Angle between two planes given xyz coordinate data from each plane

Question

Gabriella Sandberg 2022-9-8

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https://ww2.mathworks.cn/matlabcentral/answers/1800995-angle-between-two-planes-given-xyz-coordinate-data-from-each-plane

评论： Gabriella Sandberg 2022-9-9

I have 4 points in one plane and 3 points on another plane. How do I use this data to calculate the angle between the two planes generated by the xyz coordinates? Here is what I have tried so far, but I don't get a number as an answer. Any help would be appreciated!

%Proximal Plane

P1 = [1,-1,3];

P2 = [2,3,4];

P3 = [-5,6,7];

normal = cross(P1-P2, P1-P3);

syms x y z

P_p = [x,y,z]

realdot = @(u, v) u*transpose(v);

planefunction = realdot(normal, P_p-P1);

%Distal Plane

P4 = [4,-2,4];

P5 = [1,7,5];

P6 = [-3,5,9];

normal2 = cross(P4-P5, P4-P6);

syms x1 y1 z1

P_d = [x1,y1,z1]

realdot = @(u, v) u*transpose(v);

planefunction2 = realdot(normal2, P_d-P4);

angle = acosd((realdot(P_p,P_d)/norm(P_p)*norm(P_d)))

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Answer 1

David Hill 2022-9-8

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https://ww2.mathworks.cn/matlabcentral/answers/1800995-angle-between-two-planes-given-xyz-coordinate-data-from-each-plane#answer_1049160

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P1 = [1,-1,3];
P2 = [2,3,4];
P3 = [-5,6,7];
normal = cross(P1-P2, P1-P3);
P4 = [4,-2,4];
P5 = [1,7,5];
P6 = [-3,5,9];
normal2 = cross(P4-P5, P4-P6);
Angle=acosd(abs(sum(normal.*normal2))/norm(normal)/norm(normal2));