cc

class CVector 
{
public:
 union
 {
  float vec[3];
  struct  { float x,y,z;};
 };
}

class CCommonTools 
{
public:
 CCommonTools();
 virtual ~CCommonTools();
public:
 static bool ValidPoint(CVector &LinePoint, CVector &LineV,
                                  CVector &TrianglePoint1, CVector &TrianglePoint2, CVector &TrianglePoint3,CVector &result);
 static float Area(float a, float b, float c);
 static float Distance(CVector &p1, CVector &p2);
};

///////////////////////////////

CCommonTools::CCommonTools()
{

}

CCommonTools::~CCommonTools()
{

}
//計(jì)算p1到p2的距離的平方
float CCommonTools::Distance(CVector &p1, CVector &p2)
{
 float dist;
 dist = ((p2.x-p1.x)*(p2.x-p1.x)
  + (p2.y-p1.y)*(p2.y-p1.y)
  + (p2.z-p1.z)*(p2.z-p1.z));
 return (float)sqrt(dist);
}
//利用海倫公式求變成為a,b,c的三角形的面積
float CCommonTools::Area(float a, float b, float c)
{
 float s = (a+b+c)/2;
 return (float)sqrt(s*(s-a)*(s-b)*(s-c));
}
bool CCommonTools::ValidPoint(CVector &LinePoint1, CVector &LinePoint2, CVector &TrianglePoint1, CVector

&TrianglePoint2,CVector &TrianglePoint3,CVector &result)
{
  //三角形所在平面的法向量
  CVector TriangleV;
  //三角形的邊方向向量
  CVector VP12, VP13;
  //直線與平面的交點(diǎn)
  CVector CrossPoint;
  //平面方程常數(shù)項(xiàng)
  float TriD;
  CVector LineV = LinePoint2 - LinePoint1;
  /*-------計(jì)算平面的法向量及常數(shù)項(xiàng)-------*/
  //point1->point2
  VP12.x = TrianglePoint2.x - TrianglePoint1.x;
  VP12.y = TrianglePoint2.y - TrianglePoint1.y;
  VP12.z = TrianglePoint2.z - TrianglePoint1.z;
  //point1->point3
  VP13.x = TrianglePoint3.x - TrianglePoint1.x;
  VP13.y = TrianglePoint3.y - TrianglePoint1.y;
  VP13.z = TrianglePoint3.z - TrianglePoint1.z;
  //VP12xVP13
  TriangleV.x = VP12.y*VP13.z - VP12.z*VP13.y;
  TriangleV.y = -(VP12.x*VP13.z - VP12.z*VP13.x);
  TriangleV.z= VP12.x*VP13.y - VP12.y*VP13.x;
  //計(jì)算常數(shù)項(xiàng)
  TriD = -(TriangleV.x*TrianglePoint1.x
    + TriangleV.y*TrianglePoint1.y
    + TriangleV.z*TrianglePoint1.z);
  /*-------求解直線與平面的交點(diǎn)坐標(biāo)---------*/
  /* 思路：
   *     首先將直線方程轉(zhuǎn)換為參數(shù)方程形式，然后代入平面方程，求得參數(shù)t，
   * 將t代入直線的參數(shù)方程即可求出交點(diǎn)坐標(biāo)
  */
  float tempU, tempD;  //臨時(shí)變量
  tempU = TriangleV.x*LinePoint1.x + TriangleV.y*LinePoint1.y
    + TriangleV.z*LinePoint1.z + TriD;
  tempD = TriangleV.x*LineV.x + TriangleV.y*LineV.y + TriangleV.z*LineV.z;
  //直線與平面平行或在平面上
  if(tempD == 0.0)
  {
  // printf("The line is parallel with the plane.\n");
   return false;
  }
  //計(jì)算參數(shù)t
  float t = -tempU/tempD;
  //計(jì)算交點(diǎn)坐標(biāo)
  CrossPoint.x = LineV.x*t + LinePoint1.x;
  CrossPoint.y = LineV.y*t + LinePoint1.y;
  CrossPoint.z = LineV.z*t + LinePoint1.z;
  /*----------判斷交點(diǎn)是否在三角形內(nèi)部---------*/

  //計(jì)算三角形三條邊的長(zhǎng)度
  float d12 = Distance(TrianglePoint1, TrianglePoint2);
  float d13 = Distance(TrianglePoint1, TrianglePoint3);
  float d23 = Distance(TrianglePoint2, TrianglePoint3);
  //計(jì)算交點(diǎn)到三個(gè)頂點(diǎn)的長(zhǎng)度
  float c1 = Distance(CrossPoint, TrianglePoint1);
  float c2 = Distance(CrossPoint, TrianglePoint2);
  float c3 = Distance(CrossPoint, TrianglePoint3);
  //求三角形及子三角形的面積
  float areaD = Area(d12, d13, d23);  //三角形面積
  float area1 = Area(c1, c2, d12);    //子三角形1
  float area2 = Area(c1, c3, d13);    //子三角形2
  float area3 = Area(c2, c3, d23);    //子三角形3
  //根據(jù)面積判斷點(diǎn)是否在三角形內(nèi)部
  if(fabs(area1+area2+area3-areaD) > 0.001)
  {
  return false;
  }

  result = CrossPoint;
  return true;
}

這幾天同學(xué)問(wèn)我如何判斷空間中的線段和三角面片是否相交，我想這個(gè)也許對(duì)其他人也有點(diǎn)用處。

上面的代碼是判斷兩點(diǎn)構(gòu)成的直線和三點(diǎn)構(gòu)成的面片是否相交，要判斷線段的話，需要再判斷交點(diǎn)是否在線段的兩個(gè)端點(diǎn)之間:  交點(diǎn)和兩個(gè)端點(diǎn)可以形成兩個(gè)向量，判斷這兩個(gè)向量的方向即可。