正四角錐的兩面角
Author: 藍邦偉  老師

x

y

z

顯示xy平面

顯示單位向量

α

β

兩相鄰三角形所在平面的夾角

顯示座標軸

三角形與正方形所在平面之夾角

Reset

k = 9 (slider from 6 to 10, step 0.1)
O = (0.45394435695758734, -3.5883394470490493)
A: (x((Corner[3] + 39 * Corner[4]) / 40), y((Corner[1] + 9 * Corner[4]) / 10))
B: (x((4 * Corner[3] + 16 * Corner[4]) / 20), y((Corner[1] + 9 * Corner[4]) / 10))
D: (3 * B + A) / 4
C: (3 * A + B) / 4
a = Segment(A, B)
E = Point(a)
E' = Rotate(Translate[E, Vector[C, D]], 90*°, D)
c = Circle(C, E)
c' = Translate(c, Vector[C, D])
G = Point(c')
c'' = Rotate(c', 270*°, C)
F = Point(c'')
A' = Rotate(A, 270*°, C)
B' = Rotate(B, 270*°, C)
a' = Segment(A', B')
D' = Rotate(D, 270*°, C)
b = Segment(D', F)
E'' = Rotate(E', 270*°, C)
α = Angle(E'', D', F)
d = Segment(D, G)
β = Angle(G, D, E')
I: C + (b * cos(α), b * sin(α) * sin(β))
I' = Translate(I, Vector[C, O])
u = Vector(O, I')
J: C + (b * cos(α + 90°), b * sin(α + 90°) * sin(β))
K: C + (0, b * cos(β))
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
J' = Translate(J, Vector[C, O])
K' = Translate(K, Vector[C, O])
L = 10 (slider from 1 to 10, step 1)
I'' = Dilate(I', L, O)
J'' = Dilate(J', L, O)
K'' = Dilate(K', L, O)
I''' = Dilate(I'', -1, O)
J''' = Dilate(J'', -1, O)
K''' = Dilate(K'', -1, O)
u' = Vector(I''', I'')
v' = Vector(J''', J'')
w' = Vector(K''', K'')
h = Segment(D', E'')
i = Segment(D, E')
軌跡1 = Locus(I, F)
L_{axis}: L
j = false
w = Vector(O, K')
v = Vector(O, J')
k_1 = false
list1 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), t, -L, L], s, -L, L, 1)
list2 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), s, -L, L], t, -L, L, 1)
A_2: O + k * v
A_3: O - k * u
A_4: O - k * v
A_5: O + k * w
A_1: O + k * u
M = Midpoint(A_5, A_2)
多邊形1, a_3, a_2, m_1 = Polygon(A_1, M, A_3)
N = Midpoint(A_1, A_2)
多邊形2, n_1, a_5, o_1 = Polygon(A_5, O, N)
γ = Angle(A_1, M, A_3)
δ = Angle(A_5, N, O)
o = false
l = false
z = false
s, b_1 = SDLine(A_5, A_1, A_4, A_2)
a_1, c_1 = SDLine(A_5, A_2, A_1, A_3)
t, d_1 = SDLine(A_5, A_3, A_2, A_4)
r, e_1 = SDLine(A_5, A_4, A_3, A_1)
n, f_1 = SDLine(A_1, A_2, A_4, A_5)
m, g_1 = SDLine(A_4, A_1, A_3, A_5)
p, q = SDLine(A_2, A_3, A_1, A_5)
h_1, i_1 = SDLine(A_4, A_3, A_5, A_1)

Tool: SDLine
Input: A, B, C, D
Output: g, h

b: sgn(sin(Angle[D, B, A]))
a: sgn(sin(Angle[A, B, C]))
c: sgn(a + b + 0.5)
d: sqrt(c)
e: sqrt(-c)
E = Midpoint(A, B)
A' = Dilate(A, d, E)
B' = Dilate(B, d, E)
g = Segment(A', B')
A'_1 = Dilate(A, e, E)
B'_1 = Dilate(B, e, E)
h = Segment(A'_1, B'_1)