aligned <- function(A1,A2,B1,B2,M1,M2,e)
{	
	C1<-(B1-A1)*((sqrt(5)-1)/4)+(B2-A2)*sqrt(sqrt(5)/8+5/8)+B1;
	C2<-(-1)*(B1-A1)*sqrt(sqrt(5)/8+(5/8))+(B2-A2)*((sqrt(5)-1)/4)+B2;
	D1<-(C1-B1)*((sqrt(5)-1)/4)+(C2-B2)*sqrt(sqrt(5)/8+5/8)+C1;
	D2<-(-1)*(C1-B1)*sqrt(sqrt(5)/8+(5/8))+(C2-B2)*((sqrt(5)-1)/4)+C2;
	E1<-(D1-C1)*((sqrt(5)-1)/4)+(D2-C2)*sqrt(sqrt(5)/8+5/8)+D1;
	E2<-(-1)*(D1-C1)*sqrt(sqrt(5)/8+(5/8))+(D2-C2)*((sqrt(5)-1)/4)+D2;
	x1 <- c(A1,C1,E1,B1,D1);
	y1 <- c(A2,C2,E2,B2,D2);
	
	C1<-(A1-B1)*((sqrt(5)-1)/4)+(A2-B2)*sqrt(sqrt(5)/8+5/8)+A1;
	C2<-(-1)*(A1-B1)*sqrt(sqrt(5)/8+(5/8))+(A2-B2)*((sqrt(5)-1)/4)+A2;
	D1<-(C1-A1)*((sqrt(5)-1)/4)+(C2-A2)*sqrt(sqrt(5)/8+5/8)+C1;
	D2<-(-1)*(C1-A1)*sqrt(sqrt(5)/8+(5/8))+(C2-A2)*((sqrt(5)-1)/4)+C2;
	E1<-(D1-C1)*((sqrt(5)-1)/4)+(D2-C2)*sqrt(sqrt(5)/8+5/8)+D1;
	E2<-(-1)*(D1-C1)*sqrt(sqrt(5)/8+(5/8))+(D2-C2)*((sqrt(5)-1)/4)+D2;
	x2 <- c(B1,C1,E1,A1,D1);
	y2 <- c(B2,C2,E2,A2,D2);
	
	C1<-B1-(1+sqrt(5))*(B1-A1)/4-sqrt((5-sqrt(5))/2)*(B2-A2)/2;
	C2<-sqrt((5-sqrt(5))/2)*(B1-A1)/2+B2-(1+sqrt(5))*(B2-A2)/4;
	D1<-C1-(1+sqrt(5))*(C1-B1)/4-sqrt((5-sqrt(5))/2)*(C2-B2)/2;
	D2<-sqrt((5-sqrt(5))/2)*(C1-B1)/2+C2-(1+sqrt(5))*(C2-B2)/4;
	E1<-D1-(1+sqrt(5))*(D1-C1)/4-sqrt((5-sqrt(5))/2)*(D2-C2)/2;
	E2<-sqrt((5-sqrt(5))/2)*(D1-C1)/2+D2-(1+sqrt(5))*(D2-C2)/4;
	x3 <- c(A1,B1,C1,D1,E1);
	y3 <- c(A2,B2,C2,D2,E2);
	
	C1<-A1-(1+sqrt(5))*(A1-B1)/4-sqrt((5-sqrt(5))/2)*(A2-B2)/2;
	C2<-sqrt((5-sqrt(5))/2)*(A1-B1)/2+A2-(1+sqrt(5))*(A2-B2)/4;
	D1<-C1-(1+sqrt(5))*(C1-A1)/4-sqrt((5-sqrt(5))/2)*(C2-A2)/2;
	D2<-sqrt((5-sqrt(5))/2)*(C1-A1)/2+C2-(1+sqrt(5))*(C2-A2)/4;
	E1<-D1-(1+sqrt(5))*(D1-C1)/4-sqrt((5-sqrt(5))/2)*(D2-C2)/2;
	E2<-sqrt((5-sqrt(5))/2)*(D1-C1)/2+D2-(1+sqrt(5))*(D2-C2)/4;
	x4 <- c(B1,A1,C1,D1,E1);
	y4 <- c(B2,A2,C2,D2,E2);
	
	vx<-c(x1[2],x1[3],x1[5],x2[2],x2[3],x2[5],x3[3],x3[4],x3[5],x4[3],x4[4],x4[5]);
	vy<-c(y1[2],y1[3],y1[5],y2[2],y2[3],y2[5],y3[3],y3[4],y3[5],y4[3],y4[4],y4[5]);
	
	result <- FALSE;
	for(i in 1:12) result <- (result|(distance(M1,M2,vx[i],vy[i])<e));
	result
}