问多维线性插值的预计算权重

EN

% Define grid
G{1} = single([0; 1; 3; 5; 10]);
G{2} = single([15; 17; 18; 20]);

% Steps and edges are reduntant but help make interpolation a bit faster
S{1} = G{1}(2:end)-G{1}(1:end-1);
S{2} = G{2}(2:end)-G{2}(1:end-1);

gpuInf = 1e10;
% It's my workaround for a bug in GPU version of discretize in Matlab R2017a.
% It throws an error if edges contain Inf, realmin, or realmax. Seems fixed in R2017b prerelease.
E{1} = [-gpuInf; G{1}(2:end-1); gpuInf];
E{2} = [-gpuInf; G{2}(2:end-1); gpuInf];

% Generate query points
n = 50; X = gpuArray(single([rand(n,1)*14-2, 14+rand(n,1)*7]));

[G1, G2] = ndgrid(G{1},G{2});

for i = 1 : 4
    % Generate values on grid
    foo = @(x1,x2) (sin(x1+rand) + cos(x2*rand))>0;
    V = gpuArray(foo(G1,G2));

    % Interpolate
    V_interp = interpV(X, V, G, E, S);

    % Plot results
    subplot(2,2,i);
    contourf(G1, G2, V); hold on;
    scatter(X(:,1), X(:,2),50,[ones(n,1), 1-V_interp, 1-V_interp],'filled', 'MarkerEdgeColor','black'); hold off;
end

function y = interpV(X, V, G, E, S)
y = min(1, max(0, interpV_helper(X, 1, 1, 0, [], V, G, E, S) ));
end

function y = interpV_helper(X, dim, weight, curr_y, index, V, G, E, S)
if dim == ndims(V)+1
    M = [1,cumprod(size(V),2)];
    idx = 1 + (index-1)*M(1:end-1)';
    y = curr_y + weight .* single(V(idx));
else
    x = X(:,dim); grid = G{dim}; edges = E{dim}; steps = S{dim};
    iL = single(discretize(x, edges));
    weightL = weight .* (grid(iL+1) - x) ./ steps(iL);
    weightH = weight .* (x - grid(iL)) ./ steps(iL);
    y = interpV_helper(X, dim+1, weightL, curr_y, [index, iL  ], V, G, E, S) +...
        interpV_helper(X, dim+1, weightH, curr_y, [index, iL+1], V, G, E, S);
end
end