70 lines
1.6 KiB
Mathematica
70 lines
1.6 KiB
Mathematica
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function [Ax,Ay,b,K] = convexhullConvex2D(x1,f1,df1,x2,f2,df2,x3,f3,df3,x4,f4,df4,x5,f5,df5)
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% Lower bounds from tangents
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% z > f(x1) + (x-x1)*df(x1)
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% z > f(x2) + (x-x2)*df(x2)
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% z > f(x3) + (x-x3)*df(x3)
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% z > f(x4) + (x-x4)*df(x4)
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% z > f(x5) + (x-x5)*df(x5)
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% Possible upper bound from creatin hyperplane from three points
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f = [f1 f2 f3 f4];
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X = [x1 x2 x3 x4];
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[~,loc] = sort(f);
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Z = [X;f];
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[n1,d1] = ceiling(Z(:,1),Z(:,2),Z(:,3));
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[n2,d2] = ceiling(Z(:,2),Z(:,3),Z(:,4));
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[n3,d3] = ceiling(Z(:,3),Z(:,4),Z(:,1));
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[n4,d4] = ceiling(Z(:,4),Z(:,3),Z(:,2));
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b = [x1'*df1-f1;
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x2'*df2-f2;
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x3'*df3-f3;
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x4'*df4-f4;
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x5'*df5-f5];
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Ax = [df1';df2';df3';df4';df5'];
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Ay = [-1;-1;-1;-1;-1];
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d1 = max(n1'*Z);
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d2 = max(n2'*Z);
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d3 = max(n3'*Z);
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d4 = max(n4'*Z);
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if all(n1'*Z - d1 <= 0)
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b = [b;d1];
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Ax = [Ax;n1(1:2)'];
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Ay = [Ay;n1(3)];
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end
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if all(n2'*Z - d2 <= 0)
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b = [b;d2];
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Ax = [Ax;n2(1:2)'];
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Ay = [Ay;n2(3)];
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end
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if all(n3'*Z - d3 <= 0)
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b = [b;d3];
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Ax = [Ax;n3(1:2)'];
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Ay = [Ay;n3(3)];
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end
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if all(n4'*Z - d4 <= 0)
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b = [b;d4];
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Ax = [Ax;n4(1:2)'];
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Ay = [Ay;n4(3)];
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end
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if 0
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sdpvar x(2,1) z
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box=[min([x1 x2 x3 x4],[],2) <= x <= max([x1 x2 x3 x4],[],2),-50 <=z <= max([f1 f2 f3 f4])]
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P = [n3'*[x;z] <= d3,
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z >= f1 + (x-x1)'*df1,
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z >= f2 + (x-x2)'*df2,
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z >= f3 + (x-x3)'*df3,
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z >= f4 + (x-x4)'*df4,
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z >= f5 + (x-x5)'*df5,
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box]
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plot([Ax*x + Ay*z <= b])
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plot(P,[x;z],[],1000)
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end
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function [n,d] = ceiling(p1,p2,p3);
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n = cross(p1 - p2, p1 - p3);
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n = n/sign(n(3));
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d = p1'*n;
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