# triangle_triangle_distance

## `triangle_triangle_distance(s0, s1, s2, t0, t1, t2)`

Compute the distance between two triangles.

Parameters:

Name Type Description Default
`s0` `(3,) array`

First vertex of first triangle.

required
`s1` `(3,) array`

Second vertex of first triangle.

required
`s2` `(3,) array`

Third vertex of first triangle.

required
`t0` `(3,) array`

First vertex of second triangle.

required
`t1` `(3,) array`

Second vertex of second triangle.

required
`t2` `(3,) array`

Third vertex of second triangle.

required

Returns:

Name Type Description
`d` `float`

Distance between the two triangles.

`s` `(3,) array`

Closest point on first triangle.

`t` `(3,) array`

Closest point on second triangle.

Notes

This function is based on the algorithm from the "Proximity Query Pack" by Eric Larsen and Stefan Gottschalk. It would be nice to also output the closest point but this is hard in the case where the triangles intersect each other. Whenever we have a pure python triangle-triangle intersection function, we can use it here.

Examples:

``````import numpy as np
from gpytoolbox import triangle_triangle_distance
s0 = np.array([0.0,0.0,0.0])
s1 = np.array([1.0,0.0,0.0])
s2 = np.array([0.0,1.0,0.0])
t0 = np.array([0.0,0.0,1.0])
t1 = np.array([1.0,0.0,1.0])
t2 = np.array([0.0,1.0,1.0])
dist,s,t = triangle_triangle_distance(s0,s1,s2,t0,t1,t2)
``````
Source code in `src/gpytoolbox/triangle_triangle_distance.py`
 ``` 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181``` ``````def triangle_triangle_distance(s0,s1,s2,t0,t1,t2): """Compute the distance between two triangles. Parameters ---------- s0 : (3,) array First vertex of first triangle. s1 : (3,) array Second vertex of first triangle. s2 : (3,) array Third vertex of first triangle. t0 : (3,) array First vertex of second triangle. t1 : (3,) array Second vertex of second triangle. t2 : (3,) array Third vertex of second triangle. Returns ------- d : float Distance between the two triangles. s : (3,) array Closest point on first triangle. t : (3,) array Closest point on second triangle. Notes ----- This function is based on the algorithm from the "Proximity Query Pack" by Eric Larsen and Stefan Gottschalk. It would be nice to also output the closest point but this is hard in the case where the triangles intersect each other. Whenever we have a pure python triangle-triangle intersection function, we can use it here. Examples -------- ```python import numpy as np from gpytoolbox import triangle_triangle_distance s0 = np.array([0.0,0.0,0.0]) s1 = np.array([1.0,0.0,0.0]) s2 = np.array([0.0,1.0,0.0]) t0 = np.array([0.0,0.0,1.0]) t1 = np.array([1.0,0.0,1.0]) t2 = np.array([0.0,1.0,1.0]) dist,s,t = triangle_triangle_distance(s0,s1,s2,t0,t1,t2) ``` """ shown_disjoint = False S = [s0,s1,s2] T = [t0,t1,t2] Sv = [s1 - s0, s2 - s1, s0 - s2] Tv = [t1 - t0, t2 - t1, t0 - t2] # Sv1 = s2 - s1 # Sv2 = s0 - s2 mindd = np.sum((S[0]-T[0])**2) + 10.0 for i in range(3): for j in range(3): # print("S[i] : ", S[i]) # print("Sv[i] : ", S[i]+Sv[i]) # print("T[j] : ", T[j]) # print("Tv[j] : ", T[j]+Tv[j]) _,P,Q = edge_edge_distance(S[i],S[i]+Sv[i],T[j],T[j]+Tv[j]) # print("P : ", P) # print("Q : ", Q) # # print(P) # # print(Q) VEC = Q - P V = Q - P dd = np.dot(V,V) # # print("BB") if dd <= mindd: minP = P.copy() minQ = Q.copy() mindd = dd.copy() Z = S[(i+2)%3] - P a = np.dot(Z,VEC) Z = T[(j+2)%3] - Q b = np.dot(Z,VEC) if ((a <= 0) and (b >= 0)): # print("Here0") # return np.sqrt(mindd), minP, minQ return np.sqrt(mindd) p = np.dot(V,VEC) if a<0: a = 0 if b>0: b = 0 if ((p - a + b) > 0): shown_disjoint = True # ..... # # print("Sv[0] : ", Sv[0]) # # print("Sv[1] : ", Sv[1]) Sn = np.cross(Sv[0],Sv[1]) # # print("Sn : ", Sn) Snl = np.dot(Sn,Sn) if (Snl > 1e-15): # V = S[0] - T[0] Tp = [np.dot(Sn,S[0] - T[0]), np.dot(Sn,S[0] - T[1]), np.dot(Sn,S[0] - T[2])] point = -1 if ((Tp[0] > 0) and (Tp[1] > 0) and (Tp[2] > 0)): if (Tp[0] < Tp[1]): point = 0 else: point = 1 if (Tp[2] < Tp[point]): point = 2 elif ((Tp[0] < 0) and (Tp[1] < 0) and (Tp[2] < 0)): if (Tp[0] > Tp[1]): point = 0 else: point = 1 if (Tp[2] > Tp[point]): point = 2 if (point >= 0): shown_disjoint = True V = T[point] - S[0] Z = np.cross(Sn,Sv[0]) if (np.dot(V,Z) > 0): V = T[point] - S[1] Z = np.cross(Sn,Sv[1]) if (np.dot(V,Z) > 0): V = T[point] - S[2] Z = np.cross(Sn,Sv[2]) if (np.dot(V,Z) > 0): # # print("T[point] : ", T[point]) # # print("Tp[point] : ", Tp[point]) # # print("Sn : ", Sn) # # print("Snl : ", Snl) P = T[point] + Sn*(Tp[point])/Snl Q = T[point].copy() # print("Here1") # return np.sqrt(np.dot(P-Q,P-Q)), P, Q return np.sqrt(np.dot(P-Q,P-Q)) Tn = np.cross(Tv[0],Tv[1]) Tnl = np.dot(Tn,Tn) if (Tnl > 1e-15): # V = T[0] - S[0] # Sp = [T[0] - S[0], T[0] - S[1], T[0] - S[2]] Sp = [np.dot(Tn,T[0] - S[0]), np.dot(Tn,T[0] - S[1]), np.dot(Tn,T[0] - S[2])] point = -1 if ((Sp[0] > 0) and (Sp[1] > 0) and (Sp[2] > 0)): if (Sp[0] < Sp[1]): point = 0 else: point = 1 if (Sp[2] < Sp[point]): point = 2 elif ((Sp[0] < 0) and (Sp[1] < 0) and (Sp[2] < 0)): if (Sp[0] > Sp[1]): point = 0 else: point = 1 if (Sp[2] > Sp[point]): point = 2 if (point >= 0): shown_disjoint = True V = S[point] - T[0] Z = np.cross(Tn,Tv[0]) if (np.dot(V,Z) > 0): V = S[point] - T[1] Z = np.cross(Tn,Tv[1]) if (np.dot(V,Z) > 0): V = S[point] - T[2] Z = np.cross(Tn,Tv[2]) if (np.dot(V,Z) > 0): Q = S[point] + Tn*(Sp[point])/Tnl P = S[point].copy() # print("Here2") # return np.sqrt(np.dot(P-Q,P-Q)), P, Q return np.sqrt(np.dot(P-Q,P-Q)) if(shown_disjoint): # print("Here3") # return np.sqrt(mindd), minP, minQ return np.sqrt(mindd) else: # print("Here4") return 0.0 ``````