Mostrar la construcción

$\Gamma$

$\vec{\mathbf u}$

$\vec{\mathbf v}$

o = true
P_1 = (1.54350099163163, -6.53705462735789)
P_2 = (6.816521380573869, -3.5992289820900676)
P_3 = (4.456217015999724, 0.14210453196895256)
P_4 = (1.6690490961302547, -0.5609648532233465)
a = Line(P_1, P_2)
b = Line(P_3, P_4)
c = Line(P_2, P_3)
d = Line(P_1, P_4)
e = Circle(P_1, P_2, P_3)
A = Center(e)
f = Line(P_1, b)
g = OrthogonalLine(A, f)
J = Mirror(P_1, g)
h = Line(P_1, c)
i = OrthogonalLine(A, h)
K = Mirror(P_1, i)
j = OrthogonalLine(A, d)
L = Mirror(P_1, j)
k = Line(K, J)
l = Line(L, P_2)
X = Intersect(l, k)
m = Line(L, J)
n = Line(P_2, K)
Y = Intersect(m, n)
p = Line(X, Y)
N, M = Intersect(e, p)
u = Vector(P_1, M)
v = Vector(P_1, N)
q, B = IPPPP(u, P_1, P_2, P_3, P_4)
r, C = IPPPP(v, P_1, P_2, P_3, P_4)

Tool: IPPPP
Conica dada la dirección de un punto del infinto y cuatro puntos más
Input: u, P_1, P_2, P_3, P_4
Output: h, X

a = Line(P_4, u)
M = Point(a)
b = Line(P_1, M)
d = Line(P_1, P_2)
V = Intersect(a, d)
c = Line(P_3, P_4)
U = Intersect(b, c)
e = Line(V, U)
f = Line(P_2, P_3)
W = Intersect(e, f)
g = Line(W, u)
X = Intersect(b, g)
h = Conic(P_1, P_2, P_3, P_4, X)

Tool: PPPPC_P
Parábolas por cuatro puntos
Input: P_1, P_2, P_3, P_4
Output: u, q, v, r

$\Gamma$

$\vec{\mathbf u}$

$\vec{\mathbf v}$

b = Line(P_3, P_4)
c = Line(P_2, P_3)
d = Line(P_1, P_4)
e = Circle(P_1, P_2, P_3)
A = Center(e)
f = Line(P_1, b)
g = OrthogonalLine(A, f)
J = Mirror(P_1, g)
h = Line(P_1, c)
i = OrthogonalLine(A, h)
K = Mirror(P_1, i)
j = OrthogonalLine(A, d)
L = Mirror(P_1, j)
k = Line(K, J)
l = Line(L, P_2)
X = Intersect(l, k)
m = Line(L, J)
n = Line(P_2, K)
Y = Intersect(m, n)
p = Line(X, Y)
N, M = Intersect(e, p)
u = Vector(P_1, M)
v = Vector(P_1, N)
q, B = IPPPP(u, P_1, P_2, P_3, P_4)
r, C = IPPPP(v, P_1, P_2, P_3, P_4)