BASH, Dihedral angle with four points

Question

Points:

A -2.08576        1.76533       -0.46417
B -0.95929        0.87554        0.03365
C  0.28069        1.66193        0.42640
D  0.62407        2.22927              


        

Answer 1

After a long night, I found the solution:

awk -v var=$((x+2)) 'NR==var' $FILE > LINEaa
awk -v var=$((y+2)) 'NR==var' $FILE > LINEbb
awk -v var=$((z+2)) 'NR==var' $FILE > LINEcc
awk -v var=$((w+2)) 'NR==var' $FILE > LINEd
x1=`awk '{print $2}' LINEaa` # x1
y1=`awk '{print $3}' LINEaa` # y1
z1=`awk '{print $4}' LINEaa` # z1
x2=`awk '{print $2}' LINEbb` # x2
y2=`awk '{print $3}' LINEbb` # y2
z2=`awk '{print $4}' LINEbb` # z2
x3=`awk '{print $2}' LINEcc` # x3
y3=`awk '{print $3}' LINEcc` # y3
z3=`awk '{print $4}' LINEcc` # z3
x4=`awk '{print $2}' LINEd` # x4
y4=`awk '{print $3}' LINEd` # y4
z4=`awk '{print $4}' LINEd` # z4
v1x=`calc "($x2)-($x1)" | sed 's/^\t//g'` #plane1
v1y=`calc "($y2)-($y1)" | sed 's/^\t//g'` #plane1
v1z=`calc "($z2)-($z1)" | sed 's/^\t//g'` #plane1
v2x=`calc "($x3)-($x2)" | sed 's/^\t//g'` #plane1
v2y=`calc "($y3)-($y2)" | sed 's/^\t//g'` #plane1
v2z=`calc "($z3)-($z2)" | sed 's/^\t//g'` #plane1
v3x=`calc "($x2)-($x3)" | sed 's/^\t//g'` #plane2
v3y=`calc "($y2)-($y3)" | sed 's/^\t//g'` #plane2
v3z=`calc "($z2)-($z3)" | sed 's/^\t//g'` #plane2
v4x=`calc "($x3)-($x4)" | sed 's/^\t//g'` #plane2
v4y=`calc "($y3)-($y4)" | sed 's/^\t//g'` #plane2
v4z=`calc "($z3)-($z4)" | sed 's/^\t//g'` #plane2
plane1_x=`calc "($v1y)*($v2z)-($v1z)*($v2y)" | sed 's/^\t//g'` # normal vector 1
plane1_y=`calc "($v2x)*($v1z)-($v2z)*($v1x)" | sed 's/^\t//g'` # normal vector 1
plane1_z=`calc "($v1x)*($v2y)-($v1y)*($v2x)" | sed 's/^\t//g'` # normal vector 1
plane2_x=`calc "($v3y)*($v4z)-($v3z)*($v4y)" | sed 's/^\t//g'` # normal vector 2
plane2_y=`calc "($v4x)*($v3z)-($v4z)*($v3x)" | sed 's/^\t//g'` # normal vector 2
plane2_z=`calc "($v3x)*($v4y)-($v3y)*($v4x)" | sed 's/^\t//g'` # normal vector 2
v1mag=`calc "sqrt(($plane1_x)**2+($plane1_y)**2+($plane1_z)**2)" | sed 's/^\t//g'`  # magnitude normal vector 1
v2mag=`calc "sqrt(($plane2_x)**2+($plane2_y)**2+($plane2_z)**2)" | sed 's/^\t//g'`  # magnitude normal vector 2
vn1x=`calc "($plane1_x)/($v1mag)" | sed 's/^\t//g'`  # normalization normal vector 1
vn1y=`calc "($plane1_y)/($v1mag)" | sed 's/^\t//g'`  # normalization normal vector 1
vn1z=`calc "($plane1_z)/($v1mag)" | sed 's/^\t//g'`  # normalization normal vector 1
vn2x=`calc "($plane2_x)/($v2mag)" | sed 's/^\t//g'`  # normalization normal vector 2
vn2y=`calc "($plane2_y)/($v2mag)" | sed 's/^\t//g'`  # normalization normal vector 2
vn2z=`calc "($plane2_z)/($v2mag)" | sed 's/^\t//g'`  # normalization normal vector 2
calc "acos(($vn1x)*($vn2x)+($vn1y)*($vn2y)+($vn1z)*($vn2z))*180/3.141592653589793" | sed 's/^\t//g' | sed 's/^~//g'