HCR - Proxy Algorithm

• Edgy object (Oggetto spigoloso):
  
  • Notice how for a small displacement of $x_h$ the direction of the Force changes drastically.

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• Proxy algorithm:
  • IDEA: Remember where you entered from.
  1. In case of collision, for the first time @ $t_k=0$ (→ $x_h(0)$) we compute the normal proxy and we take the tangent circle for the proxy $x_p$ given a small radius $ϵ$ (in the figure below $C_p(0)$):
     
  2. Then given the haptic point @ $t_k=1$ → $x_h(1)$ we find which triangle in my triangular mesh is “ACTIVE”.
     The ACTIVE triangle is the one that intersect the segment $\overline{x_h(k)C_p(k-1)}$
     
  • Let’s see how this proxy algorithm changes things:
    
  • In the new case the proxy cannot change triangle so easily, so it results in a more smooth experience.

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• How do we change triangle with the new algorithm?
  • Let’s take for example the following passages:
    
  • As we can see there is a small error for $C_p(1)$ but it’s accepted.
  • And for $C_p(2)$ we have indeed changed triangle, now the second triangle is active.