道格拉斯-普克 Douglas-Peuker抽稀演算法

道格拉斯-普克抽稀演算法，是用來對大量冗餘的圖形資料點進行壓縮以提取必要的資料點。
該演算法實現抽稀的過程是：
1）對曲線的首末點虛連一條直線，求曲線上所有點與直線的距離，並找出最大距離值dmax，用dmax與事先給定的閾值D相比： 
2）若dmax<D，則將這條曲線上的中間點全部捨去；則該直線段作為曲線的近似，該段曲線處理完畢。 
　 若dmax≥D，保留dmax對應的座標點，並以該點為界，把曲線分為兩部分，對這兩部分重複使用該方法，即重複1），2）步，直到所有dmax均<D，即完成對曲線的抽稀。 

顯然，本演算法的抽稀精度也與閾值相關，閾值越大，簡化程度越大，點減少的越多，反之，化簡程度越低，點保留的越多，形狀也越趨於原曲線。 

bool SimplifyCurve(CurveVertexes &prevPts, CurveVertexes &nextPts, double tolerance)
{
 // Exception
 if(!prevPts.size() || tolerance < 0.)
 {
  return false;
 }
 nextPts.clear();

 // Initialization
 int ptSize = prevPts.size();
 SimpStack stack(ptSize);

 // Loop until two vertex meet with ...
 while(stack.m_curOrder >= 0)
 {
  //Get Top Elemelt;
  int lOrder = stack.m_lOrders[stack.m_curOrder];
  int rOrder = stack.m_rOrders[stack.m_curOrder];
  stack.m_curOrder--;

  //
  CGeoPoint<double> lPt = prevPts[lOrder];
  CGeoPoint<double> rPt = prevPts[rOrder];

  // Max proj distance and which point
  double maxProjDist = 0.0;
  int whichPt = 0;

  // Not in the same X or Y direction
  if((rPt.m_x - lPt.m_x) != 0 || (rPt.m_y - lPt.m_y) != 0)
  {
   // Get Max Distance;
   int i = lOrder+1;
   for(; i < rOrder; i++)
   {
                double factor = 0.;
                CGeoPoint<double> result;
                double projDist = CVectOP<double>::Point2Line(prevPts[lOrder], prevPts[rOrder], prevPts[i], factor, result);
                if(projDist > maxProjDist )
                {
                    maxProjDist = projDist;
                    whichPt = i;
               }
   }
   }
  else
  {
   if(rOrder - lOrder > 1)
   {
    stack.m_curOrder++;
    stack.m_lOrders[stack.m_curOrder] = lOrder;
    stack.m_rOrders[stack.m_curOrder] = rOrder-1;
   }
  }

  // Based on this point to split this point array
        if(maxProjDist > tolerance) //大於給定值接著二分
  { 
   stack.m_isRetain[whichPt] = true;
   if(rOrder - lOrder > 1)
   {
    stack.m_curOrder++;
    stack.m_lOrders[stack.m_curOrder] = lOrder;
    stack.m_rOrders[stack.m_curOrder] = whichPt;

    stack.m_curOrder++;
    stack.m_lOrders[stack.m_curOrder] = whichPt;
    stack.m_rOrders[stack.m_curOrder] = rOrder;
   }
  }
  else //小於給定值捨去中間點，留下首末點
  {
            stack.m_isRetain[lOrder] = true;
            stack.m_isRetain[rOrder] = true;
  }

 }

 int i = 0;
 for(; i < ptSize; i++)
 {
  if(!stack.m_isRetain[i])
  {
   continue;
  }

  nextPts.push_back(prevPts[i]);
 }

 return true;
}