Basílica del Santo Spirito. Planta.

Basílica del Santo Spirito. Florencia. Siglo XV
Proyectada por Brunelleschi es de estilo renacentista. La planta es de cruz latina. El diseño toma como base el cuadrado.

Pulsa el botón Play para iniciar una secuencia de animación que muestra elementos geométricos de la composición de la obra:

(1) Dibujamos el círculo y el cuadrado del crucero. Este cuadrado será la unidad de medida para toda la construcción.
(2) Rotaciones de los cuatro vértices dan lugar al inicio de la nave principal, la cabecera y los dos brazos de la cruz: el trasepto.
(3) La nave central está formada por cuatro cuadrados. La altura de esta nave es el doble del lado del cuadrado.
(4) Las naves laterales que rodean a la cruz se construyen con cuadrados de lado la mitad del anterior.
(5) Las capillas tienen forma semicircular que se adosa al lado exterior de los cuadrados de las naves laterales.


En esta dirección http://jmora7.com/Arte/arte.htm se encuentra una colección de cuadros analizados siguiendo esta forma de trabajar.

o = 1.995 (slider from 1.9 to 2.1, step 0.001)
d = 10.8 (slider from 1 to 15, step 0.01)
a = 28 (slider from -1 to 28, step 0.001)
a7 = Max(0, Min[1, a - 7])
c = 14 (slider from 0 to 20, step 0.01)
a1 = Max(0, Min[1, a - 1])
a3 = Max(0, Min[1, a - 3])
a16 = Max(0, Min[1, a - 16])
a17 = Max(0, Min[1, a - 17])
a2 = Max(0, Min[1, a - 2])
a4 = Max(0, Min[1, a - 4])
a8 = Max(0, Min[1, a - 8])
a9 = Max(0, Min[1, a - 9])
a11 = Max(0, Min[1, a - 11])
a12 = Max(0, Min[1, a - 12])
a15 = Max(0, Min[1, a - 15])
a18 = Max(0, Min[1, a - 18])
a19 = Max(0, Min[1, a - 19])
a5 = Max(0, Min[1, a - 5])
a10 = Max(0, Min[1, a - 10])
a13 = Max(0, Min[1, a - 13])
a14 = Max(0, Min[1, a - 14])
a55: (a5 * π / 2)
b = 16.15 (slider from 0.5 to 20, step 0.01)
a6 = Max(0, Min[1, a - 6])
a71 = Max(0, Min[0.32, a - 7.4])
DA = (-6.269090909090905, -6.76)
DB: DA + (b, 0)
rr: 1.618
A1 = (3.850909090909083, -2.18)
A2: A1 + (o, 0)
A3: A1 + (o, o)
A4: A1 + (0, o)
B1: A1 + (a2 * (A2 - A1))
B2: A2 + (a2 * (A3 - A2))
B3: A3 + (a2 * (A4 - A3))
B4: A4 + (a2 * (A1 - A4))
C1 = Segment(A1, B1)
C2 = Segment(A2, B2)
C3 = Segment(A3, B3)
C4 = Segment(A4, B4)
p1, f, g, h, i, A, B = Polygon(A1, A2, 4)
p2 = Rotate(p1, (a3 * π / 2), A1)
p3 = Rotate(p1, (a4 * π / 2), A2)
p4 = Rotate(p1, (a5 * π / 2), A3)
p5 = Rotate(p1, (a6 * π / 2), A4)
u = Vector(A1, A2)
v = Vector(A1, A4)
A5: A1 - v
A6: A2 - v
A7: A2 + u
A8: A3 + u
A9: A3 + v
A10: A4 + v
A11: A4 - u
A12: A1 - u
A13: A11 - u
A14: A12 - u
A16: A14 - u
A15: A13 - u
A17: A15 - u
A18: A16 - u
p6 = Rotate(p2, (a7 * π / 2), A12)
p7 = Rotate(p6, (a8 * π / 2), A14)
p8 = Rotate(p7, (a9 * π / 2), A16)
C = Midpoint(A17, A18)
q1, j, k, l, m, D2, D3 = Polygon(C, A17, 4)
q1' = Mirror(q1, m)
n = Line(A16, A7)
p = Line(A18, A17)
q = Line(A16, A15)
r = Line(A14, A13)
q1'' = Mirror(q1', n)
s = LineBisector(A16, A18)
t = LineBisector(A14, A16)
e = LineBisector(A12, A14)
f_1 = LineBisector(A1, A12)
g_1 = Line(A11, A12)
h_1 = Line(A4, A5)
i_1 = LineBisector(A6, A5)
j_1 = Line(A9, A6)
k_1 = LineBisector(A6, A2)
l_1 = LineBisector(A7, A8)
m_1 = Line(A8, A11)
n_1 = LineBisector(A8, A3)
p_1 = LineBisector(A3, A9)
q_1 = Line(A7, A8)
q1''' = Mirror(q1'', p)
c1 = Mirror(q1''', s)
c1' = Mirror(c1, q)
c1'' = Mirror(c1', t)
c1''' = Mirror(c1'', r)
c2 = Mirror(c1''', e)
c2' = Mirror(c2, g_1)
c2'' = Mirror(c2', f_1)
c2''' = Mirror(c2'', k_1)
r_1 = Line(A5, A6)
s_1 = Line(A10, A9)
c3 = Mirror(c2''', r_1)
c3' = Mirror(c3, h_1)
c3'' = Mirror(c3', i_1)
c3''' = Mirror(c3'', j_1)
c4 = Mirror(c3''', r_1)
c4' = Mirror(c4, k_1)
c4'' = Mirror(c4', n_1)
c4''' = Mirror(c4'', q_1)
c5 = Mirror(c4''', n)
c5' = Mirror(c5, l_1)
c5'' = Mirror(c5', m_1)
c5''' = Mirror(c5'', q_1)
c6 = Mirror(c5''', n_1)
c6' = Mirror(c6, p_1)
c6'' = Mirror(c6', s_1)
c6''' = Mirror(c6'', j_1)
c7 = Mirror(c6''', i_1)
c7' = Mirror(c7, h_1)
c7'' = Mirror(c7', s_1)
c7''' = Mirror(c7'', p_1)
c8 = Mirror(c7''', f_1)
c8' = Mirror(c8, g_1)
c8'' = Mirror(c8', e)
c8''' = Mirror(c8'', r)
c9 = Mirror(c8''', t)
c9' = Mirror(c9, q)
c9'' = Mirror(c9', s)
c9''' = Mirror(c9'', p)
t_1 = Line(D2, D3)
a_1 = Mirror(p_1, s_1)
b_1 = Mirror(k_1, r_1)
c_1 = Mirror(n_1, q_1)
D4 = Intersect(n, t_1)
D5 = Intersect(t_1, k_1)
D6 = Intersect(k_1, p)
D7 = Intersect(s, k_1)
D8 = Intersect(q, k_1)
D9 = Intersect(k_1, t)
D10 = Intersect(r, k_1)
D11 = Intersect(e, k_1)
D12 = Intersect(k_1, g_1)
D13 = Intersect(f_1, k_1)
D14 = Intersect(r_1, f_1)
D15 = Intersect(b_1, f_1)
D16 = Intersect(h_1, b_1)
D17 = Intersect(i_1, b_1)
D18 = Intersect(j_1, b_1)
D19 = Intersect(b_1, n_1)
D20 = Intersect(n_1, r_1)
D21 = Intersect(k_1, n_1)
D1 = Intersect(p_1, t_1)
Z = Intersect(m_1, t_1)
D22 = Intersect(k_1, q_1)
D24 = Intersect(n, c_1)
D25 = Intersect(c_1, l_1)
D26 = Intersect(m_1, c_1)
D27 = Intersect(p_1, c_1)
D23 = Intersect(k_1, c_1)
E1 = Semicircle(D2, D1)
E2 = Semicircle(D3, D2)
E3 = Semicircle(D4, D3)
E4 = Semicircle(D5, D4)
E5 = Semicircle(D6, D5)
E6 = Semicircle(D7, D6)
E7 = Semicircle(D8, D7)
E8 = Semicircle(D9, D8)
E9 = Semicircle(D10, D9)
E10 = Semicircle(D11, D10)
E11 = Semicircle(D12, D11)
E12 = Semicircle(D13, D12)
E13 = Semicircle(D14, D13)
E14 = Semicircle(D15, D14)
E15 = Semicircle(D16, D15)
E16 = Semicircle(D17, D16)
E17 = Semicircle(D18, D17)
E18 = Semicircle(D19, D18)
E19 = Semicircle(D20, D19)
E20 = Semicircle(D21, D20)
E21 = Semicircle(D22, D21)
E22 = Semicircle(D23, D22)
E23 = Semicircle(D24, D23)
E24 = Semicircle(D25, D24)
E25 = Semicircle(D26, D25)
E26 = Semicircle(D27, D26)
E27 = Semicircle(D28, D27)
G5 = Mirror(D5, l_1)
G6 = Mirror(D6, l_1)
G7 = Mirror(D7, l_1)
G8 = Mirror(D8, l_1)
G9 = Mirror(D9, l_1)
G10 = Mirror(D10, l_1)
G11 = Mirror(D11, l_1)
G12 = Mirror(D12, l_1)
G13 = Mirror(D13, l_1)
G14 = Mirror(D14, l_1)
G15 = Mirror(D15, l_1)
G16 = Mirror(D16, l_1)
G17 = Mirror(D17, l_1)
G18 = Mirror(D18, l_1)
G19 = Mirror(D19, l_1)
G20 = Mirror(D20, l_1)
G21 = Mirror(D21, l_1)
G22 = Mirror(D22, l_1)
G23 = Mirror(D23, l_1)
G24 = Mirror(D24, l_1)
G25 = Mirror(D25, l_1)
H5 = Semicircle(G5, G6)
H6 = Semicircle(G6, G7)
H7 = Semicircle(G7, G8)
H8 = Semicircle(G8, G9)
H9 = Semicircle(G9, G10)
H10 = Semicircle(G10, G11)
H11 = Semicircle(G11, G12)
H12 = Semicircle(G12, G13)
H13 = Semicircle(G13, G14)
H14 = Semicircle(G14, G15)
H15 = Semicircle(G15, G16)
H16 = Semicircle(G16, G17)
H17 = Semicircle(G17, G18)
H18 = Semicircle(G18, G19)
H19 = Semicircle(G19, G20)
H20 = Semicircle(G20, G21)
H21 = Semicircle(G21, G22)
H22 = Semicircle(G22, G23)
D = Intersect(i_1, l_1)
d_1 = Circle(D, o / 2 - 0.1)
c_2 = Circle(D, o / 6)
F1: 20
F2: 20.1
F3 = 20.200000000000003
F4 = 20.300000000000004
F5 = 20.400000000000006
F6 = 20.500000000000007
F7 = 20.60000000000001
F8 = 20.70000000000001
F9 = 20.80000000000001
F10 = 20.900000000000013
F11 = 21.000000000000014
F12 = 21.100000000000016
F13 = 21.200000000000017
F14 = 21.30000000000002
F15 = 21.40000000000002
F16 = 21.50000000000002
F17 = 21.600000000000023
F18 = 21.700000000000024
F19 = 21.800000000000026
F20 = 21.900000000000027
F21 = 22.00000000000003
F22 = 22.10000000000003
F23 = 22.20000000000003
F24 = 22.300000000000033
F25 = 22.400000000000034
F26 = 22.500000000000036
I22: 22.6
I21: 22.7
I20 = 22.799999999999997
I19 = 22.899999999999995
I18 = 22.999999999999993
I17 = 23.09999999999999
I5 = 24.299999999999965
I6 = 24.199999999999967
I7 = 24.09999999999997
I8 = 23.99999999999997
I9 = 23.899999999999974
I10 = 23.799999999999976
I11 = 23.699999999999978
I12 = 23.59999999999998
I13 = 23.499999999999982
I14 = 23.399999999999984
I15 = 23.299999999999986
I16 = 23.19999999999999
E = Intersect(d_1, i_1, 1)
F = Intersect(c_2, i_1, 1)
EE = Rotate(E, ((a1 * 2) * π) - 0.01, D)
e_1 = CircleArc(D, E, EE)
FF = Rotate(F, (((-a1) * 2) * π) + 0.01, D)
d_2 = CircleArc(D, FF, F)