ein/aus⇒

N_P(≤1000) =:

xxy

yyx

x - Scan:

y - Scan:

 Chladni Muster 

2D Plotter für implizite Funktionen-Methodenvergleich 

$\scalebox{1.4} \text{\copyright Roman Chijner, Heidelberg 2013}$ 
$\scalebox{1.3} \text{     Gestaltungshilfe:}\scalebox{1.3}\text{ Werner Knobloch}$

N_{V2}(≤400) =:

x Scan

y Scan

N_{V1}(≤5000) =:

Methode: Roots

Auflösung:

Genauigkeit:

►

►

x

x

►

◄

◄

►

a/b

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m=1

n=1

Bildschirmausschnitt:
(blaue Punkte bewegen)

6

1

2

3

II←

m =:

n =:

Punkteigenschaften:

Größe setzen

Spur

Spur setzen

Ausschnitt -Varianten:

0

1

-1

Zoom +

Zoom -

refresh

4

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5

7

L =:

refresh

s =:

Methode: \fgcolor{red}{R}oots\fgcolor{red}{B}y\fgcolor{red}{L}ocus

I. Spurplot

N_{V1}(≤1000) =:

a) Linienplot

b) Regionsfärbung:

II. Feste Linien

      Ausschnitt            
      Hintergrund: 





        

 Plottfarben:                                                 
                         



            

Feste Punkt-Linien

Roo' = (40, 40)
Ro' = (-40, -40)
s = 1 (slider from -1 to 1, step 1)
n = 8 (slider from 0 to 15, step 1)
m = 3 (slider from 0 to 15, step 1)
L = 20 (slider from 0 to 30, step 1)
f01(x, y) = cos(n * π * x / L) * cos(m * π * y / L) + s * cos(m * π * x / L) * cos(n * π * y / L)
N_P = 200 (slider from 1 to 1500, step 1)
a = false
N_1 = If(a, N_P, 2)
y_{max}: y(Roo')
y_{min}: y(Ro')
x_{max}: x(Roo')
x_{min}: x(Ro')
xx = Sequence(x_{min} + (x_{max} - x_{min}) / N_1 * i, i, 0, N_1)
yy = Sequence(y_{min} + (y_{max} - y_{min}) / N_1 * i, i, 0, N_1)
Pxxy = RemoveUndefined(Join[Zip[Mirror[{Roots[f01(a, x), y_{min}, y_{max}]}, y = x] + (a, 0), a, xx]])
Pyyx = Join(Zip[Reverse[{Roots[f01(x, b), x_{min}, x_{max}]}] + (0, b), b, yy])
inputBox5 = Textfield(N_P)
läxxy = Length(Pxxy)
läyyx = Length(Pyyx)
d1 = true
d2 = true
Px1: (x_{min}, 0)
Px2: (x_{max}, 0)
Py1: (0, y_{min})
Py2: (0, y_{max})
Ax = Point(Segment[Px2, Px1])
Ay = Point(Segment[Py2, Py1])
fxx(x) = f01(x, y(Ay))
fyy(x) = f01(x(Ax), x)
ε = 0.5 (slider from 0 to 1, step 0.05)
N_{V1} = 150 (slider from 0 to 10000, step 100)
m1 = 151 (slider from 1 to N_{V1} + 1, step 1)
dx: (x_{max} - x_{min}) / N_{V1}
dy: (y_{max} - y_{min}) / N_{V1}
xi: x_{min} + (m1 - 1) * dx
yi: y_{min} + (m1 - 1) * dy
Bxx1 = If(fxx(xi - ε / 2) * fxx(xi + ε / 2) < 0, (xi, y(Ay)), (0, 0))
Byy1 = If(fyy(yi - ε / 2) * fyy(yi + ε / 2) < 0, (x(Ax), yi), (0, 0))
N_{V2} = 80 (slider from 0 to 500, step 10)
Textfeld1 = Textfield(N_{V2})
b = true
d = true
dx2: (x_{max} - x_{min}) / N_{V2}
dy2: (y_{max} - y_{min}) / N_{V2}
B = (0, 0)
Textfeld2 = Textfield(N_{V1})
Pxxyy = Union(Join[{Pxxy, Pyyx}], {})
läxxyy = Length(Pxxyy)
text12: "xxyy=" + läxxyy + ""
e = false
Bxx3 = If(fxx(xi) > 0, (xi, y(Ay)))
Bxx4 = If(fxx(xi) < 0, (xi, y(Ay)))
locxx2a = If(¬e, Locus[Bxx4, Ay])
locxx1 = If(e, Locus[Bxx1, Ay], Locus[Bxx3, Ay])
locyy1 = If(e, Locus[Byy1, Ax])
o = false
Ro = (-40, -40)
Roa: (x(Ro), 200)
Rob: (200, y(Ro))
px = Ray(Ro, Roa)
py = Ray(Ro, Rob)
Ro1 = Point(py)
Ro2 = Point(px)
Roo: (x(Ro1), y(Ro2))
Gr1: -2 * L * (1, 1)
Gr2: 2 * L * (1, -1)
Gr3: 2 * L * (1, 1)
Gr4: 2 * L * (-1, 1)
Vieleck1, gr1, gr2, gr3, gr4 = Polygon(Gr1, Gr2, Gr3, Gr4)
Info1: "L=" + (LaTeX[L]) + ";\;   m=" + (LaTeX[m]) + " ; \; n=" + (LaTeX[n]) + " ;\;s=" + (LaTeX[s]) + " ;\; ε=" + (LaTeX[ε]) + ";\; Intervall_x=[" + (LaTeX[x_{min}]) + " ," + (LaTeX[x_{max}]) + " ]; \;   Intervall_y=[" + (LaTeX[y_{min}]) + " ," + (LaTeX[y_{max}]) + " ]"
Info2: "" + (LaTeX[Info1]) + ""
inputBox1 = Textfield(m)
inputBox2 = Textfield(n)
q = 2 (slider from 1 to 4, step 1)
r = false
Autor1: "" + (LaTeX[Autor]) + ""
Vieleck2, ro, ro1, roo, ro2 = Polygon(Ro, Ro1, Roo, Ro2)
oo1 = If(a, true, false)
Textfeld3 = Textfield(L)
inputBox3 = Textfield(s)
Textfeld4 = Textfield(N_{V1})
text6: "xmin = " + x_{min} + "     xmax = " + x_{max} + "  
ymin = " + y_{min} + "    ymax = " + y_{max} + "  "
text14: "$f_{m,n,s}(x,y)=0 ⇔:\;cos(\frac{n*\pi*x}{L})*cos(\frac{m*\pi*y}{L})+s*cos(\frac{m*\pi*x}{L})*cos(\frac{n*\pi*y}{L})=0$
$\;\;\;\;\;\;\;\;\;\;\;\;f_{" + (LaTeX[m]) + "," + (LaTeX[n]) + "," + (LaTeX[s]) + "}(x,y)=" + (LaTeX[f01]) + "$"
Text7: "" + Text2 + ""
rot = 0.28 (slider from 0 to 1, step 0.01)
blau = 0.57 (slider from 0 to 1, step 0.01)
grün = 1 (slider from 0 to 1, step 0.01)
Deckkraft = 0 (slider from 0 to 1, step 0.01)
Fr_x = 1 (slider from 0 to 1, step 0.1)
Fg_x = 0 (slider from 0 to 1, step 0.1)
Fb_x = 0.3 (slider from 0 to 1, step 0.1)
Fr_y = 0.7 (slider from 0 to 1, step 0.1)
Fb_y = 0 (slider from 0 to 1, step 0.1)
Fg_y = 1 (slider from 0 to 1, step 0.1)
Text15: "" + Text8 + ""
A = (44.9928332370539, 14.790012618739638)
C = (45.12016808635429, 9.951288345324798)
text9: "Länge = " + läyyx + ""
text8: "Länge = " + läxxy + ""
Linienstärke = 3 (slider from 1 to 11, step 1)
Festlinien = false