MMCs_min, vnum, []);
end

% the variable only takes thickness
function [MMCs, MMCs_max, MMCs_min, mmc_descriptor] = MMC_init2(nelx, nely, lx, t0, t1, t)
    MMCs = repmat(t, 20, nely, nelx); % 20 components in one coarse-ele
    MMCs_min = repmat(t0, 20, nely, nelx); 
    MMCs_max = repmat(t1, 20, nely, nelx); 

    mmc_descriptor = cell(nelx, nely); % saves [x,y,len,sin(theta)]

    mmc = zeros(20,4);

    % 1-8: xxxx
    mmc(1:2, 1:2) = repmat(lx/4, 2, 2);
    mmc(3:4, 1:2) = repmat([lx/4*3, lx/4], 2, 1);
    mmc(5:6, 1:2) = repmat([lx/4, lx/4*3], 2, 1);
    mmc(7:8, 1:2) = repmat(lx/4*3, 2, 2);

    mmc(1:8, 3) = lx/2 * sqrt(2) / 2;

    mmc(1:2:8, 4) = 1 / sqrt(2);
    mmc(2:2:8, 4) = -1 / sqrt(2);

    % 9-20: vertical & horizontal
    mmc(15:16, 1) = 0;
    mmc(17:18, 1) = lx/2;
    mmc(19:20, 1) = lx;
    mmc([15,17,19], 2) = lx/4;
    mmc([16,18,20], 2) = lx/4*3;
    mmc( 9:10, 2) = 0;
    mmc(11:12, 2) = lx/2;
    mmc(13:14, 2) = lx;
    mmc( [9,11,13], 1) = lx/4;
    mmc([10,12,14], 1) = lx/4*3;

    mmc(9:end, 3) = lx/2 / 2;

    mmc( 9:14, 4) = 0;
    mmc(15:20, 4) = 1;
            
    for i = 1:nelx
        for j = 1:nely
            mmc_new = mmc;
            
            % transform to global coordinates:
            % y
            % |
            % 0 -- x
            mmc_new(:, 1) = mmc(:, 1) + lx * (i-1);
            mmc_new(:, 2) = mmc(:, 2) + lx * (j-1);
            mmc_descriptor{j,i} = mmc_new;
        end
    end
end