New point insertion

Depending on $\alpha$, the angle between two consecutive edges of the front, three possibilities arise regarding the new point insertion and edge deletion [Geo91].

• $\alpha < \pi/2$. The two segments are retained and become the edges of the new triangles created. (Figure 3.1)

  
  

    

  Figure 3.1: New point insertion : $\alpha < \pi/2$

  
  
  
• $\pi/2 \leq \alpha \leq 2\pi/3$. An internal point and two triangles are generated from the two segments. (Figure 3.2)
  
    

  Figure 3.2: New point insertion : $\pi/2 \leq \alpha \leq 2\pi/3$

  
  
  
• $2\pi/3 < \alpha/2$. One segment is retained while a triangle with this edge and an internal point is created. (Figure 3.3)
  
    

  Figure 3.3: New point insertion : $\alpha \gt 2\pi/3$

  
  
  

A more detailed information and implementation details can be found in [Sha96] or [Geo91].