47 lines
816 B
Mathematica
47 lines
816 B
Mathematica
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# angle in degrees [0,60]
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# [replace :angle: with a value between 0 and 60]
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alpha_d = :angle:;
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# compute roundness of first case
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alpha = pi * alpha_d/180;
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A = [ 0 0 0 ]';
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B = [ 2*cos(alpha) 0 0 ]';
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C = [ cos(alpha) sin(alpha) 0 ]';
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#
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vecAC=C-A;
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vecAB=B-A;
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aa = norm(B-C)^2;
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bb = norm(vecAC)^2;
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cc = norm(vecAB)^2;
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AA = norm(cross(vecAC,vecAB))^2;
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nom = AA * min( aa, min(bb,cc) );
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denom = aa * bb * cc;
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nR1 = sqrt(4.0/3.0) * sqrt(nom/denom)
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# compute roundness of 2nd case
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alpha = pi * ((180-alpha_d)/2)/180;
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A = [ 0 0 0 ]';
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B = [ 2*cos(alpha) 0 0 ]';
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C = [ cos(alpha) sin(alpha) 0 ]';
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#
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vecAC=C-A;
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vecAB=B-A;
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aa = norm(B-C)^2;
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bb = norm(vecAC)^2;
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cc = norm(vecAB)^2;
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AA = norm(cross(vecAC,vecAB))^2;
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nom = AA * min( aa, min(bb,cc) );
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denom = aa * bb * cc;
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nR2 = sqrt(4.0/3.0) * sqrt(nom/denom)
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