#hw24.txt  Ross Berkowitz
#Posting Permission Granted

Help:=proc():
print(""):
end:

######################   1   ####################

#InsP(P,x,y) inputs a polygon P as a list of vertices (listed counterclockwise) 
#and outputs conditions for a point to be inside

InsP:=proc(P,x,y) local line,i,p,n,center, conditions;

n:=nops(P):
center:=add(p, p in P)/n:
conditions:=true:

for i from 1 to n do
	line:=(P[i+1 mod n+1][1]-P[i mod n+1][1])*(y-P[i mod n+1][2])-(P[i+1 mod n+1][2]-P[i mod n+1][2])*(x-P[i mod n+1][1]):
	
	conditions:=conditions and (line*subs({x=center[1],y=center[2]},line))>0:
od:
conditions:
end:
	
	
	
##########################  2  #####################


TgT:=proc(N) local i,x,y,Triangles:
Triangles:={}:
for y from 0 to evalf((N-1)/N*sqrt(3)/2) by evalf(sqrt(3)/(2*N)) do
	for x from y to 1-y-2/N by 1/N do
		Triangles:=Triangles union {[[x,y],[x+1/N,y],[x+1/(2*N),y+sqrt(3)/(2*N)]],
									[[x+1/N,y],[x+3/(2*N),y+sqrt(3)/(2*N)],[x+1/(2*N),y+sqrt(3)/(2*N)]]}:
	od:
	Triangles:=Triangles union{[[1-1/N,y],[1,y],[1-1/(2*N),y+evalf(sqrt(3)/(2*N))]]}:
od:
Triangles:
end:




##########################   3    ######################

TgC1:=proc(N) local Triangles, x,y,i:
Triangles:={}:
for y from -1 to 1-1/N do
	for x from -evalf(sqrt(1-y^2)) to evalf(sqrt(1-y^2))-1/N by 1/N do
		Triangles:=Triangles union { [[x,y],[x+1/N,y],[x+1/N,y+1/N]],[[x,y+1/N],[x+1/N,y],[x+1/N,y+1/N]]}:
	od:
od:
end:

TgC:=proc(N) local Triangles, T,x,y,i:
Triangles:={}:
for y from 0 to 1-1/N do
	x:=0:
	while x<=evalf(sqrt(1-y^2))-2/N do
		Triangles:=Triangles union { [[x,y],[x+1/N,y],[x+1/N,y+1/N]],[[x,y+1/N],[x+1/N,y],[x+1/N,y+1/N]]}:
		x:=x+1/N:
	od:
	Triangles:=Triangles union {[[x,y],[x+1/N,y],[x,y+1/N]]}:
od:
{seq(TRef([-1,1],T), T in Triangles),
seq(TRef([1,-1],T), T in Triangles),
seq(TRef([-1,-1],T), T in Triangles),
op(Triangles)}:
end:
		
		
TRef:=proc(u,T) local i:
[seq([seq(t[i]*u[i],i=1..2)],t in T)]:
end: