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Épura

(π')

(π)

(π'')

Movimente livremente as projeções A_z, A_y e 
a abcissa X_A e observe o que acontece na 
épura.

É possivel estabelecer alguma relação entre as
distâncias de A aos planos de projeção e as 
medidas das coordenadas utilizadas na épura?

Como poderíamos definir as coordenadas
x (abcissa), y (afastamento) e z (cota), tomando
por base as projeções do ponto A?

Observação:

A_z = A_v
A_y = A_h
X_A = A_t

(π'')

A_1 = Intersect(xAxis, yAxis)
B_1 = Point(xAxis)
a = Segment(A_1, B_1)
A'_2 = Rotate(A_1, 29.999999999999996°, A_1)
B'_2 = Rotate(B_1, 29.999999999999996°, A_1)
X = Segment(A'_2, B'_2)
A'_1 = Rotate(A_1, 329.99999999999994°, A'_2)
B'_1 = Rotate(B_1, 329.99999999999994°, A'_2)
a'_1 = Segment(A'_1, B'_1)
C = Mirror(B'_1, A'_1)
b = Segment(C, A'_1)
c = Line(B'_2, a'_1)
u = Vector(A'_1, C)
A'' = Translate(A'_2, u)
B'' = Translate(B'_2, u)
a'' = Segment(A'', B'')
v = Vector(A'_1, B'_1)
A''_1 = Translate(A'_2, v)
B''_1 = Translate(B'_2, v)
a''_1 = Segment(A''_1, B''_1)
D = Point(yAxis)
D' = Mirror(D, A'_1)
d = Line(D, X)
e = Line(D', X)
f = Line(B'_2, yAxis)
E = Intersect(d, f)
F = Intersect(e, f)
polígono1, a''_2, b'', b''_1, a''_3 = Polygon(A'', B'', B''_1, A''_1)
polígono2, d_1, e_1, f_1, d' = Polygon(D, E, F, D')
x_A = Point(X)
g = Line(x_A, yAxis)
h = Line(x_A, a'_1)
G = Point(h)
G' = Mirror(G, x_A)
i = Segment(G', G)
A_y = Point(i)
I = Intersect(g, d_1)
I' = Mirror(I, x_A)
j = Segment(I, I')
A_z = Point(j)
k = Line(A_z, i)
l = Line(A_y, j)
A = Intersect(k, l)
m = Segment(A_z, A)
n = Segment(A, A_y)
g_1 = Segment(x_A, A_y)
S = Point(xAxis)
w = Vector(A'_1, S)
A''_2 = Translate(A'_2, w)
B''_2 = Translate(B'_2, w)
a''_4 = Segment(A''_2, B''_2)
O' = Translate(x_A, w)
T = Rotate(A''_2, 329.99999999999994°, S)
U = Rotate(B''_2, 329.99999999999994°, S)
i_1 = Segment(T, U)
O'' = Rotate(O', 329.99999999999994°, S)
j_1 = OrthogonalLine(O'', i_1)
z_1 = Vector(x_A, O'')
A_v = Translate(A_z, z_1)
A_t = Translate(x_A, z_1)
H' = Translate(A_y, z_1)
l_1 = Segment(A_t, H')
V = Rotate(A_t, 300.00000000000006°, A_t)
A_h = Rotate(H', 300.00000000000006°, A_t)
m_1 = Segment(V, A_h)
s_1 = Segment(A_z, x_A)
distânciaAAy = Distance(A, A_y)
p = Segment(A_v, V)
q = Segment(V, A_h)
O = Point(X)
r = Line(O, b'')
s = Line(O, d')
B = Intersect(a''_2, r)
H = Intersect(b''_1, r)
J = Intersect(s, d_1)
K = Intersect(s, f_1)
t = Line(B, s)
a_1 = Line(H, s)
b_1 = Line(J, r)
c_1 = Line(K, b_1)
L = Intersect(t, b_1)
M = Intersect(t, c_1)
N = Intersect(a_1, c_1)
P = Intersect(a_1, b_1)
polígono3, l_2, p_1, n_1, m_2 = Polygon(L, P, N, M)
Y = Segment(B, H)
z = Segment(J, K)
q_1 = Line(A_y, b''_1)
r_1 = Line(A, q_1)
Q = Intersect(q_1, Y)
t_1 = Line(Q, n)
R = Intersect(r_1, t_1)
polígono4, r_2, a_2, a_y, q_2 = Polygon(R, A, A_y, Q)
u_1 = Vector(x_A, A_t)
b_2 = Segment(O, x_A)
O'_2 = Translate(O, u_1)
W = Translate(x_A, u_1)
c_2 = Segment(O'_2, W)
origem_x = Rotate(O'_2, 329.99999999999994°, W)
W' = Rotate(W, 329.99999999999994°, W)
d_2 = Segment(origem_x, W')
o = Perimeter(polígono2)
o_1 = Distance(r_2, m)
v_1 = Perimeter(polígono4)
h_1 = Line(origem_x, p)
C_1 = Point(h_1)
D_1 = Point(h_1)
k_1 = Segment(C_1, D_1)