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# -*- 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 #####
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geometry_utils.py
3d geometry calculations
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from mathutils import Vector, Matrix
from mathutils import geometry
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# 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
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@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)
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return None
return G3.closestP2L(p, c, c+n)
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@classmethod
def centerOfSphere(cls, fv):
try:
if len(fv)==3:
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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)
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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)
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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]))