//----------------------------------------------------------------------------- // Fraktaly v pocitacove grafice // Autor: Pavel Tisnovsky // // Vykresleni jednoduchych obrazcu pomoci systemu iterovanych funkci IFS // s vyuzitim modifikovaneho algoritmu nahodne prochazky // (M-RWA - Modified Random Walk Algorithm). // Pixmapu s vykreslenym fraktalem je mozne ulozit do souboru ve formatu TGA // pomoci klavesove zkratky [S]. Zmena typu IFS se provadi stiskem klaves [0]-[9]. // Ukonceni aplikace se provede klavesou [Esc] nebo klavesou [Q]. //----------------------------------------------------------------------------- #ifdef __BORLANDC__ #include #endif #include // hlavickovy soubor funkci GLUTu a OpenGL #include #include #include #include #define WINDOW_TITLE "Fraktaly 33.2" // titulek okna #define WINDOW_WIDTH 640 // pocatecni velikost okna #define WINDOW_HEIGHT 480 #define FILE_NAME "fraktaly332.tga" // jmeno souboru pro ulozeni pixmapy #define PIXMAP_WIDTH 512 // sirka pixmapy #define PIXMAP_HEIGHT 384 // vyska pixmapy typedef struct { // struktura popisujici pixmapu unsigned int width; unsigned int height; unsigned char *pixels; } pixmap; typedef enum { IterPutPixel, IterAddPixel, TransfPutPixel, TransfAddPixel } DrawType; float IFS_triangle[][7]={ // Sierpinskeho trojuhelnik { 0.5000, 0.0000, 0.0000, 0.5000, 0.0000, 0.0000, 0.33}, { 0.5000, 0.0000, 0.0000, 0.5000, 0.0000, 1.0000, 0.33}, { 0.5000, 0.0000, 0.0000, 0.5000, 1.0000, 1.0000, 0.34} }; float IFS_tree[][7]={ // binarni strom { 0.0000, 0.0000, 0.0000, 0.5000, 0.0000, 0.0000, 0.05}, { 0.4200, -0.4200, 0.4200, 0.4200, 0.0000, 0.2000, 0.40}, { 0.4200, 0.4200, -0.4200, 0.4200, 0.0000, 0.2000, 0.40}, { 0.1000, 0.0000, 0.0000, 0.1000, 0.0000, 0.2000, 1.00} }; float IFS_spiral[][7]={ // sobepodobna spirala { 0.8265, -0.4750, 0.4750, 0.8265, 0.0000, 0.0000, 0.90}, { 0.1740, -0.1000, 0.1000, 0.1740, 0.2000, 1.0000, 1.00} }; float IFS_spiral2[][7]={ // dalsi typ spiraly { 0.6250, 0.3750, -0.3750, 0.6250, -1.8679, 1.8787, 0.68}, { 0.0000, 0.2500, -0.2500, 0.1250, -4.4305, 7.9701, 0.08}, { 0.2500, -0.1250, 0.0000, 0.2500, -2.9603, 0.5506, 0.08}, { 0.0000, -0.2500, 0.2500, -0.1250, 4.4592, 2.0208, 0.08}, {-0.2500, 0.1250, 0.0000, -0.2500, 2.9890, 9.4403, 1.00} }; float IFS_dragon[][7]={ // fraktalni drak { 0.8241, 0.2815, -0.2123, 0.8642, -1.8823, -0.1106, 0.79}, { 0.0883, 0.5210, -0.4639, -0.3778, 0.7854, 8.0958, 1.00} }; float IFS_swirl[][7]={ // spiralni kvet { 0.7455, -0.4591, 0.4061, 0.8871, 1.4603, 0.6911, 0.91}, {-0.4242, -0.0652, -0.1758, -0.2182, 3.8096, 6.7415, 1.00} }; float IFS_crystal[][7]={ // krystalicka struktura { 0.6970, -0.4811, -0.3940, -0.6629, 2.1470, 10.3103, 0.75}, { 0.0910, -0.4432, 0.5152, -0.0947, 4.2866, 2.9258, 1.00} }; float IFS_ferny[][7]={ // kapradina {-0.1600, -0.6400, 0.4338, -0.1108, 5.2646, 8.1113, 0.32}, { 0.6031, 0.3354, -0.2800, 0.8800, -2.7575, -0.7991, 1.00} }; float IFS_Z[][7]={ // kaligraficke pismeno Z {-0.5481, -0.1811, 0.2573, -1.0159, 0.8180, 10.5785, 0.84}, {-0.1351, -0.4328, 0.1471, -0.3483, 2.1105, 3.2618, 1.00} }; float IFS_fern[][7]={ // kapradina Michaela Barnsleye { 0.0000, 0.0000, 0.0000, 0.1600, 0.0000, 0.0000, 0.01}, { 0.2000, -0.2600, 0.2300, 0.2200, 0.0000, 1.6000, 0.07}, {-0.1500, 0.2800, 0.2600, 0.2400, 0.0000, 0.4400, 0.08}, { 0.8500, 0.0400, -0.0400, 0.8500, 0.0000, 1.6000, 1.00} }; pixmap *pixIFS; // pixmapa pro obrazek IFS fraktalu int ifs=4; // cislo systemu iterovanych funkci int maxiter=1000; // maximalni pocet iteraci int rf=1, gf=1, bf=1; // priznaky barvovych slozek int deltar=1, deltag=1, deltab=1; // prirustky barvovych slozek double scale=30.0; // meritko fraktalu double xpos=0.0; // posun fraktalu double ypos=-150.0; // posun fraktalu int redraw=1; DrawType drawType=IterPutPixel; //----------------------------------------------------------------------------- // Funkce pro vytvoreni pixmapy o zadane velikosti //----------------------------------------------------------------------------- pixmap * createPixmap(const unsigned int width, const unsigned int height) { pixmap *p=(pixmap *)malloc(sizeof(pixmap)); // alokace struktury pixmapy if (!p) return NULL; p->width=width; // naplneni struktury p->height=height; p->pixels=(unsigned char *)malloc(3*width*height); if (!p->pixels) { // alokace pole pro pixely free(p); // alokace se nepovedla return NULL; } else { memset(p->pixels, 0, 3*width*height); // smazani pixmapy } return p; } //----------------------------------------------------------------------------- // Funkce pro zruseni pixmapy //----------------------------------------------------------------------------- void destroyPixmap(pixmap *p) { if (p->pixels) free(p->pixels); // uvolnit vlastni pixmapu if (p) free(p); // i okolni strukturu } //----------------------------------------------------------------------------- // Vymazani pixmapy //----------------------------------------------------------------------------- void clearPixmap(const pixmap *p) { if (!p) return; if (!p->pixels) return; memset(p->pixels, 0, 3*p->width*p->height); } //----------------------------------------------------------------------------- // Funkce pro vykresleni pixmapy do barvoveho bufferu //----------------------------------------------------------------------------- void drawPixmap(const pixmap *p) { if (!p || !p->pixels) return; glDrawPixels( // vykresleni pixmapy p->width, p->height, // sirka a vyska pixmapy GL_RGB, // format dat pixelu GL_UNSIGNED_BYTE, // datovy typ kazde barevne slozky p->pixels); // ukazatel na pamet s barvami pixelu } //----------------------------------------------------------------------------- // Ulozeni pixmapy do externiho souboru //----------------------------------------------------------------------------- void savePixmap(const pixmap *p, const char *fileName) { FILE *fout; unsigned int i, j, k; unsigned char tgaHeader[18]={ // hlavicka formatu typu TGA 0x00, // typ hlavicky TGA 0x00, // nepouzivame paletu 0x02, // typ obrazku je RGB TrueColor 0x00, 0x00, // delka palety je nulova 0x00, 0x00, 0x00, // pozice v palete nas nezajima 0x00, 0x00, 0x00, 0x00, // obrazek je umisteny na pozici [0, 0] 0x00, 0x00, 0x00, 0x00, // sirka a vyska obrazku (dva byty na polozku) 0x18, // format je 24 bitu na pixel 0x20 // orientace bitmapy v obrazku }; if (!p || !p->pixels) return; memcpy(tgaHeader+12, &(p->width), 2); // do hlavicky TGA zapsat velikost obrazku memcpy(tgaHeader+14, &(p->height), 2); fout=fopen(fileName, "wb"); if (fout) { fwrite(tgaHeader, 18, 1, fout); // zapsat hlavicku TGA do souboru for (j=p->height; j; j--) { // radky zapisovat v opacnem poradi unsigned int yoff=(j-1)*3*p->width; // y-ovy offset v poli unsigned int xoff=0; // x-ovy offset v poli for (i=0; iwidth; i++) { // pro kazdy pixel na radku for (k=0; k<3; k++) { // prohodit barvy RGB na BGR fputc(p->pixels[xoff+yoff+2-k], fout); // a zapsat do souboru } xoff+=3; // posun na dalsi pixel } } fclose(fout); } } //----------------------------------------------------------------------------- // Zmena barvy pixelu na zadanych souradnicich //----------------------------------------------------------------------------- void putpixel(pixmap *p, const unsigned int x, // pozice pixelu v pixmape const unsigned int y, const unsigned char r, // barva pixelu const unsigned char g, const unsigned char b) { int pos; // zde se vyuziva zkraceneho vyhodnoceni vyrazu - pokud plati !p, nic se dale netestuje if (!p || !p->pixels || x>=p->width || y>=p->height) return; pos=3*(x+y*p->width); p->pixels[pos++]=r; // nastaveni barvy pixelu p->pixels[pos++]=g; p->pixels[pos]=b; } //----------------------------------------------------------------------------- // Prirustek barvy pixelu na zadanych souradnicich //----------------------------------------------------------------------------- void addpixel(pixmap *p, const unsigned int x, const unsigned int y, const unsigned char dr, const unsigned char dg, const unsigned char db) { int pos; // zde se vyuziva zkraceneho vyhodnoceni vyrazu - pokud plati !p, nic se dale netestuje if (!p || !p->pixels || x>=p->width || y>=p->height) return; pos=3*(x+y*p->width); if (p->pixels[pos]<256-dr) p->pixels[pos]+=dr;// nastaveni cervene slozky barvy pixelu pos++; if (p->pixels[pos]<256-dg) p->pixels[pos]+=dg;// nastaveni zelene slozky barvy pixelu pos++; if (p->pixels[pos]<256-db) p->pixels[pos]+=db;// nastaveni modre slozky barvy pixelu } //----------------------------------------------------------------------------- // Prekresleni systemu iterovanych funkci IFS pomoci algoritmu M-RWA. // Bod x(n) je vybiran na zaklade pravdepodobnosti jednotlivych transformaci. //----------------------------------------------------------------------------- void recalcIFSusingMRWA(pixmap *pix, // pixmapa pro vykreslovani int maxiter, // maximalni pocet iteraci double scale, // meritko obrazce double xpos, // posun obrazce double ypos, int type, // vybrany IFS system int rf, int gf, int bf, // priznaky barvovych slozek int dr, int dg, int db, // prirustky barvovych slozek DrawType drawType) // zpusob vykresleni { int iter=0; // pocitadlo iteraci int threshold=50; // hranice poctu iteraci pro vykreslovani float x, y, hlp; // poloha iterovaneho bodu float pp; // pravdepodobnost pro vyber transformace float sum; int k; // cislo vybrane transformace int maxTransf; // maximalni pocet transformaci float (*t)[][7]; // ukazatel na vybranou mnozinu transformaci unsigned char red=rf ? dr : 0; // realne prirustky barvovych slozek unsigned char green=gf ? dg : 0; unsigned char blue=bf ? db : 0; unsigned char pal[8][3]={ {0xff, 0x00, 0x00}, {0x00, 0xff, 0x00}, {0x00, 0x00, 0xff}, {0xff, 0xff, 0x00}, {0x00, 0xff, 0xff}, {0xff, 0x00, 0xff}, {0xff, 0xff, 0xff}, {0x80, 0x80, 0x80}, }; switch (type) { // vyber IFS systemu case 0: t=&IFS_triangle; break; case 1: t=&IFS_tree; break; case 2: t=&IFS_spiral; break; case 3: t=&IFS_spiral2; break; case 4: t=&IFS_dragon; break; case 5: t=&IFS_swirl; break; case 6: t=&IFS_crystal; break; case 7: t=&IFS_Z; break; case 8: t=&IFS_ferny; break; case 9: t=&IFS_fern; break; default:t=&IFS_spiral; break; } x=0; y=0; // nastaveni pocatecni polohy bodu srand(0); xpos+=pix->width/2; // posun do stredu okna ypos+=pix->height/2; // pomocna smycka, ve ktere se zjisti pocet transformaci for (sum=0.0, maxTransf=0; sum<1.0; sum+=(*t)[maxTransf][6], maxTransf++) ; while (iter++threshold) { // je-li dosazeno hranice iteraci switch (drawType) { // vyber vykreslovaciho rezimu case IterPutPixel: putpixel(pix, xn*scale+xpos, yn*scale+ypos, rf ? 0xff:0x00, gf ? 0xff:0x00, bf ? 0xff:0x00); break; case IterAddPixel: addpixel(pix, xn*scale+xpos, yn*scale+ypos, red, green, blue); break; case TransfPutPixel: putpixel(pix, xn*scale+xpos, yn*scale+ypos, pal[k&7][0], pal[k&7][1], pal[k&7][2]); break; case TransfAddPixel: addpixel(pix, xn*scale+xpos, yn*scale+ypos, (!!pal[k&7][0])*dr, (!!pal[k&7][1])*dg, (!!pal[k&7][2])*db); break; default: break; } } } // nalezeni jedne transformace pro dalsi iteraci // na zaklade pravdepodobnosti jednotlivych transformaci pp=((float)rand())/RAND_MAX; // p lezi v rozsahu 0.0-1.0 k=0; // promenna cyklu vyhledani transformace sum=0; while (sum<=pp) { // podle nahodneho cisla sum=sum+(*t)[k][6]; // vybrat transformaci k++; } // k urcuje index transformace k--; // uprava ze smycky while hlp=(*t)[k][0]*x+(*t)[k][1]*y+(*t)[k][4]; // provedeni y =(*t)[k][2]*x+(*t)[k][3]*y+(*t)[k][5]; // transformace x =hlp; } } //----------------------------------------------------------------------------- // Vykresleni retezce na obrazovku //----------------------------------------------------------------------------- void drawString(const int x, const int y, // umisteni retezce const float r, const float g, const float b, // barva pisma char *str) // ukazatel na retezec { char *c; glColor3f(r, g, b); glRasterPos2i(x, y); for (c=str; *c!=0; c++) { glutBitmapCharacter(GLUT_BITMAP_9_BY_15, *c); } } //----------------------------------------------------------------------------- // Vypis informaci o vykreslovanem fraktalu //----------------------------------------------------------------------------- void drawInfo(int maxiter, double xpos, double ypos, double scale, int ifs, int r, int g, int b, int deltar, int deltag, int deltab, DrawType drawType) { #define drawString2(x, y, r, g, b, str) drawString((x)+1, (y), 0.0, 0.0, 0.0, (str)); drawString((x), (y)+1, (r), (g), (b), (str)); char str[100]; char *ifsNames[10]={ "Sierpinski", "Tree", "Spiral 1", "Spiral 2", "Dragon", "Swirl", "Crystal", "Z", "Ferny", "Fern", }; sprintf(str, "[0]-[9] IFS type = %s", ifsNames[ifs]); drawString2( 10, 96, 0.0, 1.0, 1.0, str); sprintf(str, "[F1] draw: IterPutPixel: %s", drawType==IterPutPixel ? "set":""); drawString2( 10, 80, 0.2, 1.0, 0.8, str); sprintf(str, "[F2] draw: IterAddPixel: %s", drawType==IterAddPixel ? "set":""); drawString2( 10, 64, 0.4, 1.0, 0.6, str); sprintf(str, "[F3] draw: TransfPutPixel: %s", drawType==TransfPutPixel ? "set":""); drawString2( 10, 48, 0.6, 1.0, 0.4, str); sprintf(str, "[F4] draw: TransfAddPixel: %s", drawType==TransfAddPixel ? "set":""); drawString2( 10, 32, 0.8, 1.0, 0.2, str); sprintf(str, "[<][>][,][.] maxiter = %d", maxiter*10); drawString2( 10, 16, 1.0, 1.0, 0.0, str); sprintf(str, "[PgUp][PgDn] scale = %4.2f ", scale); drawString2(320, 96, 1.0, 0.0, 1.0, str); sprintf(str, "[Arrows] pan = %5.3f, %5.3f", xpos, ypos); drawString2(320, 80, 0.8, 0.2, 1.0, str); sprintf(str, "[R][G][B] colors = %d %d %d", r, g, b); drawString2(320, 64, 0.6, 0.4, 1.0, str); sprintf(str, "[F5][F6] delta R = %d", deltar); drawString2(320, 48, 0.4, 0.6, 1.0, str); sprintf(str, "[F7][F8] delta G = %d", deltag); drawString2(320, 32, 0.2, 0.8, 1.0, str); sprintf(str, "[F9][F10] delta B = %d", deltab); drawString2(320, 16, 0.0, 1.0, 1.0, str); } //----------------------------------------------------------------------------- // Funkce volana pro inicializaci vykreslovani //----------------------------------------------------------------------------- void onInit(void) { glClearColor(0.0f, 0.0f, 0.0f, 0.0f); // barva pozadi glPixelStorei(GL_UNPACK_ALIGNMENT, 1); // mod ulozeni pixelu pixIFS=createPixmap(PIXMAP_WIDTH, PIXMAP_HEIGHT); } //----------------------------------------------------------------------------- // Nastaveni souradneho systemu v zavislosti na velikosti okna //----------------------------------------------------------------------------- void onResize(int w, int h) // argumenty w a h reprezentuji novou velikost okna { glViewport(0, 0, w, h); // viditelna oblast pres cele okno glMatrixMode(GL_PROJECTION); // zacatek modifikace projekcni matice glLoadIdentity(); // vymazani projekcni matice (=identita) glOrtho(0, w, 0, h, -1, 1); // mapovani abstraktnich souradnic do souradnic okna } //----------------------------------------------------------------------------- // Tato callback funkce je zavolana pri kazdem prekresleni okna //----------------------------------------------------------------------------- void onDisplay(void) { glClear(GL_COLOR_BUFFER_BIT); // vymazani vsech bitovych rovin barvoveho bufferu glDrawBuffer(GL_BACK); // pixmapa se bude kreslit do zadniho barvoveho bufferu if (redraw) { clearPixmap(pixIFS); recalcIFSusingMRWA(pixIFS, maxiter, scale, xpos, ypos, ifs, rf, gf, bf, deltar, deltag, deltab, drawType);// prepocet fraktalu redraw=0; } glRasterPos2i(0, WINDOW_HEIGHT-PIXMAP_HEIGHT); // nastaveni souradnic leveho spodniho rohu pixmapy drawPixmap(pixIFS); // vykresleni pixmapy glRasterPos2i(0, 0); drawInfo(maxiter, xpos, ypos, scale, ifs, rf, gf, bf, deltar, deltag, deltab, drawType); glFlush(); // provedeni a vykresleni vsech zmen glutSwapBuffers(); } //----------------------------------------------------------------------------- // Tato callback funkce je zavolana pri stlaceni ASCII klavesy //----------------------------------------------------------------------------- #ifdef __BORLANDC__ #pragma option -w-par #endif void onKeyboard(unsigned char key, int x, int y) { key=(key>='A' && key<='Z') ? key-'A'+'a': key; if (key>='0' && key<='9') { ifs=key-'0'; redraw=1; glutPostRedisplay(); } // nastaveni barvove palety switch (key) { case 27: // pokud byla stlacena klavesa ESC, konec programu case 'q': exit(0); break; // totez co klavesa ESC case 's': savePixmap(pixIFS, FILE_NAME); break; // ulozeni pixmapy case '<': if (maxiter>1000) maxiter-=1000; redraw=1; glutPostRedisplay(); break; case ',': if (maxiter>100) maxiter-=100; redraw=1; glutPostRedisplay(); break; // zmena poctu iteraci case '>': maxiter+=1000; redraw=1; glutPostRedisplay(); break; case '.': maxiter+=100; redraw=1; glutPostRedisplay(); break; case 'r': rf=!rf; redraw=1; glutPostRedisplay(); break; // priznaky barvovych slozek case 'g': gf=!gf; redraw=1; glutPostRedisplay(); break; case 'b': bf=!bf; redraw=1; glutPostRedisplay(); break; default: break; } } #ifdef __BORLANDC__ #pragma option -w+par #endif //----------------------------------------------------------------------------- // Tato callback funkce je zavolana pri stlaceni non-ASCII klavesy //----------------------------------------------------------------------------- #ifdef __BORLANDC__ #pragma option -w-par #endif void onSpecial(int key, int x, int y) { // posun fraktalu a zmena meritka switch (key) { case GLUT_KEY_LEFT: xpos-=5; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_RIGHT: xpos+=5; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_UP: ypos+=5; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_DOWN: ypos-=5; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_PAGE_UP: scale*=1.1; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_PAGE_DOWN: if (scale>1) scale/=1.1; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F1: drawType=IterPutPixel; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F2: drawType=IterAddPixel; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F3: drawType=TransfPutPixel; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F4: drawType=TransfAddPixel; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F5: if (deltar>1) deltar--; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F6: deltar++; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F7: if (deltag>1) deltag--; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F8: deltag++; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F9: if (deltab>1) deltab--; redraw=1; glutPostRedisplay(); break; case GLUT_KEY_F10: deltab++; redraw=1; glutPostRedisplay(); break; default: break; } } #ifdef __BORLANDC__ #pragma option -w+par #endif //----------------------------------------------------------------------------- // Hlavni funkce konzolove aplikace //----------------------------------------------------------------------------- int main(int argc, char **argv) { glutInit(&argc, argv); // inicializace knihovny GLUT glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE); glutCreateWindow(WINDOW_TITLE); // vytvoreni okna pro kresleni glutReshapeWindow(WINDOW_WIDTH, WINDOW_HEIGHT);// zmena velikosti okna glutPositionWindow(100, 100); // pozice leveho horniho rohu okna glutDisplayFunc(onDisplay); // registrace funkce volane pri prekreslovani okna glutReshapeFunc(onResize); // registrace funkce volane pri zmene velikosti okna glutKeyboardFunc(onKeyboard); // registrace funkce volane pri stlaceni klavesy glutSpecialFunc(onSpecial); // registrace funkce volane pri stlaceni specialni klavesy onInit(); // inicializace vykreslovani glutMainLoop(); // nekonecna smycka, kde se volaji zaregistrovane funkce return 0; // navratova hodnota vracena operacnimu systemu } //----------------------------------------------------------------------------- // finito //-----------------------------------------------------------------------------