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163 lines
5.4 KiB
163 lines
5.4 KiB
%--------------------------
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% @Author: Jingqiao Hu
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% @Date: 2021-02-25 17:56:07
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% @LastEditTime: 2022-01-24 23:55:27
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% control pnts of one face of this macro-ele
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% p00-p01-p02-p03
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% p10-p11-p12-p13
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% p20-p21-p22-p23
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% p30-p31-p32-p33
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% for one face, the order of c-pnts is col by col
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% NOTE: assume num_add = 0
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%--------------------------
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function B = parametric_B(microx, num_add, num_b)
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num_nodes = (microx+1)^2;
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Be = parametric_B_one_face(microx, num_add, num_b); % [3, num_nodes^2*3, nnodes]
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Be1 = permute(Be, [2,1,3]); % [~, 3, nnodes]
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Be2 = reshape(Be1, [], 3 * num_nodes)'; % [n, ~]
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[up_i, front_i, down_i, back_i, left_i, right_i, dnum_i] = surface_dofs_id(microx);
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[up_a, front_a, down_a, back_a, left_a, right_a, dnum_a] = surface_dofs_id(num_b + 1);
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B = zeros(dnum_i, dnum_a);
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% NOTE: these six faces have shared edges, which should be compute only by one face
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% B assumes the control pnts are ordered as col by col, but nodes in this surface is row by row
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Be_row = row_order(Be2, num_b);
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B(up_i, up_a) = Be_row;
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fid_saved = remove_shared_edges(up_i, front_i);
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B(front_i(fid_saved), front_a) = Be_row(fid_saved, :);
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last_id = [up_i(:); front_i(:)];
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did_saved = remove_shared_edges(last_id, down_i);
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B(down_i(did_saved), down_a) = Be_row(did_saved, :);
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last_id = [up_i(:); front_i(:); down_i(:)];
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bid_saved = remove_shared_edges(last_id, back_i);
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B(back_i(bid_saved), back_a) = Be_row(bid_saved, :);
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last_id = [up_i(:); front_i(:); down_i(:); back_i(:)];
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lid_saved = remove_shared_edges(last_id, left_i);
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B(left_i(lid_saved), left_a) = Be_row(lid_saved, :);
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last_id = [up_i(:); front_i(:); down_i(:); back_i(:); left_i(:)];
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rid_saved = remove_shared_edges(last_id, right_i);
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B(right_i(rid_saved), right_a) = Be_row(rid_saved, :);
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end
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function B3 = row_order(Be, num_b)
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num_nodes = size(Be, 2);
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B1 = reshape(Be, [], 3, num_b+2, num_b+2);
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B2 = permute(B1, [1,2,4,3]);
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B3 = reshape(B2, [], num_nodes);
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end
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function id_saved = remove_shared_edges(last_id, this_id)
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[~, id_shared, ~] = intersect(this_id, last_id,'stable');
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id_saved = setdiff(1:length(this_id), id_shared);
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end
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function B = parametric_B_one_face(microx, num_add, num_b)
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segment_length = microx / (num_add+1);
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Be = parametric_B_one_divided_face(segment_length); % 3,48,s^2
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idx0_Be = reshape(1 : 4^2, 4, 4);
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jdx0_Be = reshape(1 : (segment_length+1)^2, segment_length+1, segment_length+1);
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% for the dimension correspondance
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i1_e = 1:4;
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j1_e = 1:4;
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idx1_Be = idx0_Be(i1_e, j1_e);
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idx2_Be = [3*idx1_Be(:)-2, 3*idx1_Be(:)-1, 3*idx1_Be(:)];
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B = zeros(3, 3*(num_b+2)^2, (microx+1)^2);
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idx0 = reshape(1 : (num_b+2)^2, num_b+2, num_b+2);
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jdx0 = reshape(1 : (microx+1)^2, microx+1, microx+1);
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for i = 1 : num_add+1
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i1 = (i-1)*3 + 1 : i*3 + 1;
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if i < num_add+1
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i2 = (i-1)*segment_length + 1 : i*segment_length ;
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i2_e = 1:segment_length;
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else
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i2 = (i-1)*segment_length + 1 : i*segment_length + 1;
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i2_e = 1:segment_length + 1;
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end
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for j = 1 : num_add+1
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j1 = (j-1)*3 + 1 : j*3 + 1;
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if j < num_add+1
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j2 = (j-1)*segment_length + 1 : j*segment_length ;
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j2_e = 1:segment_length;
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else
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j2 = (j-1)*segment_length + 1 : j*segment_length + 1;
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j2_e = 1:segment_length + 1;
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end
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jdx2_Be = jdx0_Be(j2_e, i2_e);
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idx1 = idx0(i1, j1);
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idx2 = [3*idx1(:)-2, 3*idx1(:)-1, 3*idx1(:)];
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jdx1 = jdx0(j2, i2);
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B(:, idx2(:), jdx1(:)) = Be(:, idx2_Be(:), jdx2_Be(:));
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end
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end
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end
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% B assume the control pnts is col by col
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function B = parametric_B_one_divided_face(microx)
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B = zeros(3, 48, (microx+1)^2);
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I = eye(4);
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for i = 0 : microx
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for j = 0 : microx
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u = i / microx; % project to [0,1]
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v = j / microx;
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Bu = Bezier_matrix(u); % [3,12]
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Bv = Bezier_matrix(v); % [3,12]
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B(:,:,j+1+i*(microx+1)) = Bu * kron(Bv, I); % [3,12]*[12,48]=[3,48]
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end
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end
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end
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function B = Bezier_matrix(t)
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b = [1, t, t^2, t^3] * [1, 0,0,0;
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-3,3,0,0;
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3,-6,3,0;
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-1,3,-3,1]; % 1,4
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I = eye(3);
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B = kron(b, I); % 3,12
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end
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% test
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% [up_i, front_i, down_i, back_i, left_i, right_i, dnum_i] = surface_dofs_id(microx);
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% fid_saved = remove_shared_edges(up_i, front_i);
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%
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% num_b = microx-1;
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% [~, ~, edofMat_full] = assemble_bezier(nelx, nely, nelz, num_b);
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% [~, ~, ~, alldofs] = design_domain(opt_scale, optDesign, nelx, nely, nelz, microx, vF, num_b, ref_nodes, lx, 1);
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% ufull = zeros(alldofs, 1);
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% tmp = ref_nodes';
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% tmp = tmp(:);
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% for ele = 1: nelx*nely*nelz
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% edof = edofMat_ma(ele, :);
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% ue = tmp(edof);
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% ub = bezier_B * ue;
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%
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% edof = edofMat_full(ele, :);
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% ufull(edof) = ub;
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% end
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% deform_nodes = reshape(ufull, 3, [])';
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% figure; scatter3(deform_nodes(:,1), deform_nodes(:,2), deform_nodes(:,3), 'b', 'filled'); axis equal;
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% hold on; scatter3(ref_nodes(:,1), ref_nodes(:,2), ref_nodes(:,3), 'k'); axis equal;
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