Author: Daniel Mentrard

X

Y

Z

Repere

Ver desarrollos

Plegar - Desplegar

U = (1, 0)
O_r = (0, 0)
vue1 = Ellipse(O_r - (0.95, 0.0), O_r + (0.95, 0.0), 1.0)
A = Point(vue1)
vue2 = Ellipse(O_r - (0.0, 0.95), O_r + (0.0, 0.95), 1.0)
B = Point(vue2)
O_0 = (13.57294957101407, -9.259937654637621)
M = (0, 1)
Zoom = 3.2 (slider from 1 to 5, step 0.1)
E = POINT3d(A, B, M, O_0, O_r, -4.0, 0.12121212121212122, 1.0, U, Zoom)
P = POINT3d(A, B, M, O_0, O_r, -4.0, 3.0, -1.0, U, Zoom)
W = POINT3d(A, B, M, O_0, O_r, 1.0, 3.0, -1.0, U, Zoom)
l1 = Line(W, P)
C = POINT3d(A, B, M, O_0, O_r, -4.166666666666667, 4.0, -1.0, U, Zoom)
D = POINT3d(A, B, M, O_0, O_r, 1.0, 0.12121212121212122, -1.0, U, Zoom)
f1 = Line(D, C)
S = Intersect(f1, l1)
V1 = POINT3d(A, B, M, O_0, O_r, 1.0, 1.0, -1.0, U, Zoom)
V6 = POINT3d(A, B, M, O_0, O_r, -4.0, 1.0, -1.0, U, Zoom)
cubA5 = Segment(V1, V6)
K = Intersect(f1, cubA5)
t = 0 (slider from 0 to 2, step 0.01)
R1b = POINT3d(A, B, M, O_0, O_r, -4.0, 0.0, -1.0, U, Zoom)
R1a = POINT3d(A, B, M, O_0, O_r, 1.0, 0.0, -1.0, U, Zoom)
VUE1, VUE2, VUE3_1, VUE3 = Intersect(vue1, vue2)
θ = Angle(M, O_r, B)
BoutonPas = 0.01
φ = Angle(U, O_r, A)
xx: Zoom * sin(φ)
xy: Zoom * (-cos(φ) * sin(θ))
xz = 0
yx: Zoom * cos(φ)
yy: Zoom * sin(φ) * sin(θ)
yz: Zoom * cos(θ)
u = Vector(O_r, O_0)
Xr: (xx, xy)
Yr: (yx, yy)
Zr: (0.0, yz)
X0 = Translate(Xr, u)
Z0 = Translate(Zr, u)
Y0 = Translate(Yr, u)
v = Vector(O_0, Z0)
w = Vector(O_0, Y0)
z = Vector(O_0, X0)
c = Circle(O_0, Zoom)
a = Line(O_0, Y0)
b = Line(O_0, yAxis)
g = Line(O_0, X0)
j = Line(Z0, O_0)
P1x = 0
P1y = 1
P1z = 1.618033988749895
P1r: (P1x * xx + P1y * yx, P1x * xy + P1y * yy + P1z * yz)
P1 = Translate(P1r, u)
BoutonA = Rotate(A, BoutonPas, O_r)
BoutonB = Rotate(B, BoutonPas, O_r)
BoutonXA: x(BoutonA)
BoutonYA: y(BoutonA)
BoutonXB: x(BoutonB)
BoutonYB: y(BoutonB)
BoutonXAinit = -0.26216
BoutonYAinit = -0.30133
BoutonXBinit = -0.21262
BoutonYBinit = 0.73235
k = Segment(VUE3_1, VUE2)
l = Segment((-1.0, 0.0), U)
m = Segment((0.0, -1.0), M)
V4 = POINT3d(A, B, M, O_0, O_r, 1.0, -1.0, -1.0, U, Zoom)
V8 = POINT3d(A, B, M, O_0, O_r, -4.0, -1.0, -1.0, U, Zoom)
cub4M = Midpoint(V1, V6)
cub4Ang = Angle(V4, cub4M, V8)
cubA4' = Segment(V4, V1)
cubA5' = Segment(V1, V6)
cubA6' = Segment(V8, V6)
cubA7' = Segment(V4, V8)
cubA4 = Segment(V4, V1)
cubA6 = Segment(V6, V8)
cubA7 = Segment(V8, V4)
cubV1d = If(cub4Ang < 180.0°, V1, V4)
cubV6c = If(cub4Ang < 180.0°, V6, V8)
cub4, cub4v8, cub4v4, cub4v1, cub4v6 = Polygon(V8, V4, cubV1d, cubV6c)
fi = 1.618033988749895
repere = false
V2b = POINT3d(A, B, M, O_0, O_r, 1.0, 1.0 + t, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V3c = POINT3d(A, B, M, O_0, O_r, 1.0, -1.0 - t, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V3d = POINT3d(A, B, M, O_0, O_r, 1.0 + t, -1.0, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V2d = POINT3d(A, B, M, O_0, O_r, 1.0 + t, 1.0, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
poly2, v4, v3d_1, v2d_1, v1 = Polygon(V4, V3d, V2d, V1)
poly6, v1_2, v4_2, v8_2, v6_2 = Polygon(V1, V4, V8, V6)
V3f = POINT3d(A, B, M, O_0, O_r, 1.0, 3.0 * t - 1.0, sqrt(8.0 * t - 4.0 * t^(2.0)) + sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V7c = POINT3d(A, B, M, O_0, O_r, -4.0, -1.0 - t, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V5b = POINT3d(A, B, M, O_0, O_r, -4.0, 1.0 + t, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V7a = POINT3d(A, B, M, O_0, O_r, -4.0 - t, -1.0, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V5a = POINT3d(A, B, M, O_0, O_r, -4.0 - t, 1.0, sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
V7f = POINT3d(A, B, M, O_0, O_r, -4.0, 3.0 * t - 1.0, sqrt(8.0 * t - 4.0 * t^(2.0)) + sqrt(4.0 - t^(2.0)) - 1.0, U, Zoom)
v6g = POINT3d(A, B, M, O_0, O_r, -sqrt(4.0 - (t - 2.0)^(2.0)) - 4.0, 1.0 + t, t + sqrt(4.0 - t^(2.0)) - 3.0, U, Zoom)
poly1, v4_1, v3c, v7c, v8 = Polygon(V4, V3c, V7c, V8)
poly4, v8_1, v7a, v5a, v6 = Polygon(V8, V7a, V5a, V6)
poly5, v6_1, v5b, v2b, v1_1 = Polygon(V6, V5b, V2b, V1)
poly7, v5b_1, v7f, v3f, v2b_1 = Polygon(V5b, V7f, V3f, V2b)
r1b = Segment(R1a, R1b)
f = Segment(V2b, V6)
h = Segment(V1, V5b)
I = Midpoint(f)
Z = Intersect(v5b, v2b_1)
A1 = Intersect(v5b, v2b_1)
B1 = Intersect(v5b, v2b_1)
G = POINT3d(A, B, M, O_0, O_r, -4.0, 1.0 + t + 29.0 * (t - 1.0) / 33.0, sqrt(4.0 - t^(2.0)) - 1.0 + 29.0 * sqrt(2.0 * t - t^(2.0)) / 33.0, U, Zoom)
a1 = Segment(D, K)
d = Segment(V7f, V5b)
H = (4.863247105613295, 0.6615224141397282)

Tool: POINT3d
clic en A, B, M, O,
Input: A, B, M, O, O_r, P1_x, P1_y, P1_z, U, escala
Output: P1

c = Circle(O_r, 1.0)
d = Circle(O_r, 0.5)
θ = Angle(M, O_r, B)
φ = Angle(U, O_r, A)
y_z: escala * cos(θ)
u = Vector(O_r, O)
x_x: escala * sin(φ)
x_y: escala * (-cos(φ) * sin(θ))
y_x: escala * cos(φ)
y_y: escala * sin(φ) * sin(θ)
P1_r: (P1_x * x_x + P1_y * y_x, P1_x * x_y + P1_y * y_y + P1_z * y_z)
P1 = Translate(P1_r, u)