Velikost úsečky

Úsečka DE je dána svými sdruženými průměty; máme určit její velikost.

Přepínač z zobrazuje body na osách určující volný průmět.
Přepínač s zobrazuje stopníky přímky DE.

Přepínač k zobrazuje otočení úsečky do půdorysny podle osy D_1E_1.
Přepínač n zobrazuje otočení úsečky do roviny rovnoběžné s nárysnou podle osy DD_1.
Přepínač p zobrazuje otočení úsečky do půdorysny podle osy PP_2 (pouze kdyz s=1).

E_1 = (11.398967907275008, -6.8257515966454045)
a_3 = OrthogonalLine(E_1, xAxis)
x_E = Intersect(a_3, xAxis)
E2 = Point(OrthogonalLine[x_E, xAxis])
D_1 = (3.8421544740912377, -12.94317199493699)
a = 1 (slider from 0 to 1, step 1)
X = Point(xAxis)
O = Intersect(xAxis, yAxis)
j_2 = Ray(O, X)
j_1 = OrthogonalLine(D_1, j_2)
x_D = Intersect(j_1, xAxis)
D2 = Point(OrthogonalLine[x_D, xAxis])
U'_x = (1057.9120962184884, -423.3895957121764)
O' = (337.3701913523675, -153.62969942936252)
x' = Ray(O', U'_x)
X' = Point(x')
U'_y = (-1029.5365041238433, -927.6120788195796)
y' = Ray(O', U'_y)
Y' = Point(y')
Y = Point(yAxis)
z_E: (0, y(E2))
g_1 = Line(D_1, E_1)
E_0 = Point(E_1, Vector[((-y(z_E)) * UnitOrthogonalVector[g_1])])
j_6 = OrthogonalLine(E_0, yAxis)
y_{E0} = Intersect(j_6, yAxis)
e0y = If(a ≟ 1, AffineRatio[y_{E0}, Y, O], (AffineRatio[y_{E0}, Y, O] * AffineRatio[U'_y, Y', O']))
y'_{E0} = Point(O', Vector[(e0y / (e0y - 1) * Vector[O', Y'])])
l_6 = If(a ≟ 1, Line[y'_{E0}, x'], Line[y'_{E0}, U'_x])
f_6 = OrthogonalLine(E_0, xAxis)
x_{E0} = Intersect(f_6, xAxis)
e0x = If(a ≟ 1, AffineRatio[x_{E0}, X, O], (AffineRatio[x_{E0}, X, O] * AffineRatio[U'_x, X', O']))
x'_{E0} = Point(O', Vector[(e0x / (e0x - 1) * Vector[O', X'])])
k_6 = If(a ≟ 1, Line[x'_{E0}, y'], Line[x'_{E0}, U'_y])
b = Line(O, Y)
n_5 = OrthogonalLine(D_1, b)
z_D: (0, y(D2))
y_D = Intersect(n_5, b)
f_2 = OrthogonalLine(z_D, b)
D_2 = Intersect(f_2, j_1)
q_1 = OrthogonalLine(E_1, yAxis)
y_E = Intersect(q_1, yAxis)
lx = If(a ≟ 1, AffineRatio[x_D, X, O], (AffineRatio[x_D, X, O] * AffineRatio[U'_x, X', O']))
x'_D = Point(O', Vector[(lx / (lx - 1) * Vector[O', X'])])
s_3 = If(a ≟ 1, Line[x'_D, y'], Line[x'_D, U'_y])
ly = If(a ≟ 1, AffineRatio[y_D, Y, O], (AffineRatio[y_D, Y, O] * AffineRatio[U'_y, Y', O']))
y'_D = Point(O', Vector[(ly / (ly - 1) * Vector[O', Y'])])
t = If(a ≟ 1, Line[y'_D, x'], Line[y'_D, U'_x])
D'_1 = Intersect(s_3, t)
ky = If(a ≟ 1, AffineRatio[y_E, Y, O], (AffineRatio[y_E, Y, O] * AffineRatio[U'_y, Y', O']))
y'_E = Point(O', Vector[(ky / (ky - 1) * Vector[O', Y'])])
l = If(a ≟ 1, Line[y'_E, x'], Line[y'_E, U'_x])
kx = If(a ≟ 1, AffineRatio[x_E, X, O], (AffineRatio[x_E, X, O] * AffineRatio[U'_x, X', O']))
x'_E = Point(O', Vector[(kx / (kx - 1) * Vector[O', X'])])
e = If(a ≟ 1, Line[x'_E, y'], Line[x'_E, U'_y])
E'_1 = Intersect(e, l)
g'_1 = Line(D'_1, E'_1)
U'_z = (318.99037295085606, 1445.5287415390585)
z' = Ray(O', U'_z)
a_1 = If(a ≟ 1, Line[D'_1, z'], Line[U'_z, D'_1])
b_1 = If(a ≟ 1, Line[x'_D, z'], Line[U'_z, x'_D])
m_2 = If(a ≟ 1, Line[y'_E, z'], Line[U'_z, y'_E])
g = If(a ≟ 1, Line[x'_E, z'], Line[U'_z, x'_E])
Z' = Point(z')
Z = Point(yAxis)
lz = If(a ≟ 1, AffineRatio[z_D, Z, O], (AffineRatio[z_D, Z, O] * AffineRatio[U'_z, Z', O']))
z'_D = Point(O', Vector[(lz / (lz - 1) * Vector[O', Z'])])
c_1 = If(a ≟ 1, Line[z'_D, x'], Line[z'_D, U'_x])
D'_2 = Intersect(c_1, b_1)
d_1 = If(a ≟ 1, Line[D'_2, y'], Line[D'_2, U'_y])
D' = Intersect(d_1, a_1)
b_3 = OrthogonalLine(z_E, a_3)
E_2 = Intersect(b_3, a_3)
g_2 = Line(D_2, E_2)
P_2 = Intersect(g_2, xAxis)
q_4 = Circle(P_2, D_2)
E, x_{D_O} = Intersect(q_4, j_2)
t_4 = OrthogonalLine(x_{D_O}, j_2)
o_p = OrthogonalLine(P_2, xAxis)
r_4 = OrthogonalLine(D_1, o_p)
D_O = Intersect(r_4, t_4)
P_1 = Intersect(g_1, o_p)
g_O = Line(D_O, P_1)
O_x = Intersect(g_O, xAxis)
ox = If(a ≟ 1, AffineRatio[O_x, X, O], (AffineRatio[O_x, X, O] * AffineRatio[U'_x, X', O']))
O'_x = Point(O', Vector[(ox / (ox - 1) * Vector[O', X'])])
kz = If(a ≟ 1, AffineRatio[z_E, Z, O], (AffineRatio[z_E, Z, O] * AffineRatio[U'_z, Z', O']))
z'_E = Point(O', Vector[(kz / (kz - 1) * Vector[O', Z'])])
i = If(a ≟ 1, Line[z'_E, y'], Line[z'_E, U'_y])
E'_3 = Intersect(i, m_2)
j = If(a ≟ 1, Line[E'_3, x'], Line[E'_3, U'_x])
h = If(a ≟ 1, Line[z'_E, x'], Line[z'_E, U'_x])
E'_2 = Intersect(h, g)
m = If(a ≟ 1, Line[E'_2, y'], Line[E'_2, U'_y])
E' = Intersect(m, j)
g' = Line(D', E')
P' = Intersect(g'_1, g')
xx' = Line(O', X')
j_5 = If(a ≟ 1, Line[y'_D, x'], Line[y'_D, U'_x])
g'_2 = Line(D'_2, E'_2)
P'_2 = Intersect(g'_2, xx')
o'_p = Line(P', P'_2)
l_3 = Circle(O', Distance[O, X])
k0 = AffineRatio(x_E, X, O)
n = 0 (slider from 0 to 1, step 1)
r = OrthogonalLine(E_1, xAxis)
s_2 = Circle(O', Distance[O, y_E])
k = 1 (slider from 0 to 1, step 1)
pom = 1 (slider from 0 to 1, step 1)
f = If(a ≟ 1, Line[E'_1, z'], Line[U'_z, E'_1])
N_1 = Intersect(g_1, xAxis)
h_2 = OrthogonalLine(N_1, xAxis)
N_2 = Intersect(g_2, h_2)
pomq = 0 (slider from -5 to 5, step 1)
N' = Intersect(g', g'_2)
N'_1 = Intersect(g'_1, xx')
h_1 = Segment(O, N_1)
i_1 = Segment(O, P_2)
t_1 = Segment(O', N'_1)
d_2 = Segment(O', P'_2)
z = 0 (slider from 0 to 1, step 1)
p_1 = Segment(E_1, x_E)
r_1 = Segment(x_E, E_2)
s_1 = Segment(D_1, x_D)
c_2 = Segment(x_D, D_2)
k_2 = Segment(E'_1, x'_E)
l_2 = Segment(x'_E, E'_2)
n_2 = Segment(E', E'_2)
p_2 = Segment(E', E'_1)
q_2 = Segment(D'_1, x'_D)
r_2 = Segment(x'_D, D'_2)
t_2 = Segment(D'_2, D')
c_3 = Segment(D', D'_1)
d_3 = Segment(N_2, N_1)
e_3 = Segment(P_2, P_1)
f_3 = Segment(N'_1, N')
g_3 = Segment(P', P'_2)
D_0 = Point(D_1, Vector[((-y(z_D)) * UnitOrthogonalVector[g_1])])
e_1 = Segment(D_1, D_0)
f_1 = Segment(D_0, E_0)
h_3 = Segment(E_0, E_1)
vzdalenostD0E0 = Distance(D_0, E_0)
TextD0E0: "\overline{" + (Name[D_0]) + (Name[E_0]) + "} \, = \, " + vzdalenostD0E0
s = 0 (slider from 0 to 1, step 1)
i_3 = Segment(D_2, E_2)
j_3 = Segment(D_1, E_1)
k_3 = Segment(D'_2, E'_2)
m_3 = Segment(D', E')
n_3 = Segment(D'_1, E'_1)
N_0 = Point(N_1, Vector[((-y(N_2)) * UnitOrthogonalVector[g_1])])
l_1 = Line(N_0, P_1)
m_1 = Segment(N_0, N_1)
mnohoúhelník2, d_0, d_4, e_4, e_0 = Polygon(D_0, D_1, E_1, E_0)
k_1 = Line(D_1, j_2)
p_3 = Circle(D_1, E_1)
A, F_1 = Intersect(p_3, k_1)
n_1 = Line(E_2, j_2)
q_3 = OrthogonalLine(F_1, j_2)
F_2 = Intersect(q_3, n_1)
r_3 = Segment(D_2, F_2)
c = OrthogonalLine(A, n_1)
D = Intersect(n_1, c)
d = Segment(D, D_2)
a_2 = Segment(D, A)
b_2 = Segment(D, F_2)
e_2 = Segment(A, F_1)
t_3 = Segment(F_1, F_2)
vzdalenostD2F2 = Distance(D_2, F_2)
TextD2F2: "\overline{" + (Name[D_2]) + (Name[F_2]) + "} \, = \, " + vzdalenostD2F2
x_F = Intersect(xAxis, q_3)
mnohoúhelník3, d_5, x_d, x_f, f_4 = Polygon(D_2, x_D, x_F, F_2)
fx = If(a ≟ 1, AffineRatio[x_F, X, O], (AffineRatio[x_F, X, O] * AffineRatio[U'_x, X', O']))
x'_F = Point(O', Vector[(fx / (fx - 1) * Vector[O', X'])])
a_4 = If(a ≟ 1, Line[x'_F, y'], Line[x'_F, U'_y])
F'_1 = Intersect(a_4, t)
b_4 = If(a ≟ 1, Line[F'_1, z'], Line[U'_z, F'_1])
c_4 = If(a ≟ 1, Line[x'_F, z'], Line[U'_z, x'_F])
F'_2 = Intersect(c_4, h)
g_4 = If(a ≟ 1, Line[F'_2, y'], Line[U'_y, F'_2])
F' = Intersect(g_4, b_4)
h_4 = Segment(D', F')
i_4 = Segment(F', F'_1)
j_4 = Segment(F'_1, D'_1)
k_4 = Segment(F', F'_2)
l_4 = Segment(F'_2, x'_F)
m_4 = Segment(x'_F, F'_1)
mnohoúhelník4, d'_2, f', f'_1, d'_3 = Polygon(D', F', F'_1, D'_1)
n_4 = Segment(D'_2, F'_2)
s_4 = OrthogonalLine(E_1, o_p)
p = 0 (slider from 0 to 1, step 1)
c_5 = CircleArc(P_2, x_{D_O}, D_2)
e_5 = Segment(x_{D_O}, D_O)
f_5 = Segment(D_1, D_O)
H = Intersect(f_5, o_p)
i_5 = If(a ≟ 1, Line[y'_E, x'], Line[y'_E, U'_x])
J = Intersect(o'_p, g_3)
I = Intersect(o'_p, t)
k_5 = Segment(D', I)
l_5 = Segment(E', J)
o_k = Line(D_1, E_1)
o'_k = Line(D'_1, E'_1)
o_n = Line(D_2, x_D)
o'_n = Line(D', D'_1)
i_2 = OrthogonalLine(E_1, o_p)
E_O = Intersect(g_O, i_2)
G = Intersect(i_2, o_p)
p_4 = OrthogonalLine(E_O, xAxis)
B = Intersect(p_4, xAxis)
g_5 = CircleArc(P_2, B, E_2)
a_5 = Segment(B, E_O)
b_5 = Segment(E_O, E_1)
h_5 = Segment(E_O, D_O)
mnohoúhelník5, h_6, d_o, e_o, g_6 = Polygon(H, D_O, E_O, G)
C = Intersect(l, o'_p)
vzdalenostEODO = Distance(E_O, D_O)
TextEODO: "\overline{" + (Name[E_O]) + (Name[D_O]) + "} \, = \, " + vzdalenostEODO
dx = If(a ≟ 1, AffineRatio[x_{D_O}, X, O], (AffineRatio[x_{D_O}, X, O] * AffineRatio[U'_x, X', O']))
x'_{D_O} = Point(O', Vector[(dx / (dx - 1) * Vector[O', X'])])
g'_O = Line(P', O'_x)
D'_O = Intersect(g'_O, t)
E'_O = Intersect(g'_O, l)
q = Segment(E', C)
m_5 = Segment(C, E'_O)
p_5 = Segment(I, D'_O)
mnohoúhelník6, i_6, d'_o, e'_o, c_6 = Polygon(I, D'_O, E'_O, C)
q_5 = OrthogonalLine(D_0, b)
y_{D0} = Intersect(b, q_5)
d0y = If(a ≟ 1, AffineRatio[y_{D0}, Y, O], (AffineRatio[y_{D0}, Y, O] * AffineRatio[U'_y, Y', O']))
y'_{D0} = Point(O', Vector[(d0y / (d0y - 1) * Vector[O', Y'])])
a_6 = OrthogonalLine(D_0, xAxis)
x_{D0} = Intersect(a_6, xAxis)
d0x = If(a ≟ 1, AffineRatio[x_{D0}, X, O], (AffineRatio[x_{D0}, X, O] * AffineRatio[U'_x, X', O']))
x'_{D0} = Point(O', Vector[(d0x / (d0x - 1) * Vector[O', X'])])
r_5 = If(a ≟ 1, Line[x'_{D0}, y'], Line[x'_{D0}, U'_y])
s_5 = If(a ≟ 1, Line[y'_{D0}, x'], Line[y'_{D0}, U'_x])
D'_0 = Intersect(s_5, r_5)
t_5 = Segment(D'_0, D'_1)
E'_0 = Intersect(l_6, k_6)
d_6 = Segment(E'_0, E'_1)
e_6 = Segment(D'_0, E'_0)
mnohoúhelník1, d'_1, e'_1, e'_0, d'_0 = Polygon(D'_1, E'_1, E'_0, D'_0)
g'_0 = Line(D'_0, E'_0)
b_6 = Segment(D'_1, I)
m_6 = Segment(E'_1, C)