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from Point import *
from Plane import *
from utils import *
from Line import *
try:
import OpenGL.GL as GL
import OpenGL.GLU as GLU
import OpenGL.GLUT as GLUT
GL_enabled = True
except:
GL_enabled = False
class Triangle:
id = 0
# points are expected to be in ClockWise order
def __init__(self, p1=None, p2=None, p3=None, e1=None, e2=None, e3=None, n=None):
self.id = Triangle.id
Triangle.id += 1
self.p1 = p1
self.p2 = p2
self.p3 = p3
if (not e1) and p1 and p2:
self.e1 = Line(p1,p2)
else:
self.e1 = e1
if (not e2) and p2 and p3:
self.e2 = Line(p2,p3)
else:
self.e2 = e2
if (not e3) and p3 and p1:
self.e3 = Line(p3,p1)
else:
self.e3 = e3
self._normal = n
self._minx = None
self._miny = None
self._minz = None
self._maxx = None
self._maxy = None
self._maxz = None
self._center = None
self._middle = None
self._radius = None
self._radiussq = None
self._plane = None
def __repr__(self):
return "Triangle%d<%s,%s,%s>" % (self.id,self.p1,self.p2,self.p3)
def name(self):
return "triangle%d" % self.id
def to_OpenGL(self):
if not GL_enabled:
return
GL.glBegin(GL.GL_TRIANGLES)
GL.glVertex3f(self.p1.x, self.p1.y, self.p1.z)
GL.glVertex3f(self.p2.x, self.p2.y, self.p2.z)
GL.glVertex3f(self.p3.x, self.p3.y, self.p3.z)
GL.glEnd()
if False: # display surface normals
n = self.normal()
c = self.center()
d = 0.5
GL.glBegin(GL.GL_LINES)
GL.glVertex3f(c.x, c.y, c.z)
GL.glVertex3f(c.x+n.x*d, c.y+n.y*d, c.z+n.z*d)
GL.glEnd()
if False and hasattr(self, "_middle"): # display bounding sphere
GL.glPushMatrix()
GL.glTranslate(self._middle.x, self._middle.y, self._middle.z)
if not hasattr(self,"_sphere"):
self._sphere = GLU.gluNewQuadric()
GLU.gluSphere(self._sphere, self._radius, 10, 10)
GL.glPopMatrix()
if True: # draw triangle id on triangle face
GL.glPushMatrix()
cc = GL.glGetFloatv(GL.GL_CURRENT_COLOR)
c = self.center()
GL.glTranslate(c.x,c.y,c.z)
p12=self.p1.add(self.p2).mul(0.5)
p3_12=self.p3.sub(p12).normalize()
p2_1=self.p1.sub(self.p2).normalize()
pn=p2_1.cross(p3_12)
GL.glMultMatrixf((p2_1.x, p2_1.y, p2_1.z, 0, p3_12.x, p3_12.y, p3_12.z, 0, pn.x, pn.y, pn.z, 0, 0,0,0,1))
n = self.normal().mul(0.01)
GL.glTranslatef(n.x,n.y,n.z)
GL.glScalef(0.003,0.003,0.003)
w = 0
for ch in str(self.id):
w += GLUT.glutStrokeWidth(GLUT.GLUT_STROKE_ROMAN, ord(ch))
GL.glTranslate(-w/2,0,0)
GL.glColor4f(1,1,1,0)
for ch in str(self.id):
GLUT.glutStrokeCharacter(GLUT.GLUT_STROKE_ROMAN, ord(ch))
GL.glPopMatrix()
GL.glColor4f(cc[0],cc[1],cc[2],cc[3])
if False: # draw point id on triangle face
cc = GL.glGetFloatv(GL.GL_CURRENT_COLOR)
c = self.center()
p12=self.p1.add(self.p2).mul(0.5)
p3_12=self.p3.sub(p12).normalize()
p2_1=self.p1.sub(self.p2).normalize()
pn=p2_1.cross(p3_12)
n = self.normal().mul(0.01)
for p in (self.p1,self.p2,self.p3):
GL.glPushMatrix()
pp = p.sub(p.sub(c).mul(0.3))
GL.glTranslate(pp.x,pp.y,pp.z)
GL.glMultMatrixf((p2_1.x, p2_1.y, p2_1.z, 0, p3_12.x, p3_12.y, p3_12.z, 0, pn.x, pn.y, pn.z, 0, 0,0,0,1))
GL.glTranslatef(n.x,n.y,n.z)
GL.glScalef(0.001,0.001,0.001)
w = 0
for ch in str(p.id):
w += GLUT.glutStrokeWidth(GLUT.GLUT_STROKE_ROMAN, ord(ch))
GL.glTranslate(-w/2,0,0)
GL.glColor4f(0.5,1,0.5,0)
for ch in str(p.id):
GLUT.glutStrokeCharacter(GLUT.GLUT_STROKE_ROMAN, ord(ch))
GL.glPopMatrix()
GL.glColor4f(cc[0],cc[1],cc[2],cc[3])
def normal(self):
if self._normal is None:
# calculate normal, if p1-p2-pe are in clockwise order
vector = self.p3.sub(self.p1).cross(self.p2.sub(self.p1))
denom = vector.norm()
self._normal = vector.div(denom)
return self._normal
def plane(self):
if self._plane is None:
self._plane=Plane(self.center(), self.normal())
return self._plane
def point_inside(self, p):
# http://www.blackpawn.com/texts/pointinpoly/default.html
# Compute vectors
v0 = self.p3.sub(self.p1)
v1 = self.p2.sub(self.p1)
v2 = p.sub(self.p1)
# Compute dot products
dot00 = v0.dot(v0)
dot01 = v0.dot(v1)
dot02 = v0.dot(v2)
dot11 = v1.dot(v1)
dot12 = v1.dot(v2)
# Compute barycentric coordinates
denom = dot00 * dot11 - dot01 * dot01
# originally, "u" and "v" are multiplied with "1/denom"
# we don't do this, to avoid division by zero (for triangles that are "almost" invalid)
u = dot11 * dot02 - dot01 * dot12
v = dot00 * dot12 - dot01 * dot02
# Check if point is in triangle
return ((u * denom) >= 0) and ((v * denom) >= 0) and (u + v <= denom)
def minx(self):
if self._minx is None:
self._minx = min3(self.p1.x, self.p2.x, self.p3.x)
return self._minx
def miny(self):
if self._miny is None:
self._miny = min3(self.p1.y, self.p2.y, self.p3.y)
return self._miny
def minz(self):
if self._minz is None:
self._minz = min3(self.p1.z, self.p2.z, self.p3.z)
return self._minz
def maxx(self):
if self._maxx is None:
self._maxx = max3(self.p1.x, self.p2.x, self.p3.x)
return self._maxx
def maxy(self):
if self._maxy is None:
self._maxy = max3(self.p1.y, self.p2.y, self.p3.y)
return self._maxy
def maxz(self):
if self._maxz is None:
self._maxz = max3(self.p1.z, self.p2.z, self.p3.z)
return self._maxz
def center(self):
if self._center is None:
self._center = self.p1.add(self.p2).add(self.p3).mul(1.0/3)
return self._center
def middle(self):
if self._middle is None:
self.calc_circumcircle()
return self._middle
def radius(self):
if self._radius is None:
self.calc_circumcircle()
return self._radius
def radiussq(self):
if self._radiussq is None:
self.calc_circumcircle()
return self._radiussq
def calc_circumcircle(self):
# we can't use the cached value of "normal", since we don't want the normalized value
normal = self.p2.sub(self.p1).cross(self.p3.sub(self.p2))
denom = normal.norm()
self._radius = (self.p2.sub(self.p1).norm()*self.p3.sub(self.p2).norm()*self.p3.sub(self.p1).norm())/(2*denom)
self._radiussq = self._radius*self._radius
denom2 = 2*denom*denom
alpha = self.p3.sub(self.p2).normsq()*(self.p1.sub(self.p2).dot(self.p1.sub(self.p3))) / (denom2)
beta = self.p1.sub(self.p3).normsq()*(self.p2.sub(self.p1).dot(self.p2.sub(self.p3))) / (denom2)
gamma = self.p1.sub(self.p2).normsq()*(self.p3.sub(self.p1).dot(self.p3.sub(self.p2))) / (denom2)
self._middle = Point(self.p1.x*alpha+self.p2.x*beta+self.p3.x*gamma,
self.p1.y*alpha+self.p2.y*beta+self.p3.y*gamma,
self.p1.z*alpha+self.p2.z*beta+self.p3.z*gamma)
def subdivide(self, depth):
sub = []
if depth == 0:
sub.append(self)
else:
p4 = self.p1.add(self.p2).div(2)
p5 = self.p2.add(self.p3).div(2)
p6 = self.p3.add(self.p1).div(2)
sub += Triangle(self.p1,p4,p6).subdivide(depth-1)
sub += Triangle(p6,p5,self.p3).subdivide(depth-1)
sub += Triangle(p6,p4,p5).subdivide(depth-1)
sub += Triangle(p4,self.p2,p5).subdivide(depth-1)
return sub
def reset_cache(self):
self._minx = None
self._miny = None
self._minz = None
self._maxx = None
self._maxy = None
self._maxz = None
self._center = None
self._middle = None
self._radius = None
self._radiussq = None
self._normal = None
self._plane = None