► Grenzen:

$\scalebox{1.4} \text{\copyright Roman Chijner, Heidelberg 2011}$   
$\scalebox{1.3} \text{     Gestaltungshilfe: Werner Knobloch}$

► 3D-Kachelfläche:

Aufbau

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Einfarbig

Texte ausblenden

x_{min}

x_{max}

↹

↹

▽

$\scalebox{1.4} {Rotationsvolumen}$
$\scalebox{1.0}\text{ {    (Kachelflächen)} }$

f_y(u,v) = r_Y \cdot f(v) \;sin(u)

f_x(u,v) = r_X \cdot v

f_z(u,v) = r_Z \cdot f(v)\;cos(u)

► Skalierung:

a = 0.28 (slider from -5 to 5, step 0.1)
b = 0.33 (slider from -5 to 5, step 0.02)
c = 0.8 (slider from -5 to 15, step 0.1)
f0(x) = (((a * ℯ^(((-b) * x))) * cos(x)) * x) + c
Na = 10 (slider from 10 to 100, step 5)
x_{max} = 7 (slider from -15 to 20, step 0.1)
x_{min} = -8 (slider from -8 to 5, step 0.1)
f = Function((((a * ℯ^(((-b) * x))) * cos(x)) * x) + c, x_{min}, x_{max})
dy: (x_{max} - x_{min}) / Na
u_{max} = 6.28 (slider from -5 to 16, step 0.1)
u_{min} = 0 (slider from -5 to 5, step 0.1)
dx: (u_{max} - u_{min}) / Na
l1a = Sequence(Sequence[(u_{min} + (i * dx), x_{min} + (j * dy)), i, 0, Na], j, 0, Na)
uv = Join(l1a)
v: y(uv)
u: x(uv)
Y1: (f(v) * sin(u))
X1: v
Z1: (f(v) * cos(u))
r_X = 1 (slider from -5 to 5, step 0.1)
r_Y = 1 (slider from -5 to 5, step 0.1)
r_Z = 1 (slider from -5 to 5, step 0.1)
yylP = Sequence(If[i ≟ (Div[i, Na + 1] * (Na + 1)), {Polygon[(0, 0, 0), (0, 0, 0), (0, 0, 0)]}, {Polygon[((r_X * Element[X1, i]), (r_Y * Element[Y1, i]), (r_Z * Element[Z1, i])), ((r_X * Element[X1, i + Na + 1]), (r_Y * Element[Y1, i + Na + 1]), (r_Z * Element[Z1, i + Na + 1])), ((r_X * Element[X1, i + Na + 2]), (r_Y * Element[Y1, i + Na + 2]), (r_Z * Element[Z1, i + Na + 2]))], Polygon[((r_X * Element[X1, i]), (r_Y * Element[Y1, i]), (r_Z * Element[Z1, i])), ((r_X * Element[X1, i + Na + 2]), (r_Y * Element[Y1, i + Na + 2]), (r_Z * Element[Z1, i + Na + 2])), ((r_X * Element[X1, i + 1]), (r_Y * Element[Y1, i + 1]), (r_Z * Element[Z1, i + 1]))]}], i, 1, ((Na + 1) * Na))
zk3: (Na * (Na + 1))
dN = 50 (slider from 5 to 100, step 1)
ce: ceil(zk3 / dN)
Deckkraft = 1 (slider from 0 to 1, step 0.1)
e_1 = false
f1 = false
fy(u, v) = (f0(v) * sin(u))
fx(u, v) = v + (0 * u)
fz(u, v) = (f0(v) * cos(u))
f3 = Surface((fx(u, v) * r_X), (fy(u, v) * r_Y), (fz(u, v) * r_Z), u, u_{min}, u_{max}, v, x_{min}, x_{max})
f_1 = Mirror(f, xAxis)
c_1 = 0
c_2 = 0
P1: (x_{min}, 0)
P2: (x_{max}, 0)
e = Segment(P1, P2)
A = Point(e)
B: (x(A), f(x(A)))
B' = Mirror(B, e)
P01: (x(A), 0, y(B))
k = Circle(xAxis, P01)
j1: (π * NIntegral[f0(x)^(2), x_{min}, x_{max}])
d = Segment(B, B')
P02: (x(A), 0, 0)
c_3 = 0
c_4 = 0
c_5 = 0
i = IntegralBetween(f0, (-f0(x)), x_{min}, x_{max}, true)
c_6 = 0
c_7 = 0
jh = false
text5: "$\scalebox{0.9}\text{Volumen des Rotationskörpers der}$
$\scalebox{0.9}\text{Funktion f(x) bei Rotation um die x-Achse$
$f(x)=" + (LaTeX[f]) + "$"
text6: "Fläche: " + Na + " x (" + Na + "+1) = " + ((Na * (Na + 1))) + " Vierecke "
text2: "V= π\cdot\int_{x_{min} }^{x_{max} }f(x)^2 \cdot dx=" + (LaTeX[j1]) + " \;FE"
x1maxa = Max(X1)
x1mina = Min(X1)
x2maxa = Max(Y1)
x2mina = Min(Y1)
x3maxa = Max(Z1)
x3mina = Min(Z1)
yylPa = Sequence(If[i ≟ (Div[i, Na + 1] * (Na + 1)), {Polygon[(0, 0, 0), (0, 0, 0), (0, 0, 0)]}, {Polygon[((r_X * Element[X1, i]), (r_Y * Element[Y1, i]), (r_Z * Element[Z1, i])), ((r_X * Element[X1, i + Na + 1]), (r_Y * Element[Y1, i + Na + 1]), (r_Z * Element[Z1, i + Na + 1])), ((r_X * Element[X1, i + Na + 2]), (r_Y * Element[Y1, i + Na + 2]), (r_Z * Element[Z1, i + Na + 2]))], Polygon[((r_X * Element[X1, i]), (r_Y * Element[Y1, i]), (r_Z * Element[Z1, i])), ((r_X * Element[X1, i + Na + 2]), (r_Y * Element[Y1, i + Na + 2]), (r_Z * Element[Z1, i + Na + 2])), ((r_X * Element[X1, i + 1]), (r_Y * Element[Y1, i + 1]), (r_Z * Element[Z1, i + 1]))]}], i, 1, ((Na + 1) * Na))