Pyramide in 3-Tafel-Projektion und Schrägbild
Author: Prof. Dr. Dörte Haftendorn

Grundriss verschoben

gestaucht

gedreht

Höhe

Pyramide

Schrägbild

Pyramide

Ha 2010

A = (-5, -5)
B = (-1, -3)
C = (-3.5, -0.5)
D = (-3, -2.5)
Vieleck1, c, a, b = Polygon(A, B, C)
d: x = x(A)
e: x = x(B)
f: x = x(C)
g: x = x(D)
auf = 0
A': (x(A), auf)
B': (x(B), auf)
C': (x(C), auf)
D' = Point(g)
h(x) = -(x)
i = OrthogonalLine(B, yAxis)
j = OrthogonalLine(C, yAxis)
k = OrthogonalLine(D, yAxis)
l = OrthogonalLine(A, yAxis)
C_h = Intersect(h, j)
D_h = Intersect(h, k)
B_h = Intersect(h, i)
A_h = Intersect(h, l)
m = OrthogonalLine(C_h, xAxis)
n = OrthogonalLine(D_h, xAxis)
p = OrthogonalLine(B_h, xAxis)
q = OrthogonalLine(A_h, xAxis)
r = OrthogonalLine(D', yAxis)
s = OrthogonalLine(A', yAxis)
C'' = Intersect(s, m)
D''_1 = Intersect(r, n)
B'' = Intersect(s, p)
A'' = Intersect(s, q)
t = Segment(D', D''_1)
a_1 = Segment(D''_1, D_h)
b_1 = Segment(D_h, D)
c_1 = Segment(D, D')
d_1 = Segment(A, A_h)
e_1 = Segment(A_h, A'')
f_1 = Segment(A'', A')
g_1 = Segment(A', A)
h_1 = Segment(B, B_h)
i_1 = Segment(B_h, B'')
j_1 = Segment(B'', B')
k_1 = Segment(B', B)
l_1 = Segment(C', C'')
m_1 = Segment(C'', C_h)
n_1 = Segment(C_h, C)
p_1 = Segment(C, C')
Vieleck2, d_2, a_2, b_2 = Polygon(A, B, D)
Vieleck3, d_3, b_3, c_2 = Polygon(B, C, D)
Vieleck4, d_4, c_3, a_3 = Polygon(C, A, D)
Vieleck5, d', a', b' = Polygon(A', B', D')
Vieleck6, d'_1, b'_1, c' = Polygon(B', C', D')
Vieleck7, d'_2, c'_1, a'_1 = Polygon(C', A', D')
Vieleck8, d'', a'', b'' = Polygon(A'', B'', D''_1)
Vieleck9, d''_1, b''_1, c'' = Polygon(B'', C'', D''_1)
Vieleck10, d''_2, c''_1, a''_1 = Polygon(C'', A'', D''_1)
E = Point(h)
O = (0, 0)
q_1 = Segment(O, E)
F = (6.5, -5.5)
r_1 = OrthogonalLine(F, yAxis)
u = Vector(A, F)
A_s = Translate(A, u)
B'_2 = Translate(B, u)
C'_2 = Translate(C, u)
Vieleck1', c'_2, a'_2, b'_2 = Polygon(A_s, B'_2, C'_2)
D'_2 = Translate(D, u)
s_1 = OrthogonalLine(B'_2, r_1)
t_1 = OrthogonalLine(D'_2, r_1)
e_2 = OrthogonalLine(C'_2, r_1)
G = Intersect(e_2, r_1)
H = Intersect(t_1, r_1)
I = Intersect(s_1, r_1)
J = Midpoint(C'_2, G)
K = Midpoint(D'_2, H)
L = Midpoint(B'_2, I)
C_s = Rotate(J, 315.0*°, G)
K' = Rotate(K, 315.0*°, H)
B_s = Rotate(L, 315.0*°, I)
Vieleck11, f_2, l_2, j_2 = Polygon(L, J, F)
Vieleck12, j', f_3, l' = Polygon(F, B_s, C_s)
N = Intersect(c_1, d')
v = Vector(N, K')
g_2 = Segment(D', N)
D_s = Translate(D', v)
N' = Translate(N, v)
h_2 = Segment(D_s, N')
i_2 = Segment(C'_2, G)
k_2 = Segment(D'_2, H)
m_2 = Segment(B'_2, I)
o = false
w = false
z = false
o_1 = false
n_2 = Segment(B_s, I)
p_2 = Segment(N', H)
q_2 = Segment(C_s, G)
Vieleck13, d_s, f_4, b_s = Polygon(F, B_s, D_s)
Vieleck14, d_5, b_4, c_s = Polygon(B_s, C_s, D_s)
Vieleck15, f_5, c_4, d_6 = Polygon(C_s, D_s, F)
u_1 = false
v_1 = false
Text1: "Grundfläche= " + Vieleck1
Text2: "Höhe = " + g_2