118 lines
3.6 KiB
Mathematica
118 lines
3.6 KiB
Mathematica
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function W = calcul_W(N, theta, p)
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d = p - 1;
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% Define the number of angles.
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nA = length(theta);
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% The starting values both the x and the y coordinates.
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x0 = linspace(-d / 2, d / 2, p)';
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y0 = zeros(p, 1);
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% The intersection lines.
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x = (-N / 2:N / 2)';
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y = x;
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% Initialize vectors that contains the row numbers, the column numbers
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% and the values for creating the matrix W efficiently.
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rows = zeros(2 * N * nA * p, 1);
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cols = rows;
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vals = rows;
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idxend = 0;
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II = 1:nA;
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JJ = 1:p;
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% Loop over the chosen angles.
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for i = II
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% All the starting points for the current angle.
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x0theta = cosd(theta(i)) * x0 - sind(theta(i)) * y0;
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y0theta = sind(theta(i)) * x0 + cosd(theta(i)) * y0;
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% The direction vector for all rays corresponding to the current angle.
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a = -sind(theta(i));
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b = cosd(theta(i));
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% Loop over the rays.
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for j = JJ
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% Use the parametrisation of line to get the y-coordinates of
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% intersections with x = constant.
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tx = (x - x0theta(j)) / a;
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yx = b * tx + y0theta(j);
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% Use the parametrisation of line to get the x-coordinates of
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% intersections with y = constant.
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ty = (y - y0theta(j)) / b;
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xy = a * ty + x0theta(j);
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% Collect the intersection times and coordinates.
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t = [tx; ty];
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xxy = [x; xy];
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yxy = [yx; y];
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% Sort the coordinates according to intersection time.
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[~, I] = sort(t);
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xxy = xxy(I);
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yxy = yxy(I);
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% Skip the points outside the box.
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I = (xxy >= -N / 2 & xxy <= N / 2 & yxy >= -N / 2 & yxy <= N / 2);
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xxy = xxy(I);
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yxy = yxy(I);
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% Skip double points.
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I = (abs(diff(xxy)) <= 1e-10 & abs(diff(yxy)) <= 1e-10);
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xxy(I) = [];
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yxy(I) = [];
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% Calculate the length within cell and determines the number of
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% cells which is hit.
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aval = sqrt(diff(xxy).^2 + diff(yxy).^2);
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col = [];
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% Store the values inside the box.
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if numel(aval) > 0
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% If the ray is on the boundary of the box in the top or to the
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% right the ray does not by definition lie with in a valid cell.
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if ~((b == 0 && abs(y0theta(j) - N / 2) < 1e-15) || ...
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(a == 0 && abs(x0theta(j) - N / 2) < 1e-15))
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% Calculates the midpoints of the line within the cells.
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xm = 0.5 * (xxy(1:end - 1) + xxy(2:end)) + N / 2;
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ym = 0.5 * (yxy(1:end - 1) + yxy(2:end)) + N / 2;
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% Translate the midpoint coordinates to index.
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col = floor(xm) * N + (N - floor(ym));
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end
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end
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if ~isempty(col)
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% Create the indices to store the values to vector for
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% later creation of W matrix.
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idxstart = idxend + 1;
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idxend = idxstart + numel(col) - 1;
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idx = idxstart:idxend;
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% Store row numbers, column numbers and values.
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rows(idx) = (i - 1) * p + j;
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cols(idx) = col;
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vals(idx) = aval;
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end
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end % end j
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end % end i
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% Truncate excess zeros.
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rows = rows(1:idxend);
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cols = cols(1:idxend);
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vals = vals(1:idxend);
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% Create sparse matrix W from the stored values.
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W = sparse(rows, cols, vals, p * nA, N^2);
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