不规则六面体体积计算
2016-06-30 17:19阅读：
1、在不规则六面体中找一点P，将六面体的六个面（Face1---Face6）与P不规则五面体，
2、将不规则五面体，中（Face1-Face6）每一个面劈分成2个不规则的四面体
（如face1由abcd（顺时针或逆时针）四个点这分成P-abc，P-bcd)
3、计算每个四面体的体积
任意四面体P-ABC，记PA=a，PB=b，PC=c，cos角APB=x，cos角BPC=y，cos角CPA=z，
则：V=1/6*abc*sqrt(1+2xyz-x^2-y^2-z^2)
4、相加不规则六面体的体积
C#源码：
///
/// 获取中心点
///
///
private JPoint3D
CenterPoint()
{
//计算中心点
float topX =
(LeftBackTop.X + LeftFrontTop.X + RightBackTop.X + RightFrontTop.X)
/ 4;
float topY =
(LeftBackTop.Y + LeftFrontTop.Y + RightBackTop.Y + RightFrontTop.Y)
/ 4;
float topZ =
(LeftBackTop.Z + LeftFrontTop.Z + Rig
htBackTop.Z + RightFrontTop.Z) / 4;
float bottomX =
(LeftBackBottom.X + LeftFrontBottom.X + RightBackBottom.X +
RightFrontBottom.X) / 4;
float bottomY =
(LeftBackBottom.Y + LeftFrontBottom.Y + RightBackBottom.Y +
RightFrontBottom.Y) / 4;
float bottomZ =
(LeftBackBottom.Z + LeftFrontBottom.Z + RightBackBottom.Z +
RightFrontBottom.Z) / 4;
float x = (topX +
bottomX) / 2;
float y = (topY +
bottomY) / 2;
float z = (topZ +
bottomZ) / 2;
JPoint3D pCenter =
new JPoint3D(x, y, z);
return
pCenter;
}
public float Volume()
{
float fVolume =
0.0f;
//劈分成12个不规则四面体；
JPoint3D pCenter =
CenterPoint();
//上
float pPA =
Distance(LeftBackTop, pCenter);
float pPB =
Distance(LeftFrontTop, pCenter);
float pPC =
Distance(RightBackTop, pCenter);
float pAB =
Distance(LeftBackTop, LeftFrontTop);
float pAC =
Distance(LeftBackTop, RightBackTop);
float pBC =
Distance(LeftFrontTop, RightBackTop);
float x = Cos(pPA,
pPB, pAB);
float y = Cos(pPB,
pPC, pBC);
float z = Cos(pPA,
pPC, pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z))/6;
pPA =
Distance(LeftFrontTop, pCenter);
pPB =
Distance(RightFrontTop, pCenter);
pPC =
Distance(RightBackTop, pCenter);
pAB =
Distance(RightFrontTop, LeftFrontTop);
pAC =
Distance(LeftFrontTop, RightBackTop);
pBC =
Distance(RightFrontTop, RightBackTop);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
//下
pPA =
Distance(LeftFrontBottom, pCenter);
pPB =
Distance(RightFrontBottom, pCenter);
pPC =
Distance(RightBackBottom, pCenter);
pAB =
Distance(RightFrontBottom, LeftFrontBottom);
pAC =
Distance(LeftFrontBottom, RightBackBottom);
pBC =
Distance(RightFrontBottom, RightBackBottom);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
pPA =
Distance(LeftFrontBottom, pCenter);
pPB =
Distance(RightFrontBottom, pCenter);
pPC =
Distance(RightBackBottom, pCenter);
pAB =
Distance(RightFrontBottom, LeftFrontBottom);
pAC =
Distance(LeftFrontBottom, RightBackBottom);
pBC =
Distance(RightFrontBottom, RightBackBottom);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
//左
pPA =
Distance(LeftFrontTop, pCenter);
pPB =
Distance(LeftBackTop, pCenter);
pPC =
Distance(LeftBackBottom, pCenter);
pAB =
Distance(LeftFrontTop, LeftBackTop);
pAC =
Distance(LeftFrontTop, LeftBackBottom);
pBC =
Distance(LeftBackTop, LeftBackBottom);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
pPA =
Distance(LeftFrontBottom, pCenter);
pPB =
Distance(LeftBackBottom, pCenter);
pPC =
Distance(LeftFrontTop, pCenter);
pAB =
Distance(LeftFrontBottom, LeftBackBottom);
pAC =
Distance(LeftFrontBottom, LeftFrontTop);
pBC =
Distance(LeftBackBottom, LeftFrontTop);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
//右
pPA =
Distance(RightFrontTop, pCenter);
pPB =
Distance(RightBackTop, pCenter);
pPC =
Distance(RightBackBottom, pCenter);
pAB =
Distance(RightFrontTop, RightBackTop);
pAC =
Distance(RightFrontTop, RightBackBottom);
pBC =
Distance(RightBackTop, RightBackBottom);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
pPA =
Distance(RightFrontBottom, pCenter);
pPB =
Distance(RightBackBottom, pCenter);
pPC =
Distance(RightFrontTop, pCenter);
pAB =
Distance(RightFrontBottom, RightBackBottom);
pAC =
Distance(RightFrontBottom, RightFrontTop);
pBC =
Distance(RightBackBottom, RightFrontTop);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
//前
pPA =
Distance(RightFrontTop, pCenter);
pPB =
Distance(RightFrontBottom, pCenter);
pPC =
Distance(LeftFrontTop, pCenter);
pAB =
Distance(RightFrontBottom, RightFrontTop);
pAC =
Distance(RightFrontTop, LeftFrontTop);
pBC =
Distance(RightFrontBottom, LeftFrontTop);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
pPA =
Distance(LeftFrontBottom, pCenter);
pPB =
Distance(RightFrontBottom, pCenter);
pPC =
Distance(LeftFrontTop, pCenter);
pAB =
Distance(RightFrontBottom, LeftFrontBottom);
pAC =
Distance(LeftFrontBottom, LeftFrontTop);
pBC =
Distance(RightFrontBottom, LeftFrontTop);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
//后
pPA =
Distance(RightBackTop, pCenter);
pPB =
Distance(RightBackBottom, pCenter);
pPC =
Distance(LeftBackTop, pCenter);
pAB =
Distance(RightBackBottom, RightBackTop);
pAC =
Distance(RightBackTop, LeftBackTop);
pBC =
Distance(RightBackBottom, LeftBackTop);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
pPA =
Distance(LeftBackBottom, pCenter);
pPB =
Distance(RightBackBottom, pCenter);
pPC =
Distance(LeftBackTop, pCenter);
pAB =
Distance(RightBackBottom, LeftBackBottom);
pAC =
Distance(LeftBackBottom, LeftBackTop);
pBC =
Distance(RightBackBottom, LeftBackTop);
x = Cos(pPA, pPB,
pAB);
y = Cos(pPB, pPC,
pBC);
z = Cos(pPA, pPC,
pAC);
fVolume +=
(float)(pPA * pPB * pPC * Math.Sqrt(1 + 2 * x * y * z - x * x - y *
y - z * z)) / 6;
return
fVolume;
}
public float
Distance(JPoint3D p1,JPoint3D p2)
{
return
(float)Math.Sqrt(Math.Pow(p1.X - p2.X, 2) + Math.Pow(p1.Y - p2.Y,
2) + Math.Pow(p1.Z - p2.Z, 2));
}
public float Cos(float
a,float b,float c)
{
return (float)(a *
a + b * b - c * c) / (2 * a * b);
}
