Algorithm 2 Setup-Hit-Triangles

1: ${\mathit{C}}_{\mathit{n}}\leftarrow$ Combination of triangles by G mode, index:$i=\left\{0,1, \dots , N-1\right\}$ 2: $\mathit{L} \leftarrow$ Listener

3: $\mathit{S} \leftarrow$ Sound source 4: $\mathit{P}\mathit{C}\leftarrow$ PathCacheBuffer of $S$ 5: ${\mathit{T}}_{\mathit{d}}\leftarrow$ Triangle, depth:d = $\left\{0,1,2,3\right\}$ 6: $\mathit{T}\mathit{P}\left({\mathit{T}}_{\mathit{d}}\right)\leftarrow$ Type of ${\mathit{T}}_{\mathit{d}}=$ {Reflection, Diffraction, None} 7: procedure Setup-hit-triangles$\left({\mathit{C}}_{\mathit{n}}, \mathit{L}, \mathit{S}\right)$ 8:  ${\mathit{C}}_{\mathit{n}}\leftarrow$ Merge sort combinations in ${\mathit{C}}_{\mathit{n}}$ and combinations in $\mathit{P}\mathit{C}$ 9:  for $\mathit{C}\in \left\{{\mathit{C}}_{\mathbf{0}},\cdots {\mathit{C}}_{\mathit{n}\mathbf{-}\mathbf{1}}\right\} \mathit{d}\mathit{o}$ 10:   for $\mathit{T}\in \left\{{\mathit{T}}_{\mathbf{0}},\cdots {\mathit{T}}_{\mathbf{3}}\right\} \mathit{d}\mathit{o}$ 11:    $\mathit{T}\mathit{P}\left({\mathit{T}}_{\mathit{d}}\right)\leftarrow \mathrm{GetTypeOfTriangle}\left({\mathit{T}}_{\mathit{d}}, \mathit{S}\right)$ 12:    if $\mathit{T}\mathit{P}\left({\mathit{T}}_{\mathit{d}}\right)$ is a reflection type then 13:     Calculate image mirror positions based on ${\mathit{T}}_{\mathit{d}} and \mathit{L}$ 14:     $\mathit{T}\leftarrow$ update the image mirror positions 15:    else if $\mathit{T}\mathit{P}\left({\mathit{T}}_{\mathit{d}}\right)$ is a diffraction type then 16:     Calculate edge information based on ${\mathit{T}}_{\mathit{d}}, \mathit{S}, and \mathit{L}$ 17:     $\mathit{T}\leftarrow$ update edge information

18:    else // None 19:     continue 20:    end if 21:   end for

22:  end for

23: end procedure