23/07/15 06:46:29.02 X1xEkNEDH.net
Fermat_Point <- \(a1,a2,b1,b2,c1,c2){
bac <- \(B,A,C){
if(is.complex(B)|is.complex(A)|is.complex(C)){
a=c(Re(A),Im(A)); b=c(Re(B),Im(B)); c=c(Re(C),Im(C))
}else{a=A;b=B;c=C}
ab=b-a
ac=c-a
dot=sum(ab*ac)
bac=acos(dot/sqrt(sum(ab^2))/sqrt(sum(ac^2)))
return(bac)
}
intsect <- \(a,b,c,d){
a1=Re(a) ; a2=Im(a)
b1=Re(b) ; b2=Im(b)
c1=Re(c) ; c2=Im(c)
d1=Re(d) ; d2=Im(d)
if((a2-b2)*(c1-d1)==(a1-b1)*(c2-d2) | (a-b)*(c-d)==0) return(NULL)
if(a1==b1 & c1!=d1) return( a1+1i*((d2-c2)/(d1-c1)*(a1-c1)+c2) )
if(a1!=b1 & c1==d1) return( c1+1i*((a2-b2)/(a1-b1)*(c1-a1)+a2) )
p=(a2-b2)/(a1-b1)
q=(c2-d2)/(c1-d1)
x= ((p*a1 - a2) - (q*c1 - c2))/ (p-q)
y= p*x - (p*a1 - a2)
return( x + 1i*y )
}
in3 <- \(P,A,B,C){
opc=\(a,b) Re(a)*Im(b)-Im(a)*Re(b)
sum(opc(B-A,P-A)>0,opc(C-B,P-B)>0,opc(P-A,C-A)>0)%%3==0
}