Ova datoteka je s projekta Vikimedijina ostava i može se upotrebljavati i na drugim projektima.
Ispod su prikazane informacije s njene opisne stranice.
English: von Koch snowflake curve after 6 steps (4,097 points); initially created with Scilab, transformed into SVG by pstoedit, layout by Inkscape. New version was created by a text editor.
Français : Courbe du flocon de neige de von Koch après 6 étapes (4,097 points) ; initialement créé avec Scilab, transformé en SVG avec pstoedit, mis en forme avec Inkscape. La nouvelle version a été faite avec un éditeur de texte.
This media was created with Scilab, a free open-source software.
Here is a listing of the Scilab source used to create this file.
English: English version by default.
Français : Version française, si les préférences de votre compte sont réglées (voir Special:Preferences).
Iterative source code
// ******************************// * *// * "Snowflake" von Koch curve *// * *// ******************************clear;clf;// **************// * constants *// **************n=6;// number of steps // limited to 9 (262 145 points), otherwise the stacksize must be changed// 6 steps (4 097 points) are enough for a good renderingN=4^n+1;// amount of pointssin_soixante=sqrt(3)/2;// sin(60°)l=1;// length of the initial line (arbitrary unit)// ******************// * initialisation *// ******************ycourbe=[zeros(1,N)];ycourbe1=ycourbe;// *************// * functions *// *************function[xx, yy] = etape(x, y)// from a line [(x(1),y(1)) ; (x(2),y(2))]// make the line [(xx(1),yy(1)) ; (xx(2),yy(2)) ; (xx(3),yy(3))]// x and y are 2-cells tables, the ends of the basis line// xx and yy are 3-cells tables// the edges of the equilateral trianglexu=(x(2)-x(1))/3;yu=(y(2)-y(1))/3;// third of the basis line vectorxv=0.5*xu-sin_soixante*yu;yv=sin_soixante*xu+0.5*yu;// vector turned by +60°xx(1)=x(1)+xu;yy(1)=y(1)+yu;xx(3)=x(2)-xu;yy(3)=y(2)-yu;xx(2)=xx(1)+xv;yy(2)=yy(1)+yv;endfunctionfunction[xkoch, ykoch] = vonkoch(x, y, n)// builds the curve// initialisationxkoch=x;ykoch=y;xkoch1=x;ykoch1=y;fori=1:njmax=4^(i-1);// number of lines at the beginning of the step iforj=1:jmax/2+1// we work with two points which indices are j and j+1 (line #j)// thanks t the symmetry, we work with a half curvedecalage=(j-1)*4;// the new points shift the next points by this offsetx_init=xkoch(j:j+1);y_init=ykoch(j:j+1);// line #j[x_trans,y_trans]=etape(x_init,y_init);// transformed linexkoch1(decalage+1)=x_init(1);xkoch1(decalage+5)=x_init(2);ykoch1(decalage+1)=y_init(1);ykoch1(decalage+5)=y_init(2);fork=1:3xkoch1(k+decalage+1)=x_trans(k);ykoch1(k+decalage+1)=y_trans(k);// values put in the global vectorendendxkoch=xkoch1;ykoch=ykoch1;endfori=1:4^nykoch(N-i+1)=ykoch(i);xkoch(N-i+1)=l-xkoch(i);// 2nd half-curveendendfunction// ****************// * main program *// ****************xcourbe(2)=l;[xcourbe,ycourbe]=vonkoch(xcourbe,ycourbe,n);// drawing the curvexpoly(xcourbe,ycourbe)isoview(0,l,0,l*sin_soixante/3)
The following code can be added to directly generate the file (the SVG export was not implemented at the time the file was created).
// saving the filename="von_koch_"+string(n)+"_steps.svg";xs2svg(0,name)
Recursive source code
The code is more compact but the execution is slower, and does not generate the table of values.
//============================================================================// name: von_koch.sce// author: Christophe Dang Ngoc Chan// date of creation: 2012-10-23// dates of modification: // 2013-07-08: quotes ' -> "// 2013-07-2: vectorisation of the calculations//----------------------------------------------------------------------------// version of Scilab: 5.3.1// required Atoms modules: aucun//----------------------------------------------------------------------------// Objective: draws the von Koch's "snowflake"// Inputs: none (parameters are hard coded)// Outputs: graphical window with a curve; SVG file//============================================================================clear;clf;// *************// * constants *// **************n=6;// number of steps // limited to 9 (262 145 points), otherwise the stacksize must be changed// 6 steps (4 097 points) are enough for a good renderingsin_soixante=sqrt(3)/2;// sin(60°)l=1;// length of the initial line (arbitrary unit)// ******************// * initialisation *// ******************// *************// * functions *// *************function[]=vonkoch(A, B, i)u=(B-A)/3;// third of the AB vectorv=[0.5*u(1)-sin_soixante*u(2);sin_soixante*u(1)+0.5*u(2)];// vector turned by +60°C=A+u;D=C+v;E=B-u;// points of the lineifi==1then// drawing the smallest segmentsx=[A(1);C(1);D(1);E(1);B(1)];y=[A(2);C(2);D(2);E(2);B(2)];xpoly(x,y,"lines")elsej=i-1;vonkoch(A,C,j);vonkoch(C,D,j);vonkoch(D,E,j);vonkoch(E,B,j);// recursive callendendfunction// ****************// * main program *// ****************beginning=[0;0];ending=[l;0];vonkoch(beginning,ending,n)isoview(0,l,0,sin_soixante*l)// Saving the filename="von_koch_"+string(n)+"_steps.svg";xs2svg(0,name)
Licenciranje
Ja, vlasnik autorskog prava ovog djela, ovdje ga objavljujem pod sljedećim licencama:
Dopušteno je umnožavanje, dijeljenje i mijenjanje ovog dokumenta pod uslovima GNU-ove licence za slobodnu dokumentaciju, verzije 1.2 ili bilo koje novije koju objavi Fondacija za slobodni softver; bez nepromjenljivih odjeljaka i bez tekstova na naslovnoj i zadnjoj strani. Tekst licence možete pročitati ovdje.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue
dijeliti – umnožavati, raspodjeljivati i prenositi djelo
prerađivati – prilagođavati djelo
Pod sljedećim uslovima:
pripisivanje – Morate pripisati odgovarajuće autorske zasluge, osigurati link ka licenci i naznačiti jesu li napravljene izmjene. To možete uraditi na bilo koji razumni način, ali ne tako da se sugerira da davalac licence odobrava Vas ili Vašu upotrebu njegovog djela.
dijeljenje pod istim uslovima – Ako mijenjate, transformišete ili nadograđujete ovaj materijal, morate ga objaviti i distribuirati samo pod istom ili sličnom licencom poput ove.
Ova oznaka licence je dodana na ovu datoteku kao dio GFDL ažuriranja licence.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue
Možete odabrati licencu po vašem izboru.
Opisi
Dodajte objašnjenje u jednom redu što predstavlja ova datoteka
{{Information |Description= {{en|von Koch snow flake curve after 6 steps; created with Scilab, transformed into SVG by pstoedit, layout by Inkscape}} {{fr|Courbe du flocon de neige de von Koch après 6 étapes ; créé avec Scilab, transformé en SVG avec
Ova datoteka sadrži dodatne podatke koje je vjerovatno dodala digitalna kamera ili skener tokom snimanja ili digitalizacije. Ako je datoteka mijenjana, podaci možda nisu u skladu sa stvarnim stanjem.