Question

点数：

IO.read

到目前为止，我已经完成了：

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       -0.44649

我找到了这些相关链接1，2和3。

引用的值为#!/bin/bash awk 'NR==1' $FILE > LINEA awk 'NR==1' $FILE > LINEB awk 'NR==1' $FILE > LINEC awk 'NR==1' $FILE > LINED x1=`awk '{print $2}' LINEA` # x1 y1=`awk '{print $3}' LINEA` # y1 z1=`awk '{print $4}' LINEA` # z1 x2=`awk '{print $2}' LINEB` # x2 y2=`awk '{print $3}' LINEB` # y2 z2=`awk '{print $4}' LINEB` # z2 x3=`awk '{print $2}' LINEC` # x3 y3=`awk '{print $3}' LINEC` # y3 z3=`awk '{print $4}' LINEC` # z3 x4=`awk '{print $2}' LINED` # x4 y4=`awk '{print $3}' LINED` # y4 z4=`awk '{print $4}' LINED` # z4 v1x=`calc "($x1)-($x2)" | sed 's/^\t//g'` v1y=`calc "($y1)-($y2)" | sed 's/^\t//g'` v1z=`calc "($z1)-($z2)" | sed 's/^\t//g'` v2x=`calc "($x4)-($x3)" | sed 's/^\t//g'` v2y=`calc "($y4)-($y3)" | sed 's/^\t//g'` v2z=`calc "($z4)-($z3)" | sed 's/^\t//g'` v1mag=`calc "sqrt(($v1x)**2+($v1y)**2+($v1z)**2)" | sed 's/^\t//g'` v2mag=`calc "sqrt(($v2x)**2+($v2y)**2+($v2z)**2)" | sed 's/^\t//g'` calc "acos((($v1x)/($v1mag))*(($v2x)/($v2mag))+(($v1y)/($v1mag))*(($v2y)/($v2mag))+(($v1z)/($v1mag))*(($v2z)/($v2mag)))*180/3.141592653589793" | sed 's/^\t//g' | sed 's/^~//g' calc "acos((($x1)*($x4)+($y1)*($y4)+($z1)*($z4))/(sqrt(($x1)**2+($y1)**2+($z1)**2)*sqrt(($x4)**2+($y4)**2+($z4)**2)))*180/3.141592653589793" | sed 's/^\t//g' | sed 's/^~//g'

我得到的价值是：58.7 $^{o}$和70.62525933704842342761 $^{o}$

有人知道获得它的最佳算法是什么？

Answer 1

编辑：如果您的互联网搜索torsion.awk已将您带到此处，请跳过上面接受的答案，因为它使用OP精炼算法来计算扭转，但仍然显示转换shell代码为awk。

以前的读者也注意到在下面的第二个编辑中使用此代码的改进。

我刚注意到最后的“正确”资格; - /

这是您的代码转换为一个awk进程。

我没有这种数学水平的经验，所以不能说它确实在计算你需要的结果。

此外，经常有关于awk程序精度的问题，这些问题与编译的基础c语言库有关。

无论如何，对于所有注意事项，这是对代码的基本转换。

cat torsion_docd.awk

#!/bin/awk -f

function acos(x)        { return atan2((1.-x^2)^0.5,x) }

# x1=`awk '{print $2}' LINEA` # x1
# y1=`awk '{print $3}' LINEA` # y1
# z1=`awk '{print $4}' LINEA` # z1
# x2=`awk '{print $2}' LINEB` # x2
# y2=`awk '{print $3}' LINEB` # y2
# z2=`awk '{print $4}' LINEB` # z2
# x3=`awk '{print $2}' LINEC` # x3
# y3=`awk '{print $3}' LINEC` # y3
# z3=`awk '{print $4}' LINEC` # z3
# x4=`awk '{print $2}' LINED` # x4
# y4=`awk '{print $3}' LINED` # y4
# z4=`awk '{print $4}' LINED` # z4
NR==1 {x1=$2; y=$3; z1=$4}
NR==2 {x2=$2; y=$3; z2=$4}
NR==3 {x3=$2; y=$3; z3=$4}
NR==4 {
        x4=$2; y=$3; z4=$4

        # all of this code below is only executed when you read in the 4th line
        # becuase then you have all the data
        # v1x=`calc "($x1)-($x2)" | sed 's/^\t//g'`
        # v1y=`calc "($y1)-($y2)" | sed 's/^\t//g'`
        # v1z=`calc "($z1)-($z2)" | sed 's/^\t//g'`
        # v2x=`calc "($x4)-($x3)" | sed 's/^\t//g'`
        # v2y=`calc "($y4)-($y3)" | sed 's/^\t//g'`
        # v2z=`calc "($z4)-($z3)" | sed 's/^\t//g'`

        v1x=x1-x2 ; v1y=y1-y2 ; v1z=z1-z2
        v2x=x4-x3 ; v2y=y4-y3 ; v2z=z4-z3

        # v1mag=`calc "sqrt(($v1x)**2+($v1y)**2+($v1z)**2)" | sed 's/^\t//g'`
        # v2mag=`calc "sqrt(($v2x)**2+($v2y)**2+($v2z)**2)" | sed 's/^\t//g'`

        v1mag=sqrt((v1x)**2+(v1y)**2+(v1z)**2)
        v2mag=sqrt((v2x)**2+(v2y)**2+(v2z)**2)   

        # calc "acos((($v1x)/($v1mag))*(($v2x)/($v2mag))+(($v1y)/($v1mag))*(($v2y)/($v2mag))+(($v1z)/($v1mag))*(($v2z)/($v2mag)))*180/3.141
592653589793" | sed 's/^\t//g' | sed 's/^~//g'
        # calc "acos((($x1)*($x4)+($y1)*($y4)+($z1)*($z4))/(sqrt(($x1)**2+($y1)**2+($z1)**2)*sqrt(($x4)**2+($y4)**2+($z4)**2)))*180/3.14159
2653589793" | sed 's/^\t//g' | sed 's/^~//g'

        print acos(((v1x)/(v1mag))*((v2x)/(v2mag))+((v1y)/(v1mag))*((v2y)/(v2mag))+((v1z)/(v1mag))*((v2z)/(v2mag)))*180/3.141592653589793
        print acos(((x1)*(x4)+(y1)*(y4)+(z1)*(z4))/(sqrt((x1)**2+(y1)**2+(z1)**2)*sqrt((x4)**2+(y4)**2+(z4)**2)))*180/3.141592653589793
}

没有转换文档，它看起来像

cat torsion.awk

#!/bin/awk -f

function acos(x)        { return atan2((1.-x^2)^0.5,x) }

NR==1 {x1=$2; y=$3; z1=$4}
NR==2 {x2=$2; y=$3; z2=$4}
NR==3 {x3=$2; y=$3; z3=$4}
NR==4 {
        x4=$2; y=$3; z4=$4

        # all of this code below is only executed when you read in the 4th line
        # because then you have all the data

        v1x=x1-x2 ; v1y=y1-y2 ; v1z=z1-z2
        v2x=x4-x3 ; v2y=y4-y3 ; v2z=z4-z3

        v1mag=sqrt((v1x)**2+(v1y)**2+(v1z)**2)
        v2mag=sqrt((v2x)**2+(v2y)**2+(v2z)**2)   

        print acos(((v1x)/(v1mag))*((v2x)/(v2mag))+((v1y)/(v1mag))*((v2y)/(v2mag))+((v1z)/(v1mag))*((v2z)/(v2mag)))*180/3.141592653589793
        print acos(((x1)*(x4)+(y1)*(y4)+(z1)*(z4))/(sqrt((x1)**2+(y1)**2+(z1)**2)*sqrt((x4)**2+(y4)**2+(z4)**2)))*180/3.141592653589793
}

请注意，我在最后两行acos前添加了打印语句。

在我的机器上，我将其作为

运行

awk -f torsion.awk data.txt

编辑：我已将#!/bin/awk修复为脚本顶部。因此，您需要使用

将脚本标记为可执行文件

 chmod +x ./torsion.awk

然后你可以像

那样运行它

`./torsion.awk data.txt

您的系统可能需要与awk不同的路径，如顶部的she-bang行（#!/bin/awk）。输入which awk，然后在#!之后使用该值。此外，传统的Unix实现通常安装了awk的其他版本，因此，如果这是您的操作环境，请进行一些研究以找出系统中哪个是最好的awk（通常是gawk # -------------- end edit -------------------- 1}}）。

87.6318
131.872

<强>输出

-58.7

但鉴于您同意acos是您想要的输出，我将留给您如何使用2 awk计算。

在任何情况下，希望您可以看到使用{{1}}进行此类计算还有多么直接。

当然，希望真正的数学家能够嘲笑（在笑声之后）并帮助纠正这个问题（或者提出他们自己的想法）。

IHTH

Answer 2

根据您在此主题中其他地方的精炼shell代码，我也将其转录为awk解决方案。由于人们似乎找到了_docd版本的使用，我将在最后添加。我还包括一个调试版本（在回复的中间）。

cat torsion2.awk

-

#!/bin/awk -f  
BEGIN {
  # dbg=0 # turns off dbg output
  # see below for debug version of this script
}
function acos(x)  { return atan2((1.-x^2)^0.5,x) }    
NR==1 {x1=$2; y1=$3; z1=$4}
NR==2 {x2=$2; y2=$3; z2=$4}
NR==3 {x3=$2; y3=$3; z3=$4}
NR==4 {
  x4=$2; y4=$3; z4=$4  
  # all of this code below is only executed when you read in the 4th line
  # because then you have all the data
  #
  v1x=x2-x1 ; v1y=y2-y1 ; v1z=z2-z1     #plane1
  v2x=x3-x2 ; v2y=y3-y2 ; v2z=z3-z2     #plane1
  v3x=x2-x3 ; v3y=y2-y3 ; v3z=z2-z3     #plane2
  v4x=x3-x4 ; v4y=y3-y4 ; v4z=z3-z4     #plane2

  plane1_x=(v1y*v2z)-(v1z*v2y)  # normal vector 1
  plane1_y=(v2x*v1z)-(v2z*v1x)  # normal vector 1
  plane1_z=(v1x*v2y)-(v1y*v2x)  # normal vector 1
  plane2_x=(v3y*v4z)-(v3z*v4y)  # normal vector 2
  plane2_y=(v4x*v3z)-(v4z*v3x)  # normal vector 2
  plane2_z=(v3x*v4y)-(v3y*v4x)  # normal vector 2

  v1mag=sqrt(((plane1_x)**2)+((plane1_y)**2)+((plane1_z)**2)) # magnitude normal vector 1
  v2mag=sqrt(((plane2_x)**2)+((plane2_y)**2)+((plane2_z)**2)) # magnitude normal vector 2
  vn1x=(plane1_x)/(v1mag) ; vn1y=(plane1_y)/(v1mag) ; vn1z=(plane1_z)/(v1mag) # normalization normal vector 1
  vn2x=(plane2_x)/(v2mag) ; vn2y=(plane2_y)/(v2mag) ; vn2z=(plane2_z)/(v2mag) # normalization normal vector 2

  print acos((vn1x*vn2x)+(vn1y*vn2y)+(vn1z*vn2z))*180/3.141592653589793
}

保存文件后，您必须将脚本标记为可执行文件：

chmod +x ./torsion2.awk

然后您可以使用提供的示例数据运行它：

./torsion2.awk data.txt

输出

58.6892

这是完整的调试版本。我需要它，因为我有编辑错误，例如将y2=$3更改为y=$3！（这些事情发生了; - /）

cat torsion2_debug.awk
#!/bin/awk -f

BEGIN {
  dbg=1   # turns on dbg output
  # dbg=0 # turns off dbg output
}
function acos(x)  { return atan2((1.-x^2)^0.5,x) }

NR==1 {x1=$2; y1=$3; z1=$4}
NR==2 {x2=$2; y2=$3; z2=$4}
NR==3 {x3=$2; y3=$3; z3=$4}
NR==4 {
  x4=$2; y4=$3; z4=$4

  if (dbg) {
    print "x1="x1 "\ty1="y1 "\tz1=" z1
    print "x2="x2 "\ty2="y2 "\tz2=" z2
    print "x3="x3 "\ty3="y3 "\tz3=" z3
    print "x4="x4 "\ty4="y4 "\tz4=" z4
  }

  # all of this code below is only executed when you read in the 4th line
  # because then you have all the data
  #
  v1x=x2-x1 ; v1y=y2-y1 ; v1z=z2-z1     #plane1
  v2x=x3-x2 ; v2y=y3-y2 ; v2z=z3-z2     #plane1
  v3x=x2-x3 ; v3y=y2-y3 ; v3z=z2-z3     #plane2
  v4x=x3-x4 ; v4y=y3-y4 ; v4z=z3-z4     #plane2

  if (dbg) {
    print "#dbg: v1x="v1x "\tv1y=" v1y "\tv1z="v1z
    print "#dbg: v2x="v2x "\tv2y=" v2y "\tv2z="v2z
    print "#dbg: v3x="v3x "\tv3y=" v3y "\tv3z="v3z
    print "#dbg: v4x="v4x "\tv4y=" v4y "\tv4z="v4z
  }

  plane1_x=(v1y*v2z)-(v1z*v2y)  # normal vector 1
  plane1_y=(v2x*v1z)-(v2z*v1x)  # normal vector 1
  plane1_z=(v1x*v2y)-(v1y*v2x)  # normal vector 1
  plane2_x=(v3y*v4z)-(v3z*v4y)  # normal vector 2
  plane2_y=(v4x*v3z)-(v4z*v3x)  # normal vector 2
  plane2_z=(v3x*v4y)-(v3y*v4x)  # normal vector 2
  if (dbg) {
    print "#dbg: plane1_x=" plane1_x "\tplane1_y=" plane1_y "\tplane1_z=" plane1_z
    print "#dbg: plane2_x=" plane2_x "\tplane2_y=" plane2_y "\tplane2_z=" plane2_z
  }

  v1mag=sqrt(((plane1_x)**2)+((plane1_y)**2)+((plane1_z)**2)) # magnitude normal vector 1
  v2mag=sqrt(((plane2_x)**2)+((plane2_y)**2)+((plane2_z)**2)) # magnitude normal vector 2
  if (dbg) {
    print "#dbg: v1mag=" v1mag "\tv2mag="v2mag
  }

  vn1x=(plane1_x)/(v1mag) ; vn1y=(plane1_y)/(v1mag) ; vn1z=(plane1_z)/(v1mag) # normalization normal vector 1
  vn2x=(plane2_x)/(v2mag) ; vn2y=(plane2_y)/(v2mag) ; vn2z=(plane2_z)/(v2mag) # normalization normal vector 2

  if (dbg) {
    print "#dbg: " (vn1x*vn2x) " "  (vn1y*vn2y)  " " ((vn1z*vn2z)*180/3.141592653589793)
  }
  print acos((vn1x*vn2x)+(vn1y*vn2y)+(vn1z*vn2z))*180/3.141592653589793
}

这里是awk版本的转录shell

我强烈建议Grymoire's Awk Tutorial帮助您了解awk编程范例及其内置变量，例如NR（Number（of）Record）。

cat torsion2_docd.awk
#!/bin/awk -f

function acos(x)  { return atan2((1.-x^2)^0.5,x) }

# x1=`awk '{print $2}' LINEA` # x1
# y1=`awk '{print $3}' LINEA` # y1
# z1=`awk '{print $4}' LINEA` # z1
# x2=`awk '{print $2}' LINEB` # x2
# y2=`awk '{print $3}' LINEB` # y2
# z2=`awk '{print $4}' LINEB` # z2
# x3=`awk '{print $2}' LINEC` # x3
# y3=`awk '{print $3}' LINEC` # y3
# z3=`awk '{print $4}' LINEC` # z3
# x4=`awk '{print $2}' LINED` # x4
# y4=`awk '{print $3}' LINED` # y4
# z4=`awk '{print $4}' LINED` # z4
NR==1 {x1=$2; y1=$3; z1=$4}
NR==2 {x2=$2; y2=$3; z2=$4}
NR==3 {x3=$2; y3=$3; z3=$4}
NR==4 {
  x4=$2; y=$3; z4=$4

  # all of this code below is only executed when you read in the 4th line
  # because then you have all the data
  #
  # 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

  v1x=x2-x1 ; v1y=y2-y1 ; v1z=z2-z1     #plane1
  v2x=x3-x2 ; v2y=y3-y2 ; v2z=z3-z2     #plane1
  v3x=x2-x3 ; v3y=y2-y3 ; v3z=z2-z3     #plane2
  v1x=x2-x1 ; v1y=y2-y1 ; v1z=z2-z1     #plane1
  v2x=x3-x2 ; v2y=y3-y2 ; v2z=z3-z2     #plane1
  v3x=x2-x3 ; v3y=y2-y3 ; v3z=z2-z3     #plane2
  v4x=x3-x4 ; v4y=y3-y4 ; v4z=z3-z4     #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

  plane1_x=(v1y*v2z)-(v1z*v2y)  # normal vector 1
  plane1_y=(v2x*v1z)-(v2z*v1x)  # normal vector 1
  plane1_z=(v1x*v2y)-(v1y*v2x)  # normal vector 1
  plane2_x=(v3y*v4z)-(v3z*v4y)  # normal vector 2
  plane2_y=(v4x*v3z)-(v4z*v3x)  # normal vector 2
  plane2_z=(v3x*v4y)-(v3y*v4x)  # 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

  v1mag=sqrt((plane1_x)**2+(plane1_y)**2+(plane1_z)**2) # magnitude normal vector 1
  v2mag=sqrt((plane2_x)**2+(plane2_y)**2+(plane2_z)**2) # 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

  vn1x=(plane1_x)/(v1mag) ; vn1y=(plane1_y)/(v1mag) ; vn1z=(plane1_z)/(v1mag) # normalization normal vector 1
  vn2x=(plane2_x)/(v2mag) ; vn2y=(plane2_y)/(v2mag) ; vn2z=(plane2_z)/(v2mag) # normalization normal vector 2

  # calc "acos(($vn1x)*($vn2x)+($vn1y)*($vn2y)+($vn1z)*($vn2z))*180/3.141592653589793" | sed 's/^\t//g' | sed 's/^~//g'

  print acos((vn1x*vn2x)+(vn1y*vn2y)+(vn1z*vn2z))*180/3.141592653589793
}

Answer 3

经过漫长的一夜，我找到了解决方案：

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'

BASH，二面角有四个点

3 个答案: