ಚಿತ್ರ:BMonSphere.jpg

testwikiದಿಂದ
ನ್ಯಾವಿಗೇಷನ್‌ಗೆ ಹೋಗು ಹುಡುಕಲು ಹೋಗು

BMonSphere.jpg ‎(೩೬೫ × ೩೫೬ ಚಿತ್ರಬಿಂದು, ಫೈಲಿನ ಗಾತ್ರ: ೧೦ KB, MIME ಪ್ರಕಾರ: image/jpeg)

ಈ ಕಡತವು Wikimedia Commons ಇಂದ ಬಂದಿದ್ದು, ಬೇರೆ ಯೋಜನೆಗಳಲ್ಲೂ ಉಪಯೋಗಿಸಲ್ಪಡಬಹುದು. [ಕಡತ ವಿವರಣಾ ಪುಟ]ದಲ್ಲಿರುವ ವಿವರಣೆಯನ್ನು ಕೆಳಗೆ ಕೊಡಲಾಗಿದೆ.

This image was uploaded in the JPEG format even though it consists of non-photographic data. This information could be stored more efficiently or accurately in the PNG or SVG format. If possible, please upload a PNG or SVG version of this image without compression artifacts, derived from a non-JPEG source (or with existing artifacts removed). After doing so, please tag the JPEG version with {{Superseded|NewImage.ext}} and remove this tag. This tag should not be applied to photographs or scans. If this image is a diagram or other image suitable for vectorisation, please tag this image with {{Convert to SVG}} instead of {{BadJPEG}}. If not suitable for vectorisation, use {{Convert to PNG}}. For more information, see {{BadJPEG}}.
ವಿವರ Brownian Motion on a Sphere. The generator of ths process is ½ times the Laplace-Beltrami-Operator
ದಿನಾಂಕ Summer ೨೦೦೭
date QS:P,+2007-00-00T00:00:00Z/9,P4241,Q40720564
(blender file as of 28.06.2007)
ಆಕರ read some papers (eg Price, Gareth C.; Williams, David: "Rolling with “slipping”" : I. Séminaire de probabilités de Strasbourg, 17 (1983), p. 194-197 You can download it from http://www.numdam.org/item?id=SPS_1983__17__194_0) use the GNU R code and the python code (in blender3d) to create this image.
ಕರ್ತೃ Thomas Steiner
ಅನುಮತಿ
(ಈ ಕಡತವನ್ನು ಮರುಬಳಕೆ ಮಾಡಲಾಗುತ್ತಿದೆ)		 Thomas Steiner put it under the CC-by-SA 2.5. If you use the python code or the R code, please give a reference to Christian Bayer and Thomas Steiner.
 
This image was created with Blender.
w:en:Creative Commons
ವೈಶಿಷ್ಟ್ಯ ಇರುವುದರಂತೆಯೇ ಹಂಚು
This file is licensed under the Creative Commons Attribution-Share Alike 2.5 Generic license.
ನೀವು ಮುಕ್ತ:
  • ಹಂಚಿಕೆಗೆ – ಕೆಲಸವನ್ನು ನಕಲು ಮಾಡಲು, ವಿತರಣೆ ಮತ್ತು ಸಾಗಿಸಲು
  • ರೀಮಿಕ್ಸ್ ಮಾಡಲು – ಕೆಲಸವನ್ನು ಬಳಸಿಕೊಳ್ಳಲು
ಈ ಕೆಳಗಿನ ಷರತ್ತುಗಳಲ್ಲಿ:
  • ವೈಶಿಷ್ಟ್ಯ – ನೀವು ಸೂಕ್ತವಾದ ಕ್ರೆಡಿಟ್ ನೀಡಬೇಕು, ಪರವಾನಗಿಗೆ ಲಿಂಕ್ ಅನ್ನು ಒದಗಿಸಬೇಕು ಮತ್ತು ಯಾವುದೇ ಬದಲಾವಣೆಗಳನ್ನು ಮಾಡಿದ್ದರೆ ಸೂಚಿಸಬೇಕು. ನೀವು ಯಾವುದೇ ಸಮಂಜಸವಾದ ರೀತಿಯಲ್ಲಿ ಮಾಡಬಹುದು, ಆದರೆ ಪರವಾನಗಿದಾರರು ನಿಮ್ಮನ್ನು ಅಥವಾ ನಿಮ್ಮ ಯಾವುದೇ ಬಳಕೆಯನ್ನು ಅನುಮೋದಿಸಿದಂತೆ ರೀತಿಯಲ್ಲಿ ಉಪಯೋಗಿಸಬಾರದು.
  • ಇರುವುದರಂತೆಯೇ ಹಂಚು – ನೀವು ರೀಮಿಕ್ಸ್ ಮಾಡಿದರೆ, ರೂಪಾಂತರಗೊಳಿಸಿದರೆ ಅಥವಾ ವಸ್ತುವಿನ ಮೇಲೆ ನಿರ್ಮಿಸಿದರೆ, ನಿಮ್ಮ ಕೊಡುಗೆಗಳನ್ನು ನೀವು ಮೂಲದಂತೆ ಅದೇ ಅಥವಾ ಹೊಂದಾಣಿಕೆಯ ಪರವಾನಗಿ ಅಡಿಯಲ್ಲಿ ವಿತರಿಸಬೇಕು.

code

Perhaps you grab the source from the "edit" page without the wikiformating.

GNU R

This creates the paths and saves them into textfiles that can be read by blender. There are also paths for BMs on a torus. 

# calculate a Brownian motion on the sphere; the output is a list
# consisting of:
# Z ... BM on the sphere
# Y ... tangential BM, see Price&Williams
# b ... independent 1D BM (see Price & Williams)
# B ... generating 3D BM
# n ... number of time-steps in the discretization
# T ... the above processes are given on a uniform mesh of size
#       n on [0,T]
euler = function(x0, T, n) {
  # initialize objects
  dt = T/(n-1);
  dB = matrix(rep(0,3*(n-1)),ncol=3, nrow=n-1);
  dB[,1] = rnorm(n-1, 0, sqrt(dt));
  dB[,2] = rnorm(n-1, 0, sqrt(dt));
  dB[,3] = rnorm(n-1, 0, sqrt(dt));
  Z = matrix(rep(0,3*n), ncol=3, nrow=n);
  dZ = matrix(rep(0,3*(n-1)), ncol=3, nrow=n-1);
  Y = matrix(rep(0,3*n), ncol=3, nrow=n);
  B = matrix(rep(0,3*n), ncol=3, nrow=n);
  b = rep(0, n);
  Z[1,] = x0;

  #do the computation
  for(k in 2:n){
    B[k,] = B[k-1,] + dB[k-1,];
    dZ[k-1,] = cross(Z[k-1,],dB[k-1,]) - Z[k-1,]*dt;
    Z[k,] = Z[k-1,] + dZ[k-1,];
    Y[k,] = Y[k-1,] - cross(Z[k-1,],dZ[k-1,]);
    b[k] = b[k-1] + dot(Z[k-1,],dB[k-1,]);
  }
  return(list(Z = Z, Y = Y, b = b, B = B, n = n, T = T));
}

# write the output from euler in csv-files
euler.write = function(bms, files=c("Z.csv","Y.csv","b.csv","B.csv"),steps=bms$n){
  bigsteps=round(seq(1,bms$n,length=steps))
  write.table(bms$Z[bigsteps,],file=files[1],col.names=F,row.names=F,sep=",",dec=".");
  write.table(bms$Y[bigsteps,],file=files[2],col.names=F,row.names=F,sep=",",dec=".");
  write.table(bms$b[bigsteps],file=files[3],col.names=F,row.names=F,sep=",",dec=".");
  write.table(bms$B[bigsteps,],file=files[4],col.names=F,row.names=F,sep=",",dec=".");
}

# calculate a Brownian motion on a 3-d torus with outer
# radius R and inner radius r
eulerTorus = function(x0, r, R, t, n) {
  # initialize objects
  dt = t/(n-1);
  dB = matrix(rep(0,3*(n-1)),ncol=3, nrow=n-1);
  dB[,1] = rnorm(n-1, 0, sqrt(dt));
  dB[,2] = rnorm(n-1, 0, sqrt(dt));
  dB[,3] = rnorm(n-1, 0, sqrt(dt));
  Z = matrix(rep(0,3*n), ncol=3, nrow=n);
  B = matrix(rep(0,3*n), ncol=3, nrow=n);
  dZ = matrix(rep(0,3*(n-1)), ncol=3, nrow=n-1);
  Z[1,] = x0;
  nT = rep(0,3);

  #do the computation
  for(k in 2:n){
    B[k,] = B[k-1,] + dB[k-1,];
    nT = nTorus(Z[k-1,],r,R);
    dZ[k-1,] = cross(nT, dB[k-1,]) + HTorus(Z[k-1,],r,R)*nT*dt;
    Z[k,] = Z[k-1,] + dZ[k-1,];
  }
  return(list(Z = Z, B = B, n = n, t = t));
}

# write the output from euler in csv-files
torus.write = function(bmt, files=c("tZ.csv","tB.csv"),steps=bmt$n){
  bigsteps=round(seq(1,bmt$n,length=steps))
  write.table(bmt$Z[bigsteps,],file=files[1],col.names=F,row.names=F,sep=",",dec=".");
  write.table(bmt$B[bigsteps,],file=files[2],col.names=F,row.names=F,sep=",",dec=".");
}

# "defining" function of a torus
fTorus = function(x,r,R){
  return((x[1]^2+x[2]^2+x[3]^2+R^2-r^2)^2 - 4*R^2*(x[1]^2+x[2]^2));
}

# normal vector of a 3-d torus with outer radius R and inner radius r
nTorus = function(x, r, R) {
  c1 = x[1]*(x[1]^2+x[2]^2+x[3]^2-R^2-r^2)/(3*x[1]^4*x[2]^2+3*x[3]^4*x[2]^2
    +3*x[3]^4*x[1]^2+6*x[3]^2*x[1]^2*x[2]^2+3*x[1]^2*x[2]^4+3*x[3]^2*x[2]^4
    -2*x[3]^2*R^2*r^2-4*x[1]^2*x[2]^2*R^2+x[1]^6+x[2]^6+x[3]^6+3*x[3]^2*x[1]^4
    -4*x[1]^2*x[2]^2*r^2-4*x[1]^2*x[3]^2*r^2+2*R^2*x[1]^2*r^2
    -4*x[2]^2*x[3]^2*r^2+2*R^2*x[2]^2*r^2-2*x[1]^4*R^2-2*x[1]^4*r^2
    +R^4*x[1]^2+x[1]^2*r^4-2*x[2]^4*R^2-2*x[2]^4*r^2+R^4*x[2]^2+x[2]^2*r^4
    +x[3]^2*R^4+x[3]^2*r^4-2*x[3]^4*r^2+2*x[3]^4*R^2)^(1/2);
  c2 = x[2]*(x[1]^2+x[2]^2+x[3]^2-R^2-r^2)/(3*x[1]^4*x[2]^2+3*x[3]^4*x[2]^2
    +3*x[3]^4*x[1]^2+6*x[3]^2*x[1]^2*x[2]^2+3*x[1]^2*x[2]^4+3*x[3]^2*x[2]^4
    -2*x[3]^2*R^2*r^2-4*x[1]^2*x[2]^2*R^2+x[1]^6+x[2]^6+x[3]^6
    +3*x[3]^2*x[1]^4-4*x[1]^2*x[2]^2*r^2-4*x[1]^2*x[3]^2*r^2+2*R^2*x[1]^2*r^2
    -4*x[2]^2*x[3]^2*r^2+2*R^2*x[2]^2*r^2-2*x[1]^4*R^2-2*x[1]^4*r^2+R^4*x[1]^2
    +x[1]^2*r^4-2*x[2]^4*R^2-2*x[2]^4*r^2+R^4*x[2]^2+x[2]^2*r^4+x[3]^2*R^4
    +x[3]^2*r^4-2*x[3]^4*r^2+2*x[3]^4*R^2)^(1/2);
  c3 = (x[1]^2+x[2]^2+x[3]^2+R^2-r^2)*x[3]/(3*x[1]^4*x[2]^2+3*x[3]^4*x[2]^2
                                            +3*x[3]^4*x[1]^2
                                            +6*x[3]^2*x[1]^2*x[2]^2
                                            +3*x[1]^2*x[2]^4+3*x[3]^2*x[2]^4
                                            -2*x[3]^2*R^2*r^2
                                            -4*x[1]^2*x[2]^2*R^2+x[1]^6
                                            +x[2]^6+x[3]^6+3*x[3]^2*x[1]^4
                                            -4*x[1]^2*x[2]^2*r^2
                                            -4*x[1]^2*x[3]^2*r^2
                                            +2*R^2*x[1]^2*r^2
                                            -4*x[2]^2*x[3]^2*r^2
                                            +2*R^2*x[2]^2*r^2-2*x[1]^4*R^2
                                            -2*x[1]^4*r^2+R^4*x[1]^2
                                            +x[1]^2*r^4-2*x[2]^4*R^2
                                            -2*x[2]^4*r^2+R^4*x[2]^2
                                            +x[2]^2*r^4+x[3]^2*R^4
                                            +x[3]^2*r^4-2*x[3]^4*r^2
                                            +2*x[3]^4*R^2)^(1/2);
  return(c(c1,c2,c3));
}

# mean curvature of a 3-d torus with outer radius R and inner radius r
HTorus = function(x, r, R){
  return( -(3*x[1]^4*r^4+4*x[2]^6*x[3]^2+4*x[1]^6*x[2]^2-3*x[2]^4*x[3]^2*R^2
            -2*x[1]^6*R^2+4*x[1]^2*x[3]^6+x[3]^6*R^2+4*x[2]^4*R^2*r^2-x[1]^2*r^6
            -x[2]^2*r^6+x[2]^4*R^4+4*x[2]^2*x[3]^2*R^4+6*x[2]^2*x[3]^2*r^4
            -2*x[1]^2*R^2*r^4-x[1]^2*R^4*r^2-9*x[1]^4*x[2]^2*r^2
            -9*x[1]^4*x[3]^2*r^2+4*x[1]^4*R^2*r^2+12*x[1]^2*x[3]^4*x[2]^2
            -3*x[2]^6*r^2+4*x[1]^6*x[3]^2+3*x[3]^4*r^4-x[3]^4*R^4
            -9*x[2]^4*x[3]^2*r^2+2*x[2]^2*x[3]^2*R^2*r^2+4*x[1]^2*x[2]^6
            -6*x[1]^2*x[3]^2*x[2]^2*R^2-x[3]^2*r^6+6*x[2]^4*x[3]^4+x[3]^8
            +x[1]^8+x[2]^8-3*x[1]^6*r^2+6*x[1]^4*x[3]^4+12*x[1]^2*x[3]^2*x[2]^4
            -6*x[1]^2*x[2]^4*R^2-2*x[3]^4*R^2*r^2-2*x[2]^2*R^2*r^4-x[2]^2*R^4*r^2
            -9*x[2]^2*x[3]^4*r^2+x[3]^2*R^2*r^4+x[3]^2*R^4*r^2-9*x[1]^2*x[2]^4*r^2
            +2*x[1]^2*R^4*x[2]^2+6*x[1]^2*x[2]^2*r^4-3*x[1]^4*x[3]^2*R^2
            -6*x[1]^4*x[2]^2*R^2+4*x[1]^2*x[3]^2*R^4+6*x[1]^2*x[3]^2*r^4
            -9*x[1]^2*x[3]^4*r^2+8*x[1]^2*R^2*x[2]^2*r^2+2*x[1]^2*x[3]^2*R^2*r^2
            +x[1]^4*R^4-3*x[3]^6*r^2-2*x[2]^6*R^2+6*x[1]^4*x[2]^4-x[3]^2*R^6
            -18*x[1]^2*x[2]^2*x[3]^2*r^2+4*x[2]^2*x[3]^6+12*x[1]^4*x[3]^2*x[2]^2
            +3*x[2]^4*r^4)/(3*x[1]^4*x[2]^2+3*x[3]^4*x[2]^2+3*x[3]^4*x[1]^2
                            +6*x[3]^2*x[1]^2*x[2]^2+3*x[1]^2*x[2]^4+3*x[3]^2*x[2]^4
                            -2*x[3]^2*R^2*r^2-4*x[1]^2*x[2]^2*R^2+x[1]^6+x[2]^6
                            +x[3]^6+3*x[3]^2*x[1]^4-4*x[1]^2*x[2]^2*r^2
                            -4*x[1]^2*x[3]^2*r^2+2*R^2*x[1]^2*r^2
                            -4*x[2]^2*x[3]^2*r^2+2*R^2*x[2]^2*r^2-2*x[1]^4*R^2
                            -2*x[1]^4*r^2+R^4*x[1]^2+x[1]^2*r^4-2*x[2]^4*R^2
                            -2*x[2]^4*r^2+R^4*x[2]^2+x[2]^2*r^4+x[3]^2*R^4
                            +x[3]^2*r^4-2*x[3]^4*r^2+2*x[3]^4*R^2)^(3/2));
}

# calculate the cross product of the two 3-dim vectors
# x and y. No argument-checking for performance reasons
cross = function(x,y){
  res = rep(0,3);
  res[1] = x[2]*y[3] - x[3]*y[2];
  res[2] = -x[1]*y[3] + x[3]*y[1];
  res[3] = x[1]*y[2] - x[2]*y[1];
  return(res);
}

# calculate the inner product of two vectors of dim 3
# returns a number, not a 1x1-matrix!
dot = function(x,y){
  return(sum(x*y));
}

# calculate the cross product of the two 3-dim vectors
# x and y. No argument-checking for performance reasons
cross = function(x,y){
  res = rep(0,3);
  res[1] = x[2]*y[3] - x[3]*y[2];
  res[2] = -x[1]*y[3] + x[3]*y[1];
  res[3] = x[1]*y[2] - x[2]*y[1];
  return(res);
}

#############
### main-teil
set.seed(280180)
et=eulerTorus(c(3,0,0),3,5,19,10000)
torus.write(et,steps=9000)
#
#bms=euler(c(1,0,0),4,70000)
#euler.write(bms,steps=10000)

blender3d

The blender (python) code to create a image that looks almost like this one. Play around... 

## import data from matlab-text-file and draw BM on the S^2

## (c) 2007 by Christan Bayer and Thomas Steiner

from Blender import Curve, Object, Scene, Window, BezTriple, Mesh, Material, Camera,
World
from math import *

##import der BM auf der Kugel aus einem csv-file
def importcurve(inpath="Z.csv"):
        infile = open(inpath,'r')
        lines = infile.readlines()
        vec=[]
        for i in lines:
                li=i.split(',')
                vec.append([float(li[0]),float(li[1]),float(li[2].strip())])
        infile.close()
        return(vec)

##function um aus einem vektor (mit den x,y,z Koordinaten) eine Kurve zu machen
def vec2Cur(curPts,name="BMonSphere"):
        bztr=[]
        bztr.append(BezTriple.New(curPts[0]))
        bztr[0].handleTypes=(BezTriple.HandleTypes.VECT,BezTriple.HandleTypes.VECT)
        cur=Curve.New(name) ##TODO wenn es das Objekt schon gibt, dann nicht neu erzeugen
        cur.appendNurb(bztr[0])
        for i in range(1,len(curPts)):
                bztr.append(BezTriple.New(curPts[i]))
                bztr[i].handleTypes=(BezTriple.HandleTypes.VECT,BezTriple.HandleTypes.VECT)
                cur[0].append(bztr[i])
        return( cur )

#erzeugt einen kreis, der später die BM umgibt (liegt in y-z-Ebene)
def circle(r,name="tubus"):
        bzcir=[]
        bzcir.append(BezTriple.New(0.,-r,-4./3.*r, 0.,-r,0., 0.,-r,4./3.*r))
        bzcir[0].handleTypes=(BezTriple.HandleTypes.FREE,BezTriple.HandleTypes.FREE)
        cur=Curve.New(name) ##TODO wenn es das Objekt schon gibt, dann nicht neu erzeugen
        cur.appendNurb(bzcir[0])
        #jetzt alle weietren pkte
        bzcir.append(BezTriple.New(0.,r,4./3.*r, 0.,r,0., 0.,r,-4./3.*r))
        bzcir[1].handleTypes=(BezTriple.HandleTypes.FREE,BezTriple.HandleTypes.FREE)
        cur[0].append(bzcir[1])
        bzcir.append(BezTriple.New(0.,-r,-4./3.*r, 0.,-r,0., 0.,-r,4./3.*r))
        bzcir[2].handleTypes=(BezTriple.HandleTypes.FREE,BezTriple.HandleTypes.FREE)
        cur[0].append(bzcir[2])
        return ( cur )

#erzeuge mit skript eine (glas)kugel (UVSphere)
def sphGlass(r=1.0,name="Glaskugel",n=40,smooth=0):
        glass=Mesh.New(name) ##TODO wenn es das Objekt schon gibt, dann nicht neu erzeugen
        for i in range(0,n):
                for j in range(0,n):
                        x=sin(j*pi*2.0/(n-1))*cos(-pi/2.0+i*pi/(n-1))*1.0*r
                        y=cos(j*pi*2.0/(n-1))*(cos(-pi/2.0+i*pi/(n-1)))*1.0*r
                        z=sin(-pi/2.0+i*pi/(n-1))*1.0*r
                        glass.verts.extend(x,y,z)
        for i in range(0,n-1): 
                for j in range(0,n-1):
                        glass.faces.extend([i*n+j,i*n+j+1,(i+1)*n+j+1,(i+1)*n+j])
                        glass.faces[i*(n-1)+j].smooth=1
        return( glass )

def torus(r=0.3,R=1.4): 
        krGro=circle(r=R,name="grTorusKreis")
        

#jetzt das material ändern
def verglasen(mesh):
        matGlass = Material.New("glas") ##TODO wenn es das Objekt schon gibt, dann nicht
neu erzeugen
        #matGlass.setSpecShader(0.6)
        matGlass.setHardness(30) #für spec: 30
        matGlass.setRayMirr(0.15)
        matGlass.setFresnelMirr(4.9)
        matGlass.setFresnelMirrFac(1.8)
        matGlass.setIOR(1.52)
        matGlass.setFresnelTrans(3.9)
        matGlass.setSpecTransp(2.7)
        #glass.materials.setSpecTransp(1.0)
        matGlass.rgbCol = [0.66, 0.81, 0.85]
        matGlass.mode |= Material.Modes.ZTRANSP
        matGlass.mode |= Material.Modes.RAYTRANSP
        #matGlass.mode |= Material.Modes.RAYMIRROR
        mesh.materials=[matGlass]
        return ( mesh )

def maleBM(mesh):
        matDraht = Material.New("roterDraht") ##TODO wenn es das Objekt schon gibt, dann
nicht neu erzeugen
        matDraht.rgbCol = [1.0, 0.1, 0.1]
        mesh.materials=[matDraht]
        return( mesh )

#eine solide Mesh-Ebene (Quader)
# auf der höhe ebh, dicke d, seitenlänge (quadratisch) 2*gr
def ebene(ebh=-2.5,d=0.1,gr=6.0,name="Schattenebene"):
        quader=Mesh.New(name) ##TODO wenn es das Objekt schon gibt, dann nicht neu erzeugen
        #obere ebene
        quader.verts.extend(gr,gr,ebh)
        quader.verts.extend(-gr,gr,ebh)
        quader.verts.extend(-gr,-gr,ebh)
        quader.verts.extend(gr,-gr,ebh)
        #untere ebene
        quader.verts.extend(gr,gr,ebh-d)
        quader.verts.extend(-gr,gr,ebh-d)
        quader.verts.extend(-gr,-gr,ebh-d)
        quader.verts.extend(gr,-gr,ebh-d)
        quader.faces.extend([0,1,2,3])
        quader.faces.extend([0,4,5,1])
        quader.faces.extend([1,5,6,2])
        quader.faces.extend([2,6,7,3])
        quader.faces.extend([3,7,4,0])
        quader.faces.extend([4,7,6,5])
        #die ebene einfärben
        matEb = Material.New("ebenen_material") ##TODO wenn es das Objekt schon gibt, dann
nicht neu erzeugen
        matEb.rgbCol = [0.53, 0.51, 0.31]
        matEb.mode |= Material.Modes.TRANSPSHADOW
        matEb.mode |= Material.Modes.ZTRANSP
        quader.materials=[matEb]
        return (quader)

###################
#### main-teil ####

# wechsel in den edit-mode
editmode = Window.EditMode()
if editmode: Window.EditMode(0)

dataBMS=importcurve("C:/Dokumente und Einstellungen/thire/Desktop/bmsphere/Z.csv")
#dataBMS=importcurve("H:\MyDocs\sphere\Z.csv")
BMScur=vec2Cur(dataBMS,"BMname")
#dataStereo=importcurve("H:\MyDocs\sphere\stZ.csv")
#stereoCur=vec2Cur(dataStereo,"SterName")

cir=circle(r=0.01)

glass=sphGlass()
glass=verglasen(glass)
ebe=ebene()

#jetzt alles hinzufügen
scn=Scene.GetCurrent()
obBMScur=scn.objects.new(BMScur,"BMonSphere")
obcir=scn.objects.new(cir,"round")
obgla=scn.objects.new(glass,"Glaskugel")
obebe=scn.objects.new(ebe,"Ebene")
#obStereo=scn.objects.new(stereoCur,"StereoCurObj")

BMScur.setBevOb(obcir)
BMScur.update()
BMScur=maleBM(BMScur)

#stereoCur.setBevOb(obcir)
#stereoCur.update()

cam = Object.Get("Camera") 
#cam.setLocation(-5., 5.5, 2.9) 
#cam.setEuler(62.0,-1.,222.6)
#alternativ, besser??
cam.setLocation(-3.3, 8.4, 1.7) 
cam.setEuler(74,0,200)

world=World.GetCurrent()
world.setZen([0.81,0.82,0.61])
world.setHor([0.77,0.85,0.66])

if editmode: Window.EditMode(1)  # optional, zurück n den letzten modus

        
#ergebnis von
#set.seed(24112000)
#sbm=euler(c(0,0,-1),T=1.5,n=5000)
#euler.write(sbm)

Captions

Add a one-line explanation of what this file represents
Brownian Motion on a Sphere, as a process generated by the Laplace-Beltrami-Operator

Items portrayed in this file

depicts ಇಂಗ್ಲಿಷ್

copyright status ಇಂಗ್ಲಿಷ್

copyrighted ಇಂಗ್ಲಿಷ್

media type ಇಂಗ್ಲಿಷ್

image/jpeg

checksum ಇಂಗ್ಲಿಷ್

f51c8d9194ca77a5c2a7d77d21c292e592d5c6c5

determination method or standard ಇಂಗ್ಲಿಷ್: SHA-1

data size ಇಂಗ್ಲಿಷ್

೧೦,೬೯೩ byte

height ಇಂಗ್ಲಿಷ್

೩೫೬ pixel

width ಇಂಗ್ಲಿಷ್

೩೬೫ pixel

ಕಡತದ ಇತಿಹಾಸ

ದಿನ/ಕಾಲ ಒತ್ತಿದರೆ ಆ ಸಮಯದಲ್ಲಿ ಈ ಕಡತದ ವಸ್ತುಸ್ಥಿತಿ ತೋರುತ್ತದೆ.

ದಿನ/ಕಾಲಕಿರುನೋಟಆಯಾಮಗಳುಬಳಕೆದಾರಟಿಪ್ಪಣಿ
ಪ್ರಸಕ್ತ೨೦:೫೩, ೨೨ ಡಿಸೆಂಬರ್ ೨೦೧೩೨೦:೫೩, ೨೨ ಡಿಸೆಂಬರ್ ೨೦೧೩ ವರೆಗಿನ ಆವೃತ್ತಿಯ ಕಿರುನೋಟ೩೬೫ × ೩೫೬ (೧೦ KB)wikimediacommons>Olli NiemitaloCropped (in a JPEG-lossless way)

ಈ ಕೆಳಗಿನ ಪುಟವು ಈ ಚಿತ್ರಕ್ಕೆ ಸಂಪರ್ಕ ಹೊಂದಿದೆ:

"https://kn.beta.math.wmflabs.org/wiki/ಚಿತ್ರ:BMonSphere.jpg" ಇಂದ ಪಡೆಯಲ್ಪಟ್ಟಿದೆ