1
2
3
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
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
|
# -*- coding: utf-8 -*-
# ##### BEGIN GPL LICENSE BLOCK #####
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
#
# ##### END GPL LICENSE BLOCK #####
'''
geometry_utils.py
3d geometry calculations
'''
from mathutils import Vector, Matrix
from mathutils import geometry
# 3D Geometry
class G3:
@classmethod
def distanceP2P(cls, p1, p2):
return (p1-p2).length
@classmethod
def closestP2L(cls, p, l1, l2):
vA = p - l1
vL = l2- l1
vL.normalize()
return vL * (vL.dot(vA)) + l1
@classmethod
def closestP2E(cls, p, e1, e2):
q = G3.closestP2L(p, e1, e2)
de = G3.distanceP2P(e1, e2)
d1 = G3.distanceP2P(q, e1)
d2 = G3.distanceP2P(q, e2)
if d1>de and d1>d2:
q = e2
if d2>de and d2>d1:
q = e1
return q
@classmethod
def heightP2S(cls, p, sO, sN):
return (p-sO).dot(sN) / sN.dot(sN)
@classmethod
def closestP2S(cls, p, sO, sN):
k = - G3.heightP2S(p, sO, sN)
q = p+sN*k
return q
@classmethod
def closestP2F(cls, p, fv, sN):
q = G3.closestP2S(p, fv[0], sN)
#pi = MeshEditor.addVertex(p)
#qi = MeshEditor.addVertex(q)
#MeshEditor.addEdge(pi, qi)
#print ([d0,d1,d2])
if len(fv)==3:
h = G3.closestP2L(fv[0], fv[1], fv[2])
d = (fv[0]-h).dot(q-h)
if d<=0:
return G3.closestP2E(q, fv[1], fv[2])
h = G3.closestP2L(fv[1], fv[2], fv[0])
d = (fv[1]-h).dot(q-h)
if d<=0:
return G3.closestP2E(q, fv[2], fv[0])
h = G3.closestP2L(fv[2], fv[0], fv[1])
d = (fv[2]-h).dot(q-h)
if d<=0:
return G3.closestP2E(q, fv[0], fv[1])
return q
if len(fv)==4:
h = G3.closestP2L(fv[0], fv[1], fv[2])
d = (fv[0]-h).dot(q-h)
if d<=0:
return G3.closestP2E(q, fv[1], fv[2])
h = G3.closestP2L(fv[1], fv[2], fv[3])
d = (fv[1]-h).dot(q-h)
if d<=0:
return G3.closestP2E(q, fv[2], fv[3])
h = G3.closestP2L(fv[2], fv[3], fv[0])
d = (fv[2]-h).dot(q-h)
if d<=0:
return G3.closestP2E(q, fv[3], fv[0])
h = G3.closestP2L(fv[3], fv[0], fv[1])
d = (fv[3]-h).dot(q-h)
if d<=0:
return G3.closestP2E(q, fv[0], fv[1])
return q
@classmethod
def medianTriangle(cls, vv):
m0 = (vv[1]+vv[2])/2
m1 = (vv[0]+vv[2])/2
m2 = (vv[0]+vv[1])/2
return [m0, m1, m2]
@classmethod
def orthoCenter(cls, fv):
try:
h0 = G3.closestP2L(fv[0], fv[1], fv[2])
h1 = G3.closestP2L(fv[1], fv[0], fv[2])
#h2 = G3.closestP2L(fm[2], fm[0], fm[1])
return geometry.intersect_line_line (fv[0], h0, fv[1], h1)[0]
except(RuntimeError, TypeError):
return None
# Poor mans approach of finding center of circle
@classmethod
def circumCenter(cls, fv):
fm = G3.medianTriangle(fv)
return G3.orthoCenter(fm)
@classmethod
def ThreePnormal(cls, fv):
n = (fv[1]-fv[0]).cross(fv[2]-fv[0])
n.normalize()
return n
@classmethod
def closestP2CylinderAxis(cls, p, fv):
n = G3.ThreePnormal(fv)
c = G3.circumCenter(fv)
if(c==None):
return None
return G3.closestP2L(p, c, c+n)
# Poor mans approach of finding center of sphere
@classmethod
def centerOfSphere(cls, fv):
try:
if len(fv)==3:
return G3.circumCenter(fv) # Equator
if len(fv)==4:
fv3 = [fv[0],fv[1],fv[2]]
c1 = G3.circumCenter(fv)
n1 = G3.ThreePnormal(fv)
fv3 = [fv[1],fv[2],fv[3]]
c2 = G3.circumCenter(fv3)
n2 = G3.ThreePnormal(fv3)
d1 = c1+n1
d2 = c2+n2
return geometry.intersect_line_line (c1, d1, c2, d2)[0]
except(RuntimeError, TypeError):
return None
@classmethod
def closestP2Sphere(cls, p, fv):
#print ("G3.closestP2Sphere")
try:
c = G3.centerOfSphere(fv)
if c==None:
return None
pc = p-c
if pc.length == 0:
pc = pc + Vector((1,0,0))
else:
pc.normalize()
return c + (pc * G3.distanceP2P(c, fv[0]))
except(RuntimeError, TypeError):
return None
@classmethod
def closestP2Cylinder(cls, p, fv):
#print ("G3.closestP2Sphere")
c = G3.closestP2CylinderAxis(p, fv)
if c==None:
return None
r = (fv[0] - G3.centerOfSphere(fv)).length
pc = p-c
if pc.length == 0:
pc = pc + Vector((1,0,0))
else:
pc.normalize()
return c + (pc * r)
#@classmethod
#def closestP2Sphere4(cls, p, fv4):
##print ("G3.closestP2Sphere")
#fv = [fv4[0],fv4[1],fv4[2]]
#c1 = G3.circumCenter(fv)
#n1 = G3.ThreePnormal(fv)
#fv = [fv4[1],fv4[2],fv4[3]]
#c2 = G3.circumCenter(fv)
#n2 = G3.ThreePnormal(fv)
#d1 = c1+n1
#d2 = c2+n2
#c = geometry.intersect_line_line (c1, d1, c2, d2)[0]
#pc = p-c
#if pc.length == 0:
#pc = pc + Vector((1,0,0))
#else:
#pc.normalize()
#return c + (pc * G3.distanceP2P(c, fv[0]))
|
