Development of a Casting Process Database for Rapid Process Design Using Case-Based Reasoning

. 2025 Jan 23;18(3):505. doi: 10.3390/ma18030505

Algorithm 1 $Find point P_{o p t i m a l}^{'}$ on the target part to serve as the end of an ingate.
Input: $S T L_m o d e l$ : List of triangular faces ${F a c e_{i} : (P o i n t A_{i}, P o i n t B_{i}, P o i n t C_{i})}$ $P$ : The endpoint of the streamline in an ingate of the source part’s process $T$ : The threshold of distance $N_{s o u r c e}$ : The normal vector at point P. $H_{s o u r c e}$ : The mean curvature at point P. $K_{s o u r c e}$ : The Gaussian curvature at point P.
1:	Initialize List $C e n t e r s = []$
2:	Initialize Dictionary $F a c e_M a p = {}$
3:	For $F a c e_{i}$ in $S T L_m o d e l$ do
4:	Calculate the center point $C_{i}$ of $F a c e_{i}$
5:	$C e n t e r s . a p p e n d (C_{i})$
6:	$F a c e_M a p [C_{i}] = F a c e_{i}$
7:	End For
8:	Build K-D Tree $k d T r e e$ using $C e n t e r s$
9:	The cluster of center points closest to $P$ $C_{c a n d i d a t e} = k d T r e e . r a n g e Q u e r y (P, T)$
10:	Initialize List $C a n d i d a t e_P o i n t_I n f o = []$
11:	For $C_{i}$ in $C_{c a n d i d a t e}$ do
12:	$F a c e_{i} = F a c e_M a p [C_{i}]$
13:	Calculate the projection point $P_{i}^{'}$ of $P$ on the $F a c e_{i}$ plane
14:	If $P_{i}^{'}$ is outside of $F a c e_{i}$ then
15:	Choose the vertex of $F a c e_{i}$ that is closet to $P$ as the new $P_{i}^{'}$
16:	End If
17:	$C a n d i d a t e_P o i n t_I n f o . a p p e n d (P_{i}^{'}, F a c e_{i})$
18:	End For
19:	Initialize $m i n_t o t a l_e r r o r = \infty$
20:	Initialize $P_{o p t i m a l}^{'} = N o n e$
21:	For $(P_{i}^{'}, F a c e_{i})$ in $C a n d i d a t e_P^{'}$ do
22:	Approximate the normal vector $N_{i}$ of $P_{i}^{'}$ by the normal vector of $F a c e_{i}$
23:	Compute the mean curvature $H_{i}$ and Gaussian curvature $K_{i}$ at $P^{'}$ using barycentric coordinate interpolation
24:	Substitute $N_{s o u r c e}$ , $H_{s o u r c e}$ , $K_{s o u r c e}$ , $N_{i}$ , $H_{i}$ , $K_{i}$ to calculate the total error $E r r_{i}$ using Equation (1)
25:	If $(E r r_{i} < m i n_t o t a l_e r r o r)$ then
26:	$m i n_t o t a l_e r r o r = E r r_{i}$
27:	$P_{o p t i m a l}^{'} = P_{i}^{'}$
28:	End If
29:	End For
Output: The position of the optimal point $P_{o p t i m a l}^{'}$ on the STL surface of the target part.