用于UV映射的多边形点从3D到2D的正投影

Question

我想要使用简单的正交投影在一个平面上转换或投影多边形点的位置 - 用于UV映射并获得填充 。 代码：

CPolygonFaceRefArray lPolygons = lPolygonMesh.GetPolygons(); 

    for(long f=0; f < lPolygons.GetCount(); f++) 
    { 
     PolygonFace lFace = lPolygons[ f ]; 
     CPointRefArray lPoints = lFace.GetPoints(); 

     Point lPoint1 = lPoints[ 0 ]; 
     Point lPoint2 = lPoints[ 1 ]; 
     Point lPoint3 = lPoints[ 2 ]; 

     CVector3 lPoint1Position = lPoint1.GetPosition(); 
     CVector3 lPoint2Position = lPoint2.GetPosition(); 
     CVector3 lPoint3Position = lPoint3.GetPosition(); 

     _LogValue2(f, L"--------------------------------------"); 

     // Vector A->B, that becomes the X axis of the local plane. 
     CVector3 lLocalX = lLocalX.Sub(lPoint1Position, lPoint2Position); 
     lLocalX.NormalizeInPlace(); 

     // Vector A->C 
     CVector3 lVector13 = lVector13.Sub(lPoint1Position, lPoint3Position); 
     lVector13.NormalizeInPlace(); 

     // Determine the Z vector of the local plane:. 
     CVector3 lLocalZ = lLocalZ.Cross(lLocalX, lVector13); 
     lLocalZ.NormalizeInPlace(); 

     // Determine Y vector of the local plane, assuming that it’s perpendicular to already known X and Z. 
     CVector3 lLocalY = lLocalY.Cross(lLocalZ, lLocalX); 
     lLocalY.NormalizeInPlace(); 

     // In result we got three axis of the local plane: 
     // lLocalX.Dot(lLocalY) == lLocalX.Dot(lLocalZ) == lLocalY.Dot(lLocalZ) == 0; 

     /* 
     Now use system of equations to determine the positions of all points in reference to the local plane. 

     double GetBase(const double& a1, const double& b1, const double& c1, const double& a2, const double& b2, const double& c2, const double& a3, const double& b3, const double& c3) 
     {return (a1*b2*c3)+(a3*b1*c2)+(a2*b3*c1)-((a3*b2*c1)+(a1*b3*c2)+(a2*b1*c3));} 

     double GetX(const double& a1, const double& b1, const double& c1, const double& d1, const double& a2, const double& b2, const double& c2, const double& d2, const double& a3, const double& b3, const double& c3, const double& d3, const double& in_Base) 
     {return ((d1*b2*c3)+(d2*b1*c2)+(d2*b3*c1)-((d3*b2*c1)+(d1*b3*c2)+(d2*b1*c3)))/in_Base;} 

     double GetY(const double& a1, const double& b1, const double& c1, const double& d1, const double& a2, const double& b2, const double& c2, const double& d2, const double& a3, const double& b3, const double& c3, const double& d3, const double& in_Base) 
     {return ((a1*d2*c3)+(a3*d1*c2)+(a2*d3*c1)-((a3*d2*c1)+(a1*d3*c2)+(a2*b1*c3)))/in_Base;} 

     double GetZ(const double& a1, const double& b1, const double& c1, const double& d1, const double& a2, const double& b2, const double& c2, const double& d2, const double& a3, const double& b3, const double& c3, const double& d3, const double& in_Base) 
     {return ((a1*b2*d3)+(a3*b1*d2)+(a2*b3*d1)-((a3*b2*d1)+(a1*b3*d2)+(a2*b1*d3)))/in_Base;} 
     */ 

     double fU; 
     double fV; 
     double fW; 
     double fBase; 

     // For each point, except the first one (lPoint1Position), which we aleady know. 

     for(long p=1; p < lPoints.GetCount(); p++) 
     { 
      Point lPoint = lPoints[ p ]; 
      CVector3 lPointPosition = lPoint.GetPosition(); 
      CVector3 lPointVector = lPointVector.Sub(lPoint1Position, lPointPosition); 

      fBase = GetBase( 
         lLocalX.GetX(), lLocalY.GetX(), lLocalZ.GetX(), 
         lLocalX.GetY(), lLocalY.GetY(), lLocalZ.GetY(), 
         lLocalX.GetZ(), lLocalY.GetZ(), lLocalZ.GetZ()); 

      fU = GetX(lLocalX.GetX(), lLocalY.GetX(), lLocalZ.GetX(), lPointVector.GetX(), 
         lLocalX.GetY(), lLocalY.GetY(), lLocalZ.GetY(), lPointVector.GetY(), 
         lLocalX.GetZ(), lLocalY.GetZ(), lLocalZ.GetZ(), lPointVector.GetZ() 
         ,fBase); 

      fV = GetY(lLocalX.GetX(), lLocalY.GetX(), lLocalZ.GetX(), lPointVector.GetX(), 
         lLocalX.GetY(), lLocalY.GetY(), lLocalZ.GetY(), lPointVector.GetY(), 
         lLocalX.GetZ(), lLocalY.GetZ(), lLocalZ.GetZ(), lPointVector.GetZ() 
         ,fBase); 

      fW = GetZ(lLocalX.GetX(), lLocalY.GetX(), lLocalZ.GetX(), lPointVector.GetX(), 
         lLocalX.GetY(), lLocalY.GetY(), lLocalZ.GetY(), lPointVector.GetY(), 
         lLocalX.GetZ(), lLocalY.GetZ(), lLocalZ.GetZ(), lPointVector.GetZ() 
         ,fBase); 

      _LogRoundValue3(p, fU, fV, fW); 
     } 

     // Result for a cube with the center in 0,0,0 (global coords) is: 
     // INFO : Values: 0, -------------------------------------- 
     // INFO : 1 = 0, 0, 0 
     // INFO : 2 = 0, 1, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 1, -------------------------------------- 
     // INFO : 1 = 1, 1, 0 
     // INFO : 2 = 1, 1, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 2, -------------------------------------- 
     // INFO : 1 = 1, 0, 0 
     // INFO : 2 = 1, 1, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 3, -------------------------------------- 
     // INFO : 1 = 1, 0, 0 
     // INFO : 2 = 1, 1, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 4, -------------------------------------- 
     // INFO : 1 = 1, 0, 0 
     // INFO : 2 = 1, 1, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 5, -------------------------------------- 
     // INFO : 1 = 0, 0, 0 
     // INFO : 2 = 0, 1, 0 
     // INFO : 3 = 0, 1, 0 

     // and for a rotated cube at the same place: 
     // INFO : Values: 0, -------------------------------------- 
     // INFO : 1 = 0.027506, 0.033672, 0 
     // INFO : 2 = 0.487751, 0.969746, 0 
     // INFO : 3 = 0.460245, 1, 0 
     // INFO : Values: 1, -------------------------------------- 
     // INFO : 1 = 1.15549, 0.753083, 0 
     // INFO : 2 = 1.03428, 1, 0 
     // INFO : 3 = -0.121205, 1, 0 
     // INFO : Values: 2, -------------------------------------- 
     // INFO : 1 = 1, 0.04442, 0 
     // INFO : 2 = 1, 1.04442, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 3, -------------------------------------- 
     // INFO : 1 = 1, -0.093859, 0 
     // INFO : 2 = 1, 0.906141, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 4, -------------------------------------- 
     // INFO : 1 = 1, -0.04442, 0 
     // INFO : 2 = 1, 0.95558, 0 
     // INFO : 3 = 0, 1, 0 
     // INFO : Values: 5, -------------------------------------- 
     // INFO : 1 = 0.027506, 0.09418, 0 
     // INFO : 2 = -0.43274, 1.03025, 0 
     // INFO : 3 = -0.460245, 1, 0 
    } 

它仅是每聚投影，我以为 - 这并非总是如此，但它并不重要 - 所有多边形点都在同一局部平面。

我开始确定局部平面很好，然后使用方程系统试图找到本地平面上点的坐标。但结果是错误的。

该代码使用XSI” API和矢量类文档是在这里：

http://download.autodesk.com/global/docs/softimage2013/en_us/sdkguide/index.html?url=si_cpp/classXSI_1_1MATH_1_1CVector3.html,topicNumber=si_cpp_classXSI_1_1MATH_1_1CVector3_html

• 第一个问题是：这是一个正确的做法？
• 如果是，那么它有什么问题？

...是的，我已经阅读了http://en.wikipedia.org/wiki/3D_projection :)

我会很感激的任何建议。

Answer 1

我建议你使用计算点积映射坐标：

fU = lPointVector.Dot(lLocalX); 
fV = lPointVector.Dot(lLocalY); 
fW = lPointVector.Dot(lLocalZ); // should be zero if points lie in plane 

这将带您从三维坐标到2D，这似乎是你的要求。如果不是，你应该澄清你的问题。