x = sinh(v)/(cosh(v)-cos(u)) у — sin(u)/(cosh(v)-cos(u))

cardioid:

x = l/2*(u^2-v^2)/(u^2+v^2)^2 
у = u*v/(u^2+v^2)^2

cartesian:

x = u
У = v

cassinian:

x = a*2^(l/2)/2*((exp(2*u)+2*exp(u)*cos(v)+1)^(1/2) + exp(u)*cos(v)+1^(l/2)
 у = a*2^(l/2)/2*((exp(2*u)+2*exp(u)*cos(v)+1)^(1/2) -exp(u)*cos(v)-1)^(l/2)]

elliptic:

x = cosh(u)*cos(v) у = sinh(u)*sin(v)

hyperbolic:

x = ((u^2+v^2)^(l/2)+u)^(l/2) 
у = ((u^2+v~2)^(l/2)-u)^(l/2)

invcassinian:

x = a*2^(l/2)/2*((exp(2*u)+2*exp(u)*cos(v)+l)^(l/2) + exp(u)*cos(v)+1)^(1/2)/(exp(2*u)+2*exp(u)*cos(v)+1)^(l/2)
 у = a*2^(l/2)/2*((exp(2*u)+2*exp(u)*cos(v)+l)^(l/2) -exp(u)*cos(v)-l)^(l/2)/(exp(2*u)+2*exp(u)*cos(v)+l)^(l/2)

invelliptic:

x = a*cosh(u)*cos(v)/(cosh(u)*2-sin(v)*2)
 у = a*sinh(u)*sin(v)/(cosh(u)^2-sin(vr2)

logarithmic:

x = a/Pi*ln(u^2+v^2)
 у = 2*a/Pi*arctan(v/u)

logcosh:

x = a/Pi*ln(cosh(ur2-sin(vr2)
у =2*a/Pi*arctan(tanh(u)*tan(v))

maxwell :

x — a/Pi*(u+l+exp(u)*cos(v))
 у = a/Pi*(v+exp(u)*sin(v))

parabolic:

x = (u^2-v^2)/2 •
у — u*v

polar:

x = u*cos(v) у = u*sin(v)

rose:

x = ((u^2+v^2)^(l/2)+u)^(l/2)/(u^2+v^2)^(l/2)
 у — ((u^2+v^(1/2)+u)^(1/2)/(u^2+v^2)^(1/2)

tangent:

x = u/(u^2+v^2) 
у =v/(u^2+v^2)

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