mightyscape-1.2/extensions/fablabchemnitz/strip_line/geometry/Triangle.py

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2022-10-13 00:05:56 +02:00
#!/usr/bin/env python3
class Triangle():
#given segment
def __init__(self,_a,_b,_c):
self.a=_a
self.b=_b
self.c=_c
def __repr__(self):
return "Triangle:("+str(self.a)+","+str(self.b)+","+str(self.c)+")"
# Center of gravity centered on #a
# @return u how much to b
# @return v how much in the c direction
def barycentric(self,p):
#How to use barycentric coordinates
#http://www.blackpawn.com/texts/pointinpoly/default.html
ca = self.c-self.a
ba = self.b-self.a
pa = p-self.a
#Calculate dot product
dotca = ca.dot(ca)
dotcba = ca.dot(ba)
dotcpa = ca.dot(pa)
dotba = ba.dot(ba)
dotbpa = ba.dot(pa)
#Calculation of barycentric coordinates
invDenom = 1 / (dotca * dotba - dotcba * dotcba);
u = (dotba * dotcpa-dotcba*dotbpa)*invDenom
v = (dotca * dotbpa - dotcba * dotcpa) * invDenom
return u,v
# Whether there is a point inside the triangle
def isContain(self,p):
u,v=self.barycentric(p)
inkex.errormsg("\n u="+str(u)+" v="+str(v))
If #u=v=0, the same point as the triangle point
#Check if there is a point in the triangle
return (u > 0) and (v > 0) and (u + v < 1)
def toSVG(self):
return str(self.a.x)+","+str(self.a.y)+","+str(self.b.x)+","+str(self.b.y)+","+str(self.c.x)+","+str(self.c.y)
# Is the arrangement of vertices a, b, c clockwise?
def isClockWise(self):
circle=self.circumcircle()
center=circle.center
aTob=self.b-self.a
aToc=self.c-self.a
#Let's find the cross product
cross=aTob.cross(aToc)
inkex.errormsg(" cross"+str(cross))
if(cross>0):
return True
return False#Counterclockwise
def circumcircle(self):
#Find the length of each side
ab=(self.a-self.b).length()
bc=(self.b-self.c).length()
ca=(self.c-self.a).length()
s=(ab+bc+ca)/2.0;
area=math.sqrt(s*(s-ab)*(s-bc)*(s-ca));
maxlength=0
if(maxlength<ab):
maxlength=ab;longestEdge=2
if(maxlength<bc):
maxlength=bc;longestEdge=0;
if(maxlength<ca):
maxlength=ca;longestEdge=1
if longestEdge==0:
ha=2*area/bc;
angleB=math.asin(ha/ab);
angleC=math.asin(ha/ca);
angleA=math.pi-angleB-angleC;
if longestEdge== 1:
hb=2*area/ca;
angleA=math.asin(hb/ab);
angleC=math.asin(hb/bc);
angleB=math.pi-angleC-angleA;
if longestEdge== 2:
hc=2*area/ab;
angleB=math.asin(hc/bc);
angleA=math.asin(hc/ca);
angleC=math.pi-angleA-angleB;
A = math.sin(2.0*angleA);
B = math.sin(2.0*angleB);
C = math.sin(2.0*angleC);
center=Vertex((self.a.x * A + self.b.x * B + self.c.x * C) / (A+B+C),
(self.a.y * A + self.b.y * B + self.c.y * C) / (A+B+C));
rad=bc / math.sin(angleA) / 2.0
return Circle(center,rad);