Animation

x=

y=

+

-

-

+

a0 = 1.2 (slider from -0.2 to 1.2, step 0.01)
a = Max(Min[a0, 1], 0)
T1(u, v) = u^(2) - v^(2)
T2(u, v) = 2 * u * v
f1(u, v) = a * T1(u, v) + (1 - a) * u
f2(u, v) = a * T2(u, v) + (1 - a) * v
nu = 10
nv = 10
OLR = (1.7502222222222221, 0.14666666666666667)
OTL = (-1.222222222222222, 2.063111111111111)
minu: x(OTL)
maxu: x(OLR)
minv: y(OLR)
maxv: y(OTL)
du: (maxu - minu) / nu
dv: (maxv - minv) / nv
list1 = Sequence(Segment[(minu, v), (maxu, v)], v, minv + dv, maxv - dv, dv)
list2 = Sequence(Segment[(u, minv), (u, maxv)], u, minu + du, maxu - du, du)
b = PolyLine(Sequence[(f1(u, minv), f2(u, minv)), u, minu, maxu, du])
c = PolyLine(Sequence[(f1(u, maxv), f2(u, maxv)), u, minu, maxu, du])
d = PolyLine(Sequence[(f1(minu, v), f2(minu, v)), v, minv, maxv, dv])
e = PolyLine(Sequence[(f1(maxu, v), f2(maxu, v)), v, minv, maxv, dv])
f = Segment((minu, minv), (maxu, minv))
g = Segment((minu, maxv), (maxu, maxv))
h = Segment((minu, minv), (minu, maxv))
i = Segment((maxu, minv), (maxu, maxv))
j = PolyLine(Sequence[(f1(u, minv + dv), f2(u, minv + dv)), u, minu, maxu, du])
k = PolyLine(Sequence[(f1(u, minv + 2 * dv), f2(u, minv + 2 * dv)), u, minu, maxu, du])
l = PolyLine(Sequence[(f1(u, minv + 3 * dv), f2(u, minv + 3 * dv)), u, minu, maxu, du])
m = PolyLine(Sequence[(f1(u, minv + 4 * dv), f2(u, minv + 4 * dv)), u, minu, maxu, du])
n = PolyLine(Sequence[(f1(u, minv + 5 * dv), f2(u, minv + 5 * dv)), u, minu, maxu, du])
p = PolyLine(Sequence[(f1(u, minv + 6 * dv), f2(u, minv + 6 * dv)), u, minu, maxu, du])
q = PolyLine(Sequence[(f1(u, minv + 7 * dv), f2(u, minv + 7 * dv)), u, minu, maxu, du])
r = PolyLine(Sequence[(f1(u, minv + 8 * dv), f2(u, minv + 8 * dv)), u, minu, maxu, du])
s = PolyLine(Sequence[(f1(u, minv + 9 * dv), f2(u, minv + 9 * dv)), u, minu, maxu, du])
t = PolyLine(Sequence[(f1(minu + du, v), f2(minu + du, v)), v, minv, maxv, dv])
a_1 = PolyLine(Sequence[(f1(minu + 2 * du, v), f2(minu + 2 * du, v)), v, minv, maxv, dv])
b_1 = PolyLine(Sequence[(f1(minu + 3 * du, v), f2(minu + 3 * du, v)), v, minv, maxv, dv])
c_1 = PolyLine(Sequence[(f1(minu + 4 * du, v), f2(minu + 4 * du, v)), v, minv, maxv, dv])
d_1 = PolyLine(Sequence[(f1(minu + 5 * du, v), f2(minu + 5 * du, v)), v, minv, maxv, dv])
e_1 = PolyLine(Sequence[(f1(minu + 6 * du, v), f2(minu + 6 * du, v)), v, minv, maxv, dv])
f_1 = PolyLine(Sequence[(f1(minu + 7 * du, v), f2(minu + 7 * du, v)), v, minv, maxv, dv])
g_1 = PolyLine(Sequence[(f1(minu + 8 * du, v), f2(minu + 8 * du, v)), v, minv, maxv, dv])
h_1 = PolyLine(Sequence[(f1(minu + 9 * du, v), f2(minu + 9 * du, v)), v, minv, maxv, dv])
inputBox1 = Textfield(T1)
inputBox2 = Textfield(T2)
OBLL = (-2.4444444444444446, -2.4444444444444446)
OBUR = (2.4444444444444446, 2.4444444444444446)
CBLL = (-12, -12)
CBUR = (12, 12)