Author: Roman Chijner, Heidelberg
Date: 2012

komplementäre Ansicht

Punkte-Netz

hin/her

punktweise

Färbung:listenweise / punktweise

Regler/Maus

Move me

a/b

a

b

Frontfläche (aktuell)

Startpunkt

Auflösung (≤ 500)

Rot

Grün

Blau

Startpunkt

γ-Animation

\scalebox{1.0}{ R_x}

► Winkellage:

Bildschirmsteuerung (Grafikhintergrund)

β-Animation

α-Animation

x

y

z

Koordinaten-Box

Achsen

1

2

3

"Move me"

Opacity

\left|\begin{array}  \  \ \ \\\\\\\\\\\\\\\\\\\\\\end{array}\right.

Panel Steuerung

A1

A4

A2

A3

B4

B3

Fläche: z = (z_{min}+z_{max})/2

Grundfläche(Start)

Animation (t)

II←

R

L

Frontfläche (Start)

orthogonale -Projektion

Fläche: z = a_z

refresh

►

◄

:

$min:$
 
$max:$
 
$scaling:$

Farbwahl:

x_{min}= :

y_{min}= :

z_{min}= :

x_{max}= :

y_{max}= :

z_{max}= :

v_t = :

Δt = :

N_P = :

Zoom

.                                                            .





























.

Zoom

II←

II←

\scalebox{1.0}{ R_y}

\scalebox{1.0}{ R_z}

$\scalebox{1.4} \text{ \copyright Roman Chijner, Heidelberg 2012}$   
$\scalebox{1.3} \text{      Gestaltungshilfe:}\scalebox{1.3}\text{ Werner Knobloch}$

t = :

refresh

 3D-Plotter für implizite  Funktionen 5a

II←

→II

delete

→

Auflösung(≤100) :

erzeugen:

Punktgröße 1-9 :

$\scalebox{0.8} \text{II. Spurplot }$

.                                                                               .





























.

.                                                                                                                                                .













.

a/b

2 Färbungen:

für hin her

hin

her

Animation

◄

►

II←

→II

:

Step:

f_{l,m,n,s}(x,y,z) = \fgcolor{red}{f_a(x,y,z)} + \fgcolor{#009f00}{f_b(x,y,z)} +\fgcolor{#0000ff}{f_c(x,y,z) = 0

►

◄

►

◄

◄

►

l =:

m =:

n =:

-1

+1

s=

L =:

$\fgcolor{red}{f_a(x,y,z)= cos(\frac{l* x* \pi }{L})* [cos(\frac{m* y* \pi}{L})*cos(\frac{n* x* \pi}{L})+s* cos(\frac{n* y *\pi}{L})*cos(\frac{m* x* \pi}{L})]}$
$\fgcolor{009f00}{f_b(x,y,z)= cos(\frac{m* x* \pi }{L})* [cos(\frac{n* y* \pi}{L})*cos(\frac{l* x* \pi}{L})+s*cos(\frac{l* y *\pi}{L})*cos(\frac{n* x* \pi}{L})]}$
$$\fgcolor{blue}{f_c(x,y,z)= cos(\frac{n* x* \pi }{L})* [cos(\frac{l* y* \pi}{L})*cos(\frac{m* x* \pi}{L})+s* cos(\frac{m* y *\pi}{L})*cos(\frac{l* x* \pi}{L})]}$

3D-stehende Wellen

s = 1 (slider from -1 to 1, step 2)
L = 20 (slider from 0 to 40, step 1)
n = 3 (slider from 0 to 10, step 1)
m = 1 (slider from 0 to 10, step 1)
l = 4 (slider from 0 to 10, step 1)
arichtung = true
d_1 = 31 (slider from 0 to Nn + 1, step dstep)
Nn = 30 (slider from 0 to 100, step 1)
t = -10 (slider from x_{min} to x_{max}, step Step)
x_{max} = 12 (slider from -40 to 40, step 0.1)
x_{min} = -10 (slider from -40 to 40, step 0.1)
xM: x_{min} + x_{max}
hh = true
PTyp = 12 (slider from 1 to 13, step 1)
v_{Animation} = 0.1 (slider from 0 to 2, step 0.02)
iz = false
N_P = 200 (slider from 0 to 500, step 10)
γ = 0 (slider from 0 to 6.283185307179586, step 0.1)
α = 0 (slider from 0 to 6.28318531, step 0.1)
Eckpunkt1 = Corner(1)
c = true
C = (14.402076089900197, -2.293237380779629)
c_{Move} = 12.566370614359172 (slider from -50 to 50, step 0.1)
Eckpunkt2 = Corner(2)
dEx: x(Eckpunkt2 - Eckpunkt1)
α1 = If(c, α, x(C - Eckpunkt1) / dEx * c_{Move})
α2 = Mod(α1, 6.283)
Eckpunkt3 = Corner(3)
dEy: y(Eckpunkt3 - Eckpunkt2)
β = 0 (slider from 0 to 6.283185307179586, step 0.1)
β1 = If(c, β, y(C - Eckpunkt2) / dEy * c_{Move})
β2 = Mod(β1, 6.283)
a13: cos(α1) * sin(β1) * cos(γ) + sin(α1) * sin(γ)
a12: cos(α1) * sin(β1) * sin(γ) - sin(α1) * cos(γ)
a11: cos(α1) * cos(β1)
z_{max} = 10 (slider from -40 to 40, step 0.1)
z_{min} = -10 (slider from -40 to 40, step 0.1)
zWZ1: {1, 1, 1, 1} * (z_{min} + z_{max}) / 2
y_{max} = 10 (slider from -40 to 40, step 0.1)
y_{min} = -10 (slider from -40 to 40, step 0.1)
zWY1: {y_{min}, y_{max}, y_{max}, y_{min}}
zWX1: {x_{max}, x_{max}, x_{min}, x_{min}}
zWX1' = Sequence(a11 * Element[zWX1, i] + a12 * Element[zWY1, i] + a13 * Element[zWZ1, i], i, 1, 4)
zWW_0: y(Sort[{(Element[zWX1', 1], 1), (Element[zWX1', 2], 2), (Element[zWX1', 3], 3), (Element[zWX1', 4], 4)}])
zW_1 = Element(zWW_0, 4)
zW_2 = Element(zWW_0, 3)
dBB4 = If(zW_1 ≟ 2 ∧ zW_2 ≟ 3 ∨ zW_1 ≟ 3 ∧ zW_2 ≟ 2, true, false)
dBB3 = If(zW_1 ≟ 4 ∧ zW_2 ≟ 1 ∨ zW_1 ≟ 1 ∧ zW_2 ≟ 4, true, false)
ddd1 = If(dBB3 ∨ dBB4, true, false)
r_x = 1 (slider from 0 to 5, step 0.1)
r_z = 1 (slider from -5 to 5, step 0.1)
r_y = 1 (slider from 0 to 5, step 0.1)
h = false
listenweise: "listenweise " + (If[h, aText, bText]) + ""
p = false
a_z = -2.7 (slider from z_{min} to z_{max}, step 0.1)
B = (3.192444289327133, 2.353046472454224)
zl10x: {x_{max}, x_{max}, x_{min}, x_{min}, x_{min}, x_{min}, x_{max}, x_{max}, x_{max}, x_{max}, x_{min}, x_{min}, 1, 0, 0}
zl10y: {y_{min}, y_{max}, y_{max}, y_{min}, y_{min}, y_{max}, y_{max}, y_{min}, y_{min}, y_{max}, y_{max}, y_{min}, 0, 1, 0}
zl10z: {z_{min}, z_{min}, z_{min}, z_{min}, z_{max}, z_{max}, z_{max}, z_{max}, a_z, a_z, a_z, a_z, 0, 0, 1}
P11: ((-cos(α1) * cos(β1)) / sqrt(8) + sin(α1) * cos(β1), (-cos(α1) * cos(β1)) / sqrt(8) - sin(β1))
P13: ((-cos(α1) * sin(β1) * cos(γ) - sin(α1) * sin(γ)) / sqrt(8) + sin(α1) * sin(β1) * cos(γ) - cos(α1) * sin(γ), (-cos(α1) * sin(β1) * cos(γ) - sin(α1) * sin(γ)) / sqrt(8) + cos(β1) * cos(γ))
P12: ((-cos(α1) * sin(β1) * sin(γ) + sin(α1) * cos(γ)) / sqrt(8) + sin(α1) * sin(β1) * sin(γ) + cos(α1) * cos(γ), (-cos(α1) * sin(β1) * sin(γ) + sin(α1) * cos(γ)) / sqrt(8) + cos(β1) * sin(γ))
b = false
N_1 = If(b, N_P, 2)
z1 = Sequence(z_{min} + (z_{max} - z_{min}) / N_1 * i, i, 0, N_1)
y1 = Sequence(y_{min} + (y_{max} - y_{min}) / N_1 * i, i, 0, N_1)
x1 = Sequence(x_{min} + (x_{max} - x_{min}) / N_1 * i, i, 0, N_1)
g(x, y, z) = cos(l * x * π / L) * (cos(m * y * π / L) * cos(n * z * π / L) + s * cos(n * y * π / L) * cos(m * z * π / L)) + cos(m * x * π / L) * (cos(n * y * π / L) * cos(l * z * π / L) + s * cos(l * y * π / L) * cos(n * z * π / L)) + cos(n * x * π / L) * (cos(l * y * π / L) * cos(m * z * π / L) + s * cos(m * y * π / L) * cos(l * z * π / L))
tt = If(hh, t, xM - t)
dBB1 = If(zW_1 ≟ 1 ∧ zW_2 ≟ 2 ∨ zW_1 ≟ 2 ∧ zW_2 ≟ 1, true, false)
ddd2 = If(dBB1 ∨ dBB4, true, false)
za: x(Sequence[RemoveUndefined[{Roots[g(tt, Element[y1, i], x), z_{min}, z_{max}]}], i, 1, N_1 + 1])
Pa = Join(Sequence[Sequence[(Element[y1, i], Element[Element[za, i], j]), j, 1, Length[Element[za, i]]], i, 1, N_1 + 1])
xyz: x(Sequence[RemoveUndefined[{Roots[g(tt, x, Element[z1, i]), y_{min}, y_{max}]}], i, 1, N_1 + 1])
Pb = Join(Sequence[Sequence[(Element[Element[xyz, i], j], Element[z1, i]), j, 1, Length[Element[xyz, i]]], i, 1, N_1 + 1])
Pab = If(b, Sort[Join[{Pa, Pb}]], {(1000, 1000)})
lä = Length(Pab)
max = If(b ∧ (¬iz), lä, 2)
ym: y_{max} - y_{min}
xm: x_{max} - x_{min}
y_1 = -2
Y1_1 = 0
zW_3 = Element(zWW_0, 2)
dBB2 = If(zW_1 ≟ 3 ∧ zW_2 ≟ 4 ∨ zW_1 ≟ 4 ∧ zW_2 ≟ 3, true, false)
Maske = 0.344 (slider from 0 to 1, step 0.002)
Eck11: Eckpunkt1 + Maske * (Eckpunkt2 - Eckpunkt1)
Eck12: (x(Eckpunkt1 + Maske * (Eckpunkt2 - Eckpunkt1)), y(Eckpunkt3))
Vieleck2, eckpunkt1, eck11, eck12, a_1 = Polygon(Eckpunkt1, Eck11, Eck12, (x(Eckpunkt1), y(Eck12)))
r_B = 0.3 (slider from 0 to 1, step 0.1)
g_B = 1 (slider from 0 to 1, step 0.1)
b_B = 1 (slider from 0 to 1, step 0.1)
fx3 = true
fx2 = true
fx1 = true
d = false
Blau = 1 (slider from 0 to 1, step 0.1)
wγ = false
v_γ = 0.5 (slider from 0 to 2, step 0.1)
bs = true
wβ = false
wα = false
v_β = 0.4 (slider from 0 to 2, step 0.1)
v_α = 0.3 (slider from 0 to 2, step 0.1)
zl10: Sequence[P11 * Element[zl10x, i] * r_x + P12 * Element[zl10y, i] * r_y + P13 * Element[zl10z, i] * r_z, i, 1, 15] + B
Box: {{x_{max}, y_{min}, z_{min}}, {x_{max}, y_{max}, z_{min}}, {x_{min}, y_{max}, z_{min}}, {x_{min}, y_{min}, z_{min}}, {x_{min}, y_{min}, z_{max}}, {x_{min}, y_{max}, z_{max}}, {x_{max}, y_{max}, z_{max}}, {x_{max}, y_{min}, z_{max}}, {x_{max}, y_{min}, a_z}, {x_{max}, y_{max}, a_z}, {x_{min}, y_{max}, a_z}, {x_{min}, y_{min}, a_z}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1}}
BoxStr = Sequence(Segment[Element[zl10, i], Element[zl10, i + 1]], i, 1, 7)
BoxStr1: {Segment[Element[zl10, 1], Element[zl10, 8]], Segment[Element[zl10, 5], Element[zl10, 8]], Segment[Element[zl10, 2], Element[zl10, 7]], Segment[Element[zl10, 3], Element[zl10, 6]], Segment[Element[zl10, 1], Element[zl10, 4]]}
zVectx = Vector(Element[zl10, 4], Element[zl10, 1])
zVecty = Vector(Element[zl10, 4], Element[zl10, 3])
zVectz = Vector(Element[zl10, 4], Element[zl10, 5])
b_1 = true
k = false
PPxx: (Element[zl10, 1] + Element[zl10, 4]) / 2
PPzz: (Element[zl10, 5] + Element[zl10, 4]) / 2
PPyy: (Element[zl10, 3] + Element[zl10, 4]) / 2
Vieleck1, eck11_1, eckpunkt2, eckpunkt3, eck12_1 = Polygon(Eck11, Eckpunkt2, Eckpunkt3, Eck12)
zTT: Sequence[P11 * Element[zWX1, i] * r_x + P12 * Element[zWY1, i] * r_y + P13 * Element[zWZ1, i] * r_z, i, 1, 4] + B
zY1 = Element(zTT, zW_1)
zY2 = Element(zTT, zW_2)
zY3 = Element(zTT, zW_3)
zTTPoly = Polygon(zTT)
i = false
l_1 = 0 (slider from 0 to 1, step 0.02)
zlN11 = Element(zl10, zW_1)
zlN111 = Element(zl10, 9 - zW_1)
zlN22 = Element(zl10, zW_2)
zlN222 = Element(zl10, 9 - zW_2)
zlN33 = Element(zl10, zW_3)
zW_4 = Element(zWW_0, 1)
zlN44 = Element(zl10, zW_4)
Vgrund01 = Polygon({zlN11, zlN22, zlN222, zlN111})
Vgrund000 = Polygon(Sequence[Element[zl10, i], i, 1, 4])
o = false
q = false
Step = 0.002 (slider from 0 to 0.2, step 0.001)
a = false
P_R = Element(zl10, 7)
P_L = Element(zl10, 8)
Vvrd0 = Polygon({Element[zl10, 1], Element[zl10, 2], Element[zl10, 7], Element[zl10, 8]})
f = false
StrRL = Segment(P_R, P_L)
m_1 = false
zlPoly, n_1, r, s_1, c_1 = Polygon(Sequence[Element[zl10, i], i, 9, 12])
e_1 = false
mi = 2 (slider from 1 to 2000, step 1)
Tachse = 1.2 (slider from 0 to 15, step 0.1)
textpymaxmin: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[(y_{min} + y_{max}) / 2]) + "}"
textpxmaxmin: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[(x_{max} + x_{min}) / 2]) + "}"
textpzmaxmin: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[(z_{max} + z_{min}) / 2]) + "}"
textpxmin: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[x_{min}]) + "}"
textpymax: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[y_{max}]) + "}"
textpzmin: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[z_{min}]) + "}"
textpzmax: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[z_{max}]) + "}"
textpxmax: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[x_{max}]) + "}"
textpymin: "\scalebox{" + (LaTeX[Tachse]) + "}{" + (LaTeX[y_{min}]) + "}"
Pab': Sequence[P11 * tt * r_x + P12 * x(Element[Pab, i]) * r_y + P13 * y(Element[Pab, i]) * r_z, i, 1, lä] + B
Pex = Element(Pab', mi)
Pbb = If(m_1, Pb + B, {1, 0})
zm: z_{max} - z_{min}
Grün = 0.8 (slider from 0 to 1, step 0.1)
Rot = 1 (slider from 0 to 1, step 0.1)
Paa = If(m_1, Pa + B, {1, 0})
Frot: Sequence[If[PTyp ≟ 1, If[ddd1, (tt - y_{min}) / ym, (x(Element[Pab, mx]) - y_{min}) / ym], If[PTyp ≟ 2, sin(x(Element[Pab, mx])), If[PTyp ≟ 3, x(Element[Pab, mx]), If[PTyp ≟ 4, tt, If[PTyp ≟ 5, tt, If[PTyp ≟ 6, tt, If[PTyp ≟ 7, ℯ^(-tt), If[PTyp ≟ 8, x(Element[Pab, mx]), If[PTyp ≟ 9, ℯ^(tt), If[PTyp ≟ 10, tt, If[PTyp ≟ 11, sin(y(Element[Pab, mx])), If[PTyp ≟ 12, sin(y(Element[Pab, mx])), sin(y(Element[Pab, mx]))]]]]]]]]]]]], mx, 1, max] * fx3 * Rot
Fgrün: Sequence[If[PTyp ≟ 1, (y(Element[Pab, mx]) - z_{min}) / zm, If[PTyp ≟ 2, sin(y(Element[Pab, mx])), If[PTyp ≟ 3, ℯ^(x(Element[Pab, mx])), If[PTyp ≟ 4, x(Element[Pab, mx]), If[PTyp ≟ 5, x(Element[Pab, mx]), If[PTyp ≟ 6, ℯ^(x(Element[Pab, mx])), If[PTyp ≟ 7, ℯ^(-x(Element[Pab, mx])), If[PTyp ≟ 8, tt, If[PTyp ≟ 9, 1 - x(Element[Pab, mx]), If[PTyp ≟ 10, sin(x(Element[Pab, mx])), If[PTyp ≟ 11, sin(x(Element[Pab, mx])), If[PTyp ≟ 12, sin(tt), sin(x(Element[Pab, mx]))]]]]]]]]]]]], mx, 1, max] * fx2 * Grün
Fblau: Sequence[If[PTyp ≟ 1, If[ddd1, (x(Element[Pab, mx]) - x_{min}) / xm, (tt - x_{min}) / xm], If[PTyp ≟ 2, sin(tt), If[PTyp ≟ 3, ℯ^(-x(Element[Pab, mx])), If[PTyp ≟ 4, ℯ^(-tt), If[PTyp ≟ 5, ℯ^(-x(Element[Pab, mx])), If[PTyp ≟ 6, ℯ^(-x(Element[Pab, mx])), If[PTyp ≟ 7, tt, If[PTyp ≟ 8, ℯ^(-x(Element[Pab, mx])), If[PTyp ≟ 9, ℯ^(-x(Element[Pab, mx])), If[PTyp ≟ 10, sin(tt), If[PTyp ≟ 11, sin(y(Element[Pab, mx])), If[PTyp ≟ 12, ℯ^(-tt), sin(tt)]]]]]]]]]]]], mx, 1, max] * fx1 * Blau
Textfeld1 = Textfield(PTyp)
Strx = Ray(B, Element[zl10, 13])
Stry = Ray(B, Element[zl10, 14])
Strz = Ray(B, Element[zl10, 15])
e = true
inputBox1 = Textfield(x_{min})
inputBox2 = Textfield(y_{min})
inputBox3 = Textfield(z_{min})
inputBox4 = Textfield(x_{max})
inputBox5 = Textfield(y_{max})
inputBox6 = Textfield(z_{max})
inputBox8 = Textfield(v_{Animation})
inputBox7 = Textfield(Step)
inputBox9 = Textfield(N_P)
mq: (t - x_{min}) / xm
SFactor = 1 (slider from 0.5 to 2, step 0.1)
SFactor_2 = 1 (slider from 0.5 to 2, step 0.1)
Text8: "β = " + (LaTeX[Mod[β1, 6.283]]) + " rad"
Text17: "α = " + (LaTeX[Mod[α1, 6.283]]) + " rad"
Autor2: "" + (LaTeX[Autor1]) + ""
Tintervall: "Intervall_x = [" + x_{min} + "," + x_{max} + "]
Intervall_y = [" + y_{min} + "," + y_{max} + "] 
Intervall_ z = [" + z_{min} + "," + z_{max} + "]
r_x = " + r_x + "  r_y = " + r_y + "  r_z = " + r_z + "
 N_P = " + N_P + "   v = " + v_{Animation} + "
 α = " + α2 + " rad→ " + (α2 * 180 / π) + "° 
 β = " + β2 + " rad→ " + (β2 * 180 / π) + "°  
 γ = " + γ + " rad→ " + (γ * 180 / π) + " °  
 p = " + ((t - x_{min}) / (x_{max} - x_{min}) * 100) + "%
 PTyp = " + (If[iz, 0, PTyp]) + " 
 " + (If[iz, listenweise, punktweise]) + ""
Text7: "" + Tintervall + ""
Textfeld2 = Textfield(t)
D: Eck11 + (Eck12 - Eck11) * 0.33
j = 6 (slider from 1 to 9, step 1)
inputBox10 = Textfield(Nn)
Textfeld3 = Textfield(j)
Farbe = false
dd: d * d
w = true
dx2: xm / Nn
z = 1 (slider from 1 to 3, step 1)
zz = If(z ≟ 1, "", If[z ≟ 2, "-hin", "-her"])
dy2: ym / Nn
dz2: zm / Nn
text10: "$\scalebox{0.8} \text{I. drehbares Ortskurven-Netz" + (LaTeX[zz]) + "}$"
anim = false
g_1 = 1 (slider from 0 to 1, step 0.1)
ltrue = Sequence(If[i > d_1, ¬arichtung, arichtung], i, 1, Nn + 1)
dstep = 5 (slider from 1 to 20, step 1)
truea = true
inputBox13 = Textfield(d_1)
inputBox14 = Textfield(dstep)
trueb = If(anim, 0, Nn + 1)
text12: "$\scalebox{0.9}{  \textit {Teilansicht: }  \scalebox{0.9}{" + (LaTeX[If[arichtung, d_1, Nn - d_1 + 1]]) + "/" + (LaTeX[Nn + 1]) + "}"
Info00: "L=" + (LaTeX[L]) + " \:,\;  l=" + (LaTeX[l]) + " \;,\;  m=" + (LaTeX[m]) + ",\;\; n=" + (LaTeX[n]) + ",\; s=" + (LaTeX[s]) + "  "
Textfeld4 = Textfield(l)
Textfeld5 = Textfield(m)
Textfeld6 = Textfield(n)
Textfeld7 = Textfield(L)
Titel2: "" + (LaTeX[Titel1]) + ""
Info01: "" + (LaTeX[Info00]) + ""
Wellentext: "" + Text12 + ""