1610 lines
49 KiB
C
1610 lines
49 KiB
C
/*********************/
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/* Graphics routines */
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/*********************/
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int writetiff(char *filename, char *description, int x, int y, int width, int height, int compression)
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{
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TIFF *file;
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GLubyte *image, *p;
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int i;
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file = TIFFOpen(filename, "w");
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if (file == NULL)
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{
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return 1;
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}
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image = (GLubyte *) malloc(width * height * sizeof(GLubyte) * 3);
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/* OpenGL's default 4 byte pack alignment would leave extra bytes at the
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end of each image row so that each full row contained a number of bytes
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divisible by 4. Ie, an RGB row with 3 pixels and 8-bit componets would
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be laid out like "RGBRGBRGBxxx" where the last three "xxx" bytes exist
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just to pad the row out to 12 bytes (12 is divisible by 4). To make sure
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the rows are packed as tight as possible (no row padding), set the pack
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alignment to 1. */
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glPixelStorei(GL_PACK_ALIGNMENT, 1);
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glReadPixels(x, y, width, height, GL_RGB, GL_UNSIGNED_BYTE, image);
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TIFFSetField(file, TIFFTAG_IMAGEWIDTH, (uint32) width);
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TIFFSetField(file, TIFFTAG_IMAGELENGTH, (uint32) height);
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TIFFSetField(file, TIFFTAG_BITSPERSAMPLE, 8);
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TIFFSetField(file, TIFFTAG_COMPRESSION, compression);
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TIFFSetField(file, TIFFTAG_PHOTOMETRIC, PHOTOMETRIC_RGB);
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TIFFSetField(file, TIFFTAG_ORIENTATION, ORIENTATION_BOTLEFT);
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TIFFSetField(file, TIFFTAG_SAMPLESPERPIXEL, 3);
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TIFFSetField(file, TIFFTAG_PLANARCONFIG, PLANARCONFIG_CONTIG);
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TIFFSetField(file, TIFFTAG_ROWSPERSTRIP, 1);
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TIFFSetField(file, TIFFTAG_IMAGEDESCRIPTION, description);
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p = image;
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for (i = height - 1; i >= 0; i--)
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{
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// if (TIFFWriteScanline(file, p, height - i - 1, 0) < 0)
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if (TIFFWriteScanline(file, p, i, 0) < 0)
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{
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free(image);
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TIFFClose(file);
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return 1;
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}
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p += width * sizeof(GLubyte) * 3;
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}
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TIFFClose(file);
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return 0;
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}
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void init() /* initialisation of window */
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{
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glLineWidth(3);
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glClearColor(0.0, 0.0, 0.0, 1.0);
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glClear(GL_COLOR_BUFFER_BIT);
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// glOrtho(XMIN, XMAX, YMIN, YMAX , -1.0, 1.0);
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glOrtho(0.0, NX, 0.0, NY, -1.0, 1.0);
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}
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void hsl_to_rgb(double h, double s, double l, double rgb[3]) /* color conversion from HSL to RGB */
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/* h = hue, s = saturation, l = luminosity */
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{
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double c = 0.0, m = 0.0, x = 0.0;
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c = (1.0 - fabs(2.0 * l - 1.0)) * s;
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m = 1.0 * (l - 0.5 * c);
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x = c * (1.0 - fabs(fmod(h / 60.0, 2) - 1.0));
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if (h >= 0.0 && h < 60.0)
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{
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rgb[0] = c+m; rgb[1] = x+m; rgb[2] = m;
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}
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else if (h < 120.0)
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{
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rgb[0] = x+m; rgb[1] = c+m; rgb[2] = m;
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}
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else if (h < 180.0)
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{
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rgb[0] = m; rgb[1] = c+m; rgb[2] = x+m;
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}
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else if (h < 240.0)
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{
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rgb[0] = m; rgb[1] = x+m; rgb[2] = c+m;
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}
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else if (h < 300.0)
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{
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rgb[0] = x+m; rgb[1] = m; rgb[2] = c+m;
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}
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else if (h < 360.0)
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{
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rgb[0] = c+m; rgb[1] = m; rgb[2] = x+m;
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}
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else
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{
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rgb[0] = m; rgb[1] = m; rgb[2] = m;
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}
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}
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double color_amplitude(double value, double scale, int time)
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/* transforms the wave amplitude into a double in [-1,1] to feed into color scheme */
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{
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return(tanh(SLOPE*value/scale)*exp(-((double)time*ATTENUATION)));
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}
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void color_scheme(int scheme, double value, double scale, int time, double rgb[3]) /* color scheme */
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{
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double hue, y, r, amplitude;
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int intpart;
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/* saturation = r, luminosity = y */
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switch (scheme) {
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case (C_LUM):
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{
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hue = COLORHUE + (double)time*COLORDRIFT/(double)NSTEPS;
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if (hue < 0.0) hue += 360.0;
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if (hue >= 360.0) hue -= 360.0;
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r = 0.9;
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amplitude = color_amplitude(value, scale, time);
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y = LUMMEAN + amplitude*LUMAMP;
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intpart = (int)y;
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y -= (double)intpart;
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hsl_to_rgb(hue, r, y, rgb);
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break;
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}
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case (C_HUE):
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{
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r = 0.9;
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amplitude = color_amplitude(value, scale, time);
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y = 0.5;
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hue = HUEMEAN + amplitude*HUEAMP;
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if (hue < 0.0) hue += 360.0;
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if (hue >= 360.0) hue -= 360.0;
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hsl_to_rgb(hue, r, y, rgb);
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break;
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}
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}
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}
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void blank()
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{
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if (BLACK) glClearColor(0.0, 0.0, 0.0, 1.0);
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else glClearColor(1.0, 1.0, 1.0, 1.0);
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glClear(GL_COLOR_BUFFER_BIT);
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}
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void save_frame()
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{
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static int counter = 0;
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char *name="wave.", n2[100];
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char format[6]=".%05i";
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counter++;
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// printf (" p2 counter = %d \n",counter);
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strcpy(n2, name);
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sprintf(strstr(n2,"."), format, counter);
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strcat(n2, ".tif");
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printf(" saving frame %s \n",n2);
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writetiff(n2, "Wave equation in a planar domain", 0, 0,
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WINWIDTH, WINHEIGHT, COMPRESSION_LZW);
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}
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void save_frame_counter(int counter)
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/* same as save_frame, but with imposed image number (for option DOUBLE_MOVIE) */
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{
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char *name="wave.", n2[100];
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char format[6]=".%05i";
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strcpy(n2, name);
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sprintf(strstr(n2,"."), format, counter);
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strcat(n2, ".tif");
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printf(" saving frame %s \n",n2);
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writetiff(n2, "Wave equation in a planar domain", 0, 0,
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WINWIDTH, WINHEIGHT, COMPRESSION_LZW);
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}
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void write_text( double x, double y, char *st)
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{
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int l,i;
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l=strlen( st ); // see how many characters are in text string.
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glRasterPos2d( x, y); // location to start printing text
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for( i=0; i < l; i++) // loop until i is greater then l
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{
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glutBitmapCharacter(GLUT_BITMAP_TIMES_ROMAN_24, st[i]); // Print a character on the screen
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// glutBitmapCharacter(GLUT_BITMAP_8_BY_13, st[i]); // Print a character on the screen
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}
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}
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/*********************/
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/* some basic math */
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/*********************/
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double vabs(double x) /* absolute value */
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{
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double res;
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if (x<0.0) res = -x;
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else res = x;
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return(res);
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}
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double module2(double x, double y) /* Euclidean norm */
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{
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double m;
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m = sqrt(x*x + y*y);
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return(m);
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}
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double argument(double x, double y)
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{
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double alph;
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if (x!=0.0)
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{
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alph = atan(y/x);
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if (x<0.0)
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alph += PI;
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}
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else
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{
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alph = PID;
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if (y<0.0)
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alph = PI*1.5;
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}
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return(alph);
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}
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/*********************/
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/* drawing routines */
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/*********************/
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/* The billiard boundary is drawn in (x,y) coordinates */
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/* However for the grid points, we use integer coordinates (i,j) */
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/* GL would allow to always work in (x,y) coordinates but using both */
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/* sets of coordinates decreases number of double computations when */
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/* drawing the field */
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void xy_to_ij(double x, double y, int ij[2])
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/* convert (x,y) position to (i,j) in table representing wave */
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{
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double x1, y1;
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x1 = (x - XMIN)/(XMAX - XMIN);
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y1 = (y - YMIN)/(YMAX - YMIN);
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ij[0] = (int)(x1 * (double)NX);
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ij[1] = (int)(y1 * (double)NY);
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}
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void xy_to_pos(double x, double y, double pos[2])
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/* convert (x,y) position to double-valued position in table representing wave */
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{
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double x1, y1;
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x1 = (x - XMIN)/(XMAX - XMIN);
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y1 = (y - YMIN)/(YMAX - YMIN);
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pos[0] = x1 * (double)NX;
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pos[1] = y1 * (double)NY;
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}
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void ij_to_xy(int i, int j, double xy[2])
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/* convert (i,j) position in table representing wave to (x,y) */
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{
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double x1, y1;
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xy[0] = XMIN + ((double)i)*(XMAX-XMIN)/((double)NX);
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xy[1] = YMIN + ((double)j)*(YMAX-YMIN)/((double)NY);
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}
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void erase_area(double x, double y, double dx, double dy)
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{
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double pos[2], rgb[3];
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hsl_to_rgb(220.0, 0.8, 0.7, rgb);
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glBegin(GL_QUADS);
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xy_to_pos(x - dx, y - dy, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x + dx, y - dy, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x + dx, y + dy, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x - dx, y + dy, pos);
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glVertex2d(pos[0], pos[1]);
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glEnd();
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}
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void erase_area_rgb(double x, double y, double dx, double dy, double rgb[3])
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{
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double pos[2];
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glBegin(GL_QUADS);
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xy_to_pos(x - dx, y - dy, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x + dx, y - dy, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x + dx, y + dy, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x - dx, y + dy, pos);
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glVertex2d(pos[0], pos[1]);
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glEnd();
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}
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void erase_area_hsl(double x, double y, double dx, double dy, double h, double s, double l)
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{
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double pos[2], rgb[3];
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hsl_to_rgb(h, s, l, rgb);
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erase_area_rgb(x, y, dx, dy, rgb);
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}
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void draw_rectangle(double x1, double y1, double x2, double y2)
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{
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double pos[2];
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glBegin(GL_LINE_LOOP);
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xy_to_pos(x1, y1, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x2, y1, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x2, y2, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(x1, y2, pos);
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glVertex2d(pos[0], pos[1]);
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glEnd();
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}
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void draw_rotated_rectangle(double x1, double y1, double x2, double y2)
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{
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double pos[2];
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double xa, ya, xb, yb, xc, yc;
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xa = 0.5*(x1 - y2);
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xb = 0.5*(x2 - y1);
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xc = 0.5*(x1 - y1);
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ya = 0.5*(x1 + y1);
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yb = 0.5*(x2 + y2);
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yc = 0.5*(x2 + y1);
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glBegin(GL_LINE_LOOP);
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xy_to_pos(xc, ya, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(xb, yc, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(xc, yb, pos);
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glVertex2d(pos[0], pos[1]);
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xy_to_pos(xa, yc, pos);
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glVertex2d(pos[0], pos[1]);
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glEnd();
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}
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void draw_circle(double x, double y, double r, int nseg)
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{
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int i;
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double pos[2], alpha, dalpha;
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dalpha = DPI/(double)nseg;
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glBegin(GL_LINE_LOOP);
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for (i=0; i<=nseg; i++)
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{
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alpha = (double)i*dalpha;
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xy_to_pos(x + r*cos(alpha), y + r*sin(alpha), pos);
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glVertex2d(pos[0], pos[1]);
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}
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glEnd();
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}
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void draw_colored_circle(double x, double y, double r, int nseg, double rgb[3])
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{
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int i;
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double pos[2], alpha, dalpha;
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dalpha = DPI/(double)nseg;
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glColor3f(rgb[0], rgb[1], rgb[2]);
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glBegin(GL_TRIANGLE_FAN);
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xy_to_pos(x, y, pos);
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glVertex2d(pos[0], pos[1]);
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for (i=0; i<=nseg; i++)
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{
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alpha = (double)i*dalpha;
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xy_to_pos(x + r*cos(alpha), y + r*sin(alpha), pos);
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glVertex2d(pos[0], pos[1]);
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}
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glEnd();
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}
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void init_circle_config()
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/* initialise the arrays circlex, circley, circlerad and circleactive */
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/* for billiard shape D_CIRCLES */
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{
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int i, j, k, n, ncirc0, n_p_active, ncandidates=5000, naccepted;
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double dx, dy, p, phi, r, r0, ra[5], sa[5], height, x, y = 0.0, gamma, dpoisson = 3.25*MU;
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short int active_poisson[NMAXCIRCLES], far;
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switch (CIRCLE_PATTERN) {
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case (C_SQUARE):
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{
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ncircles = NGRIDX*NGRIDY;
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dy = (YMAX - YMIN)/((double)NGRIDY);
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for (i = 0; i < NGRIDX; i++)
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for (j = 0; j < NGRIDY; j++)
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{
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n = NGRIDY*i + j;
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circlex[n] = ((double)(i-NGRIDX/2) + 0.5)*dy;
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circley[n] = YMIN + ((double)j + 0.5)*dy;
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circlerad[n] = MU;
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circleactive[n] = 1;
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}
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break;
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}
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case (C_HEX):
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{
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ncircles = NGRIDX*(NGRIDY+1);
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dy = (YMAX - YMIN)/((double)NGRIDY);
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dx = dy*0.5*sqrt(3.0);
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for (i = 0; i < NGRIDX; i++)
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for (j = 0; j < NGRIDY+1; j++)
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{
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n = (NGRIDY+1)*i + j;
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circlex[n] = ((double)(i-NGRIDX/2) + 0.5)*dy; /* is +0.5 needed? */
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circley[n] = YMIN + ((double)j - 0.5)*dy;
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if ((i+NGRIDX)%2 == 1) circley[n] += 0.5*dy;
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circlerad[n] = MU;
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/* activate only circles that intersect the domain */
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if ((circley[n] < YMAX + MU)&&(circley[n] > YMIN - MU)) circleactive[n] = 1;
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else circleactive[n] = 0;
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}
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break;
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}
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case (C_RAND_DISPLACED):
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{
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ncircles = NGRIDX*NGRIDY;
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dy = (YMAX - YMIN)/((double)NGRIDY);
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for (i = 0; i < NGRIDX; i++)
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for (j = 0; j < NGRIDY; j++)
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{
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n = NGRIDY*i + j;
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circlex[n] = ((double)(i-NGRIDX/2) + 0.5*((double)rand()/RAND_MAX - 0.5))*dy;
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circley[n] = YMIN + ((double)j + 0.5 + 0.5*((double)rand()/RAND_MAX - 0.5))*dy;
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circlerad[n] = MU*sqrt(1.0 + 0.8*((double)rand()/RAND_MAX - 0.5));
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circleactive[n] = 1;
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}
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break;
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}
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case (C_RAND_PERCOL):
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{
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ncircles = NGRIDX*NGRIDY;
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dy = (YMAX - YMIN)/((double)NGRIDY);
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for (i = 0; i < NGRIDX; i++)
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for (j = 0; j < NGRIDY; j++)
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{
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n = NGRIDY*i + j;
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circlex[n] = ((double)(i-NGRIDX/2) + 0.5)*dy;
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circley[n] = YMIN + ((double)j + 0.5)*dy;
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circlerad[n] = MU;
|
|
p = (double)rand()/RAND_MAX;
|
|
if (p < P_PERCOL) circleactive[n] = 1;
|
|
else circleactive[n] = 0;
|
|
}
|
|
break;
|
|
}
|
|
case (C_RAND_POISSON):
|
|
{
|
|
ncircles = NPOISSON;
|
|
for (n = 0; n < NPOISSON; n++)
|
|
{
|
|
circlex[n] = LAMBDA*(2.0*(double)rand()/RAND_MAX - 1.0);
|
|
circley[n] = (YMAX - YMIN)*(double)rand()/RAND_MAX + YMIN;
|
|
circlerad[n] = MU;
|
|
circleactive[n] = 1;
|
|
}
|
|
break;
|
|
}
|
|
case (C_CLOAK):
|
|
{
|
|
ncircles = 200;
|
|
for (i = 0; i < 40; i++)
|
|
for (j = 0; j < 5; j++)
|
|
{
|
|
n = 5*i + j;
|
|
phi = (double)i*DPI/40.0;
|
|
r = LAMBDA*0.5*(1.0 + (double)j/5.0);
|
|
circlex[n] = r*cos(phi);
|
|
circley[n] = r*sin(phi);
|
|
circlerad[n] = MU;
|
|
circleactive[n] = 1;
|
|
}
|
|
break;
|
|
}
|
|
case (C_CLOAK_A): /* optimized model A1 by C. Jo et al */
|
|
{
|
|
ncircles = 200;
|
|
ra[0] = 0.0731; sa[0] = 1.115;
|
|
ra[1] = 0.0768; sa[1] = 1.292;
|
|
ra[2] = 0.0652; sa[2] = 1.464;
|
|
ra[3] = 0.056; sa[3] = 1.633;
|
|
ra[4] = 0.0375; sa[4] = 1.794;
|
|
for (i = 0; i < 40; i++)
|
|
for (j = 0; j < 5; j++)
|
|
{
|
|
n = 5*i + j;
|
|
phi = (double)i*DPI/40.0;
|
|
r = LAMBDA*sa[j];
|
|
circlex[n] = r*cos(phi);
|
|
circley[n] = r*sin(phi);
|
|
circlerad[n] = LAMBDA*ra[j];
|
|
circleactive[n] = 1;
|
|
}
|
|
break;
|
|
}
|
|
case (C_POISSON_DISC):
|
|
{
|
|
printf("Generating Poisson disc sample\n");
|
|
/* generate first circle */
|
|
circlex[0] = LAMBDA*(2.0*(double)rand()/RAND_MAX - 1.0);
|
|
circley[0] = (YMAX - YMIN)*(double)rand()/RAND_MAX + YMIN;
|
|
active_poisson[0] = 1;
|
|
n_p_active = 1;
|
|
ncircles = 1;
|
|
|
|
while ((n_p_active > 0)&&(ncircles < NMAXCIRCLES))
|
|
{
|
|
/* randomly select an active circle */
|
|
i = rand()%(ncircles);
|
|
while (!active_poisson[i]) i = rand()%(ncircles);
|
|
// printf("Starting from circle %i at (%.3f,%.3f)\n", i, circlex[i], circley[i]);
|
|
/* generate new candidates */
|
|
naccepted = 0;
|
|
for (j=0; j<ncandidates; j++)
|
|
{
|
|
r = dpoisson*(2.0*(double)rand()/RAND_MAX + 1.0);
|
|
phi = DPI*(double)rand()/RAND_MAX;
|
|
x = circlex[i] + r*cos(phi);
|
|
y = circley[i] + r*sin(phi);
|
|
// printf("Testing new circle at (%.3f,%.3f)\t", x, y);
|
|
far = 1;
|
|
for (k=0; k<ncircles; k++) if ((k!=i))
|
|
{
|
|
/* new circle is far away from circle k */
|
|
far = far*((x - circlex[k])*(x - circlex[k]) + (y - circley[k])*(y - circley[k]) >= dpoisson*dpoisson);
|
|
/* new circle is in domain */
|
|
far = far*(vabs(x) < LAMBDA)*(y < YMAX)*(y > YMIN);
|
|
}
|
|
if (far) /* accept new circle */
|
|
{
|
|
printf("New circle at (%.3f,%.3f) accepted\n", x, y);
|
|
circlex[ncircles] = x;
|
|
circley[ncircles] = y;
|
|
circlerad[ncircles] = MU;
|
|
circleactive[ncircles] = 1;
|
|
active_poisson[ncircles] = 1;
|
|
ncircles++;
|
|
n_p_active++;
|
|
naccepted++;
|
|
}
|
|
// else printf("Rejected\n");
|
|
}
|
|
if (naccepted == 0) /* inactivate circle i */
|
|
{
|
|
// printf("No candidates work, inactivate circle %i\n", i);
|
|
active_poisson[i] = 0;
|
|
n_p_active--;
|
|
}
|
|
printf("%i active circles\n", n_p_active);
|
|
}
|
|
|
|
printf("Generated %i circles\n", ncircles);
|
|
break;
|
|
}
|
|
case (C_GOLDEN_MEAN):
|
|
{
|
|
ncircles = 300;
|
|
gamma = (sqrt(5.0) - 1.0)*0.5; /* golden mean */
|
|
height = YMAX - YMIN;
|
|
dx = 2.0*LAMBDA/((double)ncircles);
|
|
for (n = 0; n < ncircles; n++)
|
|
{
|
|
circlex[n] = -LAMBDA + n*dx;
|
|
circley[n] = y;
|
|
y += height*gamma;
|
|
if (y > YMAX) y -= height;
|
|
circlerad[n] = MU;
|
|
circleactive[n] = 1;
|
|
}
|
|
|
|
/* test for circles that overlap top or bottom boundary */
|
|
ncirc0 = ncircles;
|
|
for (n=0; n < ncirc0; n++)
|
|
{
|
|
if (circley[n] + circlerad[n] > YMAX)
|
|
{
|
|
circlex[ncircles] = circlex[n];
|
|
circley[ncircles] = circley[n] - height;
|
|
circlerad[ncircles] = MU;
|
|
circleactive[ncircles] = 1;
|
|
ncircles ++;
|
|
}
|
|
else if (circley[n] - circlerad[n] < YMIN)
|
|
{
|
|
circlex[ncircles] = circlex[n];
|
|
circley[ncircles] = circley[n] + height;
|
|
circlerad[ncircles] = MU;
|
|
circleactive[ncircles] = 1;
|
|
ncircles ++;
|
|
}
|
|
}
|
|
break;
|
|
}
|
|
case (C_GOLDEN_SPIRAL):
|
|
{
|
|
ncircles = 1;
|
|
circlex[0] = 0.0;
|
|
circley[0] = 0.0;
|
|
|
|
gamma = (sqrt(5.0) - 1.0)*PI; /* golden mean times 2Pi */
|
|
phi = 0.0;
|
|
r0 = 2.0*MU;
|
|
r = r0 + MU;
|
|
|
|
for (i=0; i<1000; i++)
|
|
{
|
|
x = r*cos(phi);
|
|
y = r*sin(phi);
|
|
|
|
phi += gamma;
|
|
r += MU*r0/r;
|
|
|
|
if ((vabs(x) < LAMBDA)&&(vabs(y) < YMAX + MU))
|
|
{
|
|
circlex[ncircles] = x;
|
|
circley[ncircles] = y;
|
|
ncircles++;
|
|
}
|
|
}
|
|
|
|
for (i=0; i<ncircles; i++)
|
|
{
|
|
circlerad[i] = MU;
|
|
/* inactivate circles outside the domain */
|
|
if ((circley[i] < YMAX + MU)&&(circley[i] > YMIN - MU)) circleactive[i] = 1;
|
|
// printf("i = %i, circlex = %.3lg, circley = %.3lg\n", i, circlex[i], circley[i]);
|
|
}
|
|
break;
|
|
}
|
|
case (C_SQUARE_HEX):
|
|
{
|
|
ncircles = NGRIDX*(NGRIDY+1);
|
|
dy = (YMAX - YMIN)/((double)NGRIDY);
|
|
dx = dy*0.5*sqrt(3.0);
|
|
for (i = 0; i < NGRIDX; i++)
|
|
for (j = 0; j < NGRIDY+1; j++)
|
|
{
|
|
n = (NGRIDY+1)*i + j;
|
|
circlex[n] = ((double)(i-NGRIDX/2) + 0.5)*dy; /* is +0.5 needed? */
|
|
circley[n] = YMIN + ((double)j - 0.5)*dy;
|
|
if (((i+NGRIDX)%4 == 2)||((i+NGRIDX)%4 == 3)) circley[n] += 0.5*dy;
|
|
circlerad[n] = MU;
|
|
/* activate only circles that intersect the domain */
|
|
if ((circley[n] < YMAX + MU)&&(circley[n] > YMIN - MU)) circleactive[n] = 1;
|
|
else circleactive[n] = 0;
|
|
}
|
|
break;
|
|
}
|
|
case (C_ONE):
|
|
{
|
|
circlex[ncircles] = 0.0;
|
|
circley[ncircles] = 0.0;
|
|
circlerad[ncircles] = MU;
|
|
circleactive[ncircles] = 1;
|
|
ncircles += 1;
|
|
break;
|
|
}
|
|
case (C_TWO): /* used for comparison with cloak */
|
|
{
|
|
circlex[ncircles] = 0.0;
|
|
circley[ncircles] = 0.0;
|
|
circlerad[ncircles] = MU;
|
|
circleactive[ncircles] = 2;
|
|
ncircles += 1;
|
|
|
|
circlex[ncircles] = 0.0;
|
|
circley[ncircles] = 0.0;
|
|
circlerad[ncircles] = 2.0*MU;
|
|
circleactive[ncircles] = 1;
|
|
ncircles += 1;
|
|
break;
|
|
}
|
|
case (C_NOTHING):
|
|
{
|
|
ncircles += 0;
|
|
break;
|
|
}
|
|
default:
|
|
{
|
|
printf("Function init_circle_config not defined for this pattern \n");
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
int xy_in_billiard(double x, double y)
|
|
/* returns 1 if (x,y) represents a point in the billiard */
|
|
// double x, y;
|
|
{
|
|
double l2, r2, r2mu, omega, c, angle, z, x1, y1, x2, y2, u, v, u1, v1, dx, dy, width;
|
|
int i, j, k, k1, k2, condition;
|
|
|
|
switch (B_DOMAIN) {
|
|
case (D_RECTANGLE):
|
|
{
|
|
if ((vabs(x) <LAMBDA)&&(vabs(y) < 1.0)) return(1);
|
|
else return(0);
|
|
break;
|
|
}
|
|
case (D_ELLIPSE):
|
|
{
|
|
if (x*x/(LAMBDA*LAMBDA) + y*y < 1.0) return(1);
|
|
else return(0);
|
|
break;
|
|
}
|
|
case (D_STADIUM):
|
|
{
|
|
if ((x > -0.5*LAMBDA)&&(x < 0.5*LAMBDA)&&(y > -1.0)&&(y < 1.0)) return(1);
|
|
else if (module2(x+0.5*LAMBDA, y) < 1.0) return(1);
|
|
else if (module2(x-0.5*LAMBDA, y) < 1.0) return(1);
|
|
else return(0);
|
|
break;
|
|
}
|
|
case (D_SINAI):
|
|
{
|
|
if (x*x + y*y > LAMBDA*LAMBDA) return(1);
|
|
else return(0);
|
|
break;
|
|
}
|
|
case (D_DIAMOND):
|
|
{
|
|
l2 = LAMBDA*LAMBDA;
|
|
r2 = l2 + (LAMBDA-1.0)*(LAMBDA-1.0);
|
|
if ((x*x + y*y < 1.0)&&((x-LAMBDA)*(x-LAMBDA) + (y-LAMBDA)*(y-LAMBDA) > r2)
|
|
&&((x-LAMBDA)*(x-LAMBDA) + (y+LAMBDA)*(y+LAMBDA) > r2)
|
|
&&((x+LAMBDA)*(x+LAMBDA) + (y-LAMBDA)*(y-LAMBDA) > r2)
|
|
&&((x+LAMBDA)*(x+LAMBDA) + (y+LAMBDA)*(y+LAMBDA) > r2)) return(1);
|
|
else return(0);
|
|
break;
|
|
}
|
|
case (D_TRIANGLE):
|
|
{
|
|
if ((x>-LAMBDA)&&(y>-1.0)&&(LAMBDA*y+x<0.0)) return(1);
|
|
else return(0);
|
|
break;
|
|
}
|
|
case (D_FLAT):
|
|
{
|
|
if (y > -LAMBDA) return(1);
|
|
else return(0);
|
|
break;
|
|
}
|
|
case (D_ANNULUS):
|
|
{
|
|
l2 = LAMBDA*LAMBDA;
|
|
r2 = x*x + y*y;
|
|
if ((r2 > l2)&&(r2 < 1.0)) return(1);
|
|
else return(0);
|
|
}
|
|
case (D_POLYGON):
|
|
{
|
|
condition = 1;
|
|
omega = DPI/((double)NPOLY);
|
|
c = cos(omega*0.5);
|
|
for (k=0; k<NPOLY; k++)
|
|
{
|
|
angle = APOLY*PID + (k+0.5)*omega;
|
|
condition = condition*(x*cos(angle) + y*sin(angle) < c);
|
|
}
|
|
// for (k=0; k<NPOLY; k++) condition = condition*(-x*sin((k+0.5)*omega) + y*cos((k+0.5)*omega) < c);
|
|
return(condition);
|
|
}
|
|
case (D_YOUNG):
|
|
{
|
|
if ((x < -MU)||(x > MU)) return(1);
|
|
else if ((vabs(y-LAMBDA) < MU)||(vabs(y+LAMBDA) < MU)) return (1);
|
|
else return(0);
|
|
}
|
|
case (D_GRATING):
|
|
{
|
|
k1 = -(int)((-YMIN)/LAMBDA);
|
|
k2 = (int)(YMAX/LAMBDA);
|
|
condition = 1;
|
|
for (i=k1; i<= k2; i++)
|
|
{
|
|
z = (double)i*LAMBDA;
|
|
condition = condition*(x*x + (y-z)*(y-z) > MU*MU);
|
|
}
|
|
// printf("x = %.3lg, y = %.3lg, k1 = %i, k2 = %i, condition = %i\n", x, y, k1, k2, condition);
|
|
return(condition);
|
|
}
|
|
case (D_EHRENFEST):
|
|
{
|
|
return(((x-1.0)*(x-1.0) + y*y < LAMBDA*LAMBDA)||((x+1.0)*(x+1.0) + y*y < LAMBDA*LAMBDA)||((vabs(x) < 1.0)&&(vabs(y) < MU)));
|
|
}
|
|
case (D_DISK_GRID):
|
|
{
|
|
dy = (YMAX - YMIN)/((double)NGRIDY);
|
|
for (i = -NGRIDX/2; i < NGRIDX/2; i++)
|
|
for (j = 0; j < NGRIDY; j++)
|
|
{
|
|
x1 = ((double)i + 0.5)*dy;
|
|
y1 = YMIN + ((double)j + 0.5)*dy;
|
|
if ((x-x1)*(x-x1) + (y-y1)*(y-y1) < MU*MU) return(0);
|
|
}
|
|
return(1);
|
|
}
|
|
case (D_DISK_HEX):
|
|
{
|
|
dy = (YMAX - YMIN)/((double)NGRIDY);
|
|
dx = dy*0.5*sqrt(3.0);
|
|
for (i = -NGRIDX/2; i < NGRIDX/2; i++)
|
|
for (j = -1; j < NGRIDY; j++)
|
|
{
|
|
x1 = ((double)i + 0.5)*dy;
|
|
y1 = YMIN + ((double)j + 0.5)*dy;
|
|
if ((i+NGRIDX)%2 == 1) y1 += 0.5*dy;
|
|
if ((x-x1)*(x-x1) + (y-y1)*(y-y1) < MU*MU) return(0);
|
|
}
|
|
return(1);
|
|
}
|
|
case (D_PARABOLA):
|
|
{
|
|
return(x > 0.25*y*y/LAMBDA - LAMBDA);
|
|
}
|
|
case (D_TWO_PARABOLAS):
|
|
{
|
|
x1 = 0.25*y*y/MU - MU - LAMBDA;
|
|
x2 = -x1;
|
|
width = 0.25*MU;
|
|
if (width > 0.2) width = 0.2;
|
|
if (vabs(y) > 1.5*MU) return(1);
|
|
else if ((x < x1 - width)||(x > x2 + width)) return(1);
|
|
else if ((x > x1)&&(x < x2)) return(1);
|
|
else return(0);
|
|
}
|
|
case (D_CIRCLES):
|
|
{
|
|
for (i = 0; i < ncircles; i++)
|
|
if (circleactive[i])
|
|
{
|
|
x1 = circlex[i];
|
|
y1 = circley[i];
|
|
r2 = circlerad[i]*circlerad[i];
|
|
if ((x-x1)*(x-x1) + (y-y1)*(y-y1) < r2) return(0);
|
|
}
|
|
return(1);
|
|
}
|
|
case (D_MENGER):
|
|
{
|
|
x1 = 0.5*(x+1.0);
|
|
y1 = 0.5*(y+1.0);
|
|
for (k=0; k<MDEPTH; k++)
|
|
{
|
|
x1 = x1*(double)MRATIO;
|
|
y1 = y1*(double)MRATIO;
|
|
if ((vabs(x)<1.0)&&(vabs(y)<1.0)&&(((int)x1 % MRATIO)==MRATIO/2)&&(((int)y1 % MRATIO)==MRATIO/2)) return(0);
|
|
}
|
|
return(1);
|
|
}
|
|
case (D_JULIA_INT):
|
|
{
|
|
u = x/JULIA_SCALE;
|
|
v = y/JULIA_SCALE;
|
|
i = 0;
|
|
while ((i<MANDELLEVEL)&&(u*u+v*v < 1000.0*MANDELLIMIT))
|
|
{
|
|
u1 = u*u - v*v + julia_x;
|
|
v = 2.0*u*v + julia_y;
|
|
u = u1;
|
|
i++;
|
|
}
|
|
if (u*u + v*v < MANDELLIMIT) return(1);
|
|
else return(0);
|
|
}
|
|
case (D_MENGER_ROTATED):
|
|
{
|
|
x2 = 1.0*(x + y);
|
|
y2 = 1.0*(x - y);
|
|
if ((vabs(x2) < 1.0)&&(vabs(y2) < 1.0))
|
|
{
|
|
x1 = 0.5*(x2 + 1.0);
|
|
y1 = 0.5*(y2 + 1.0);
|
|
for (k=0; k<MDEPTH; k++)
|
|
{
|
|
x1 = x1*(double)MRATIO;
|
|
y1 = y1*(double)MRATIO;
|
|
if ((vabs(x)<1.0)&&(vabs(y)<1.0)&&(((int)x1 % MRATIO)==MRATIO/2)&&(((int)y1 % MRATIO)==MRATIO/2)) return(0);
|
|
}
|
|
}
|
|
return(1);
|
|
}
|
|
case (D_ANNULUS_HEATED): /* returns 2 if in inner circle */
|
|
{
|
|
l2 = LAMBDA*LAMBDA;
|
|
r2 = x*x + y*y;
|
|
r2mu = (x-MU)*(x-MU) + y*y;
|
|
if ((r2mu > l2)&&(r2 < 1.0)) return(1);
|
|
else if (r2mu <= l2) return(2);
|
|
else return (0);
|
|
}
|
|
case (D_MENGER_HEATED):
|
|
{
|
|
if ((vabs(x) >= 1.0)||(vabs(y) >= 1.0)) return(0);
|
|
else
|
|
{
|
|
x1 = 0.5*(x+1.0);
|
|
y1 = 0.5*(y+1.0);
|
|
for (k=0; k<MDEPTH; k++)
|
|
{
|
|
x1 = x1*(double)MRATIO;
|
|
y1 = y1*(double)MRATIO;
|
|
if ((((int)x1 % MRATIO)==MRATIO/2)&&(((int)y1 % MRATIO)==MRATIO/2)) return(k+2);
|
|
}
|
|
return(1);
|
|
}
|
|
}
|
|
case (D_MENGER_H_OPEN): /* returns 2 if in inner circle */
|
|
{
|
|
x1 = 0.5*(x+1.0);
|
|
y1 = 0.5*(y+1.0);
|
|
for (k=0; k<MDEPTH; k++)
|
|
{
|
|
x1 = x1*(double)MRATIO;
|
|
y1 = y1*(double)MRATIO;
|
|
if ((vabs(x)<1.0)&&(vabs(y)<1.0)&&(((int)x1 % MRATIO)==MRATIO/2)&&(((int)y1 % MRATIO)==MRATIO/2)) return(k+2);
|
|
}
|
|
return(1);
|
|
}
|
|
case (D_MANDELBROT):
|
|
{
|
|
u = 0.0;
|
|
v = 0.0;
|
|
i = 0;
|
|
while ((i<MANDELLEVEL)&&(u*u+v*v < 1000.0*MANDELLIMIT))
|
|
{
|
|
u1 = u*u - v*v + x;
|
|
v = 2.0*u*v + y;
|
|
u = u1;
|
|
i++;
|
|
/* old version used */
|
|
/* u1 = u*u - v*v - x; */
|
|
/* v = 2.0*u*v - y; */
|
|
}
|
|
if (u*u + v*v < MANDELLIMIT) return(0);
|
|
else if ((x-0.5)*(x-0.5)/3.0 + y*y/1.0 > 1.2) return(2);
|
|
else return(1);
|
|
}
|
|
case (D_MANDELBROT_CIRCLE):
|
|
{
|
|
u = 0.0;
|
|
v = 0.0;
|
|
i = 0;
|
|
while ((i<MANDELLEVEL)&&(u*u+v*v < 1000.0*MANDELLIMIT))
|
|
{
|
|
u1 = u*u - v*v + x;
|
|
v = 2.0*u*v + y;
|
|
u = u1;
|
|
i++;
|
|
}
|
|
if (u*u + v*v < MANDELLIMIT) return(0);
|
|
else if ((x-LAMBDA)*(x-LAMBDA) + (y-0.5)*(y-0.5) < MU*MU) return(2);
|
|
else return(1);
|
|
}
|
|
case (D_JULIA):
|
|
{
|
|
u = x/JULIA_SCALE;
|
|
v = y/JULIA_SCALE;
|
|
i = 0;
|
|
while ((i<MANDELLEVEL)&&(u*u+v*v < 1000.0*MANDELLIMIT))
|
|
{
|
|
u1 = u*u - v*v + julia_x;
|
|
v = 2.0*u*v + julia_y;
|
|
u = u1;
|
|
i++;
|
|
// printf("x = %.5lg y = %.5lg i = %i r2 = %.5lg\n", x, y, i, u*u+v*v);
|
|
}
|
|
// printf("i = %i x = %.5lg y = %.5lg r2 = %.5lg\n", i, x, y, u*u+v*v);
|
|
if (u*u + v*v < MANDELLIMIT) return(0);
|
|
else if (x*x/3.0 + y*y/1.0 > 1.2) return(2);
|
|
// else if ((vabs(x) > XMAX - 0.01)||(vabs(y) > YMAX - 0.01)) return(2);
|
|
else return(1);
|
|
}
|
|
default:
|
|
{
|
|
printf("Function ij_in_billiard not defined for this billiard \n");
|
|
return(0);
|
|
}
|
|
}
|
|
}
|
|
|
|
int ij_in_billiard(int i, int j)
|
|
/* returns 1 if (i,j) represents a point in the billiard */
|
|
{
|
|
double xy[2];
|
|
|
|
ij_to_xy(i, j, xy);
|
|
|
|
return(xy_in_billiard(xy[0], xy[1]));
|
|
}
|
|
|
|
|
|
|
|
|
|
void draw_billiard() /* draws the billiard boundary */
|
|
{
|
|
double x0, x, y, x1, y1, dx, dy, phi, r = 0.01, pos[2], pos1[2], alpha, dphi, omega, z, l, width;
|
|
int i, j, k, k1, k2, mr2;
|
|
|
|
if (BLACK) glColor3f(1.0, 1.0, 1.0);
|
|
else glColor3f(0.0, 0.0, 0.0);
|
|
glLineWidth(BOUNDARY_WIDTH);
|
|
|
|
glEnable(GL_LINE_SMOOTH);
|
|
|
|
switch (B_DOMAIN) {
|
|
case (D_RECTANGLE):
|
|
{
|
|
glBegin(GL_LINE_LOOP);
|
|
xy_to_pos(LAMBDA, -1.0, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(LAMBDA, 1.0, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(-LAMBDA, 1.0, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(-LAMBDA, -1.0, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
break;
|
|
}
|
|
case (D_ELLIPSE):
|
|
{
|
|
glBegin(GL_LINE_LOOP);
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = (double)i*DPI/(double)NSEG;
|
|
x = LAMBDA*cos(phi);
|
|
y = sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd ();
|
|
|
|
/* draw foci */
|
|
if (FOCI)
|
|
{
|
|
glColor3f(0.3, 0.3, 0.3);
|
|
x0 = sqrt(LAMBDA*LAMBDA-1.0);
|
|
|
|
glLineWidth(2);
|
|
glEnable(GL_LINE_SMOOTH);
|
|
|
|
draw_circle(x0, 0.0, r, NSEG);
|
|
draw_circle(-x0, 0.0, r, NSEG);
|
|
}
|
|
break;
|
|
}
|
|
case (D_STADIUM):
|
|
{
|
|
glBegin(GL_LINE_LOOP);
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = -PID + (double)i*PI/(double)NSEG;
|
|
x = 0.5*LAMBDA + cos(phi);
|
|
y = sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = PID + (double)i*PI/(double)NSEG;
|
|
x = -0.5*LAMBDA + cos(phi);
|
|
y = sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd();
|
|
break;
|
|
}
|
|
case (D_SINAI):
|
|
{
|
|
draw_circle(0.0, 0.0, LAMBDA, NSEG);
|
|
break;
|
|
}
|
|
case (D_DIAMOND):
|
|
{
|
|
alpha = atan(1.0 - 1.0/LAMBDA);
|
|
dphi = (PID - 2.0*alpha)/(double)NSEG;
|
|
r = sqrt(LAMBDA*LAMBDA + (LAMBDA-1.0)*(LAMBDA-1.0));
|
|
glBegin(GL_LINE_LOOP);
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = alpha + (double)i*dphi;
|
|
x = -LAMBDA + r*cos(phi);
|
|
y = -LAMBDA + r*sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = alpha - PID + (double)i*dphi;
|
|
x = -LAMBDA + r*cos(phi);
|
|
y = LAMBDA + r*sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = alpha + PI + (double)i*dphi;
|
|
x = LAMBDA + r*cos(phi);
|
|
y = LAMBDA + r*sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = alpha + PID + (double)i*dphi;
|
|
x = LAMBDA + r*cos(phi);
|
|
y = -LAMBDA + r*sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd();
|
|
break;
|
|
}
|
|
case (D_TRIANGLE):
|
|
{
|
|
glBegin(GL_LINE_LOOP);
|
|
xy_to_pos(-LAMBDA, -1.0, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(LAMBDA, -1.0, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(-LAMBDA, 1.0, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
break;
|
|
}
|
|
case (D_FLAT):
|
|
{
|
|
glBegin(GL_LINE_LOOP);
|
|
xy_to_pos(XMIN, -LAMBDA, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(XMAX, -LAMBDA, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
break;
|
|
}
|
|
case (D_ANNULUS):
|
|
{
|
|
draw_circle(0.0, 0.0, LAMBDA, NSEG);
|
|
draw_circle(0.0, 0.0, 1.0, NSEG);
|
|
break;
|
|
}
|
|
case (D_POLYGON):
|
|
{
|
|
omega = DPI/((double)NPOLY);
|
|
glBegin(GL_LINE_LOOP);
|
|
for (i=0; i<=NPOLY; i++)
|
|
{
|
|
x = cos(i*omega + APOLY*PID);
|
|
y = sin(i*omega + APOLY*PID);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd ();
|
|
break;
|
|
}
|
|
case (D_YOUNG):
|
|
{
|
|
glBegin(GL_LINE_STRIP);
|
|
xy_to_pos(-MU, YMIN, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(-MU, -LAMBDA-MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(MU, -LAMBDA-MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(MU, YMIN, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
|
|
glBegin(GL_LINE_STRIP);
|
|
xy_to_pos(-MU, YMAX, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(-MU, LAMBDA+MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(MU, LAMBDA+MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(MU, YMAX, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
|
|
glBegin(GL_LINE_LOOP);
|
|
xy_to_pos(-MU, -LAMBDA+MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(-MU, LAMBDA-MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(MU, LAMBDA-MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
xy_to_pos(MU, -LAMBDA+MU, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
glEnd();
|
|
break;
|
|
}
|
|
case (D_GRATING):
|
|
{
|
|
k1 = -(int)(-YMIN/LAMBDA);
|
|
k2 = (int)(YMAX/LAMBDA);
|
|
for (i=k1; i<= k2; i++)
|
|
{
|
|
z = (double)i*LAMBDA;
|
|
draw_circle(0.0, z, MU, NSEG);
|
|
}
|
|
break;
|
|
}
|
|
case (D_EHRENFEST):
|
|
{
|
|
alpha = asin(MU/LAMBDA);
|
|
x0 = 1.0 - sqrt(LAMBDA*LAMBDA - MU*MU);
|
|
dphi = 2.0*(PI-alpha)/((double)NSEG);
|
|
glBegin(GL_LINE_LOOP);
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = -PI + alpha + (double)i*dphi;
|
|
x = 1.0 + LAMBDA*cos(phi);
|
|
y = LAMBDA*sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
for (i=0; i<=NSEG; i++)
|
|
{
|
|
phi = alpha + (double)i*dphi;
|
|
x = -1.0 + LAMBDA*cos(phi);
|
|
y = LAMBDA*sin(phi);
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd ();
|
|
break;
|
|
}
|
|
case (D_DISK_GRID):
|
|
{
|
|
glLineWidth(2);
|
|
for (i = -NGRIDX/2; i < NGRIDX/2; i++)
|
|
for (j = 0; j < NGRIDY; j++)
|
|
{
|
|
dy = (YMAX - YMIN)/((double)NGRIDY);
|
|
dx = dy*0.5*sqrt(3.0);
|
|
x1 = ((double)i + 0.5)*dy;
|
|
y1 = YMIN + ((double)j + 0.5)*dy;
|
|
draw_circle(x1, y1, MU, NSEG);
|
|
}
|
|
break;
|
|
}
|
|
case (D_DISK_HEX):
|
|
{
|
|
glLineWidth(2);
|
|
for (i = -NGRIDX/2; i < NGRIDX/2; i++)
|
|
for (j = -1; j < NGRIDY; j++)
|
|
{
|
|
dy = (YMAX - YMIN)/((double)NGRIDY);
|
|
x1 = ((double)i + 0.5)*dy;
|
|
y1 = YMIN + ((double)j + 0.5)*dy;
|
|
if ((i+NGRIDX)%2 == 1) y1 += 0.5*dy;
|
|
draw_circle(x1, y1, MU, NSEG);
|
|
}
|
|
break;
|
|
}
|
|
case (D_PARABOLA):
|
|
{
|
|
dy = (YMAX - YMIN)/(double)NSEG;
|
|
glBegin(GL_LINE_STRIP);
|
|
|
|
for (i = 0; i < NSEG+1; i++)
|
|
{
|
|
y = YMIN + dy*(double)i;
|
|
x = 0.25*y*y/LAMBDA - LAMBDA;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd ();
|
|
|
|
if (FOCI)
|
|
{
|
|
glColor3f(0.3, 0.3, 0.3);
|
|
draw_circle(0.0, 0.0, r, NSEG);
|
|
}
|
|
break;
|
|
}
|
|
case (D_TWO_PARABOLAS):
|
|
{
|
|
dy = 3.0*MU/(double)NSEG;
|
|
width = 0.25*MU;
|
|
if (width > 0.2) width = 0.2;
|
|
glBegin(GL_LINE_LOOP);
|
|
for (i = 0; i < NSEG+1; i++)
|
|
{
|
|
y = -1.5*MU + dy*(double)i;
|
|
x = 0.25*y*y/MU - MU - LAMBDA;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
for (i = 0; i < NSEG+1; i++)
|
|
{
|
|
y = 1.5*MU - dy*(double)i;
|
|
x = 0.25*y*y/MU - (MU + width) - LAMBDA;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd ();
|
|
|
|
glBegin(GL_LINE_LOOP);
|
|
for (i = 0; i < NSEG+1; i++)
|
|
{
|
|
y = -1.5*MU + dy*(double)i;
|
|
x = LAMBDA + MU - 0.25*y*y/MU;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
for (i = 0; i < NSEG+1; i++)
|
|
{
|
|
y = 1.5*MU - dy*(double)i;
|
|
x = LAMBDA + (MU + width) - 0.25*y*y/MU;
|
|
xy_to_pos(x, y, pos);
|
|
glVertex2d(pos[0], pos[1]);
|
|
}
|
|
glEnd ();
|
|
|
|
if (FOCI)
|
|
{
|
|
glColor3f(0.3, 0.3, 0.3);
|
|
draw_circle(-LAMBDA, 0.0, r, NSEG);
|
|
draw_circle(LAMBDA, 0.0, r, NSEG);
|
|
}
|
|
|
|
break;
|
|
}
|
|
case (D_CIRCLES):
|
|
{
|
|
glLineWidth(BOUNDARY_WIDTH);
|
|
for (i = 0; i < ncircles; i++)
|
|
if (circleactive[i]) draw_circle(circlex[i], circley[i], circlerad[i], NSEG);
|
|
break;
|
|
}
|
|
case (D_MENGER):
|
|
{
|
|
glLineWidth(3);
|
|
// draw_rectangle(XMIN, -1.0, XMAX, 1.0);
|
|
|
|
/* level 1 */
|
|
if (MDEPTH > 0)
|
|
{
|
|
glLineWidth(2);
|
|
x = 1.0/((double)MRATIO);
|
|
draw_rectangle(x, x, -x, -x);
|
|
}
|
|
|
|
/* level 2 */
|
|
if (MDEPTH > 1)
|
|
{
|
|
glLineWidth(1);
|
|
mr2 = MRATIO*MRATIO;
|
|
l = 2.0/((double)mr2);
|
|
|
|
for (i=0; i<MRATIO; i++)
|
|
for (j=0; j<MRATIO; j++)
|
|
if ((i!=MRATIO/2)||(j!=MRATIO/2))
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)MRATIO);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)MRATIO);
|
|
draw_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
/* level 3 */
|
|
if (MDEPTH > 2)
|
|
{
|
|
glLineWidth(1);
|
|
l = 2.0/((double)(mr2*MRATIO));
|
|
|
|
for (i=0; i<mr2; i++)
|
|
for (j=0; j<mr2; j++)
|
|
if ( (((i%MRATIO!=MRATIO/2))||(j%MRATIO!=MRATIO/2)) && (((i/MRATIO!=MRATIO/2))||(j/MRATIO!=MRATIO/2)) )
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)mr2);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)mr2);
|
|
draw_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
break;
|
|
}
|
|
case (D_JULIA_INT):
|
|
{
|
|
/* Do nothing */
|
|
break;
|
|
}
|
|
case (D_MENGER_ROTATED):
|
|
{
|
|
glLineWidth(3);
|
|
// draw_rectangle(XMIN, -1.0, XMAX, 1.0);
|
|
|
|
/* level 1 */
|
|
if (MDEPTH > 0)
|
|
{
|
|
glLineWidth(2);
|
|
x = 1.0/((double)MRATIO);
|
|
draw_rotated_rectangle(x, x, -x, -x);
|
|
}
|
|
|
|
/* level 2 */
|
|
if (MDEPTH > 1)
|
|
{
|
|
glLineWidth(1);
|
|
mr2 = MRATIO*MRATIO;
|
|
l = 2.0/((double)mr2);
|
|
|
|
for (i=0; i<MRATIO; i++)
|
|
for (j=0; j<MRATIO; j++)
|
|
if ((i!=MRATIO/2)||(j!=MRATIO/2))
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)MRATIO);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)MRATIO);
|
|
draw_rotated_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
/* level 3 */
|
|
if (MDEPTH > 2)
|
|
{
|
|
glLineWidth(1);
|
|
l = 2.0/((double)(mr2*MRATIO));
|
|
|
|
for (i=0; i<mr2; i++)
|
|
for (j=0; j<mr2; j++)
|
|
if ( (((i%MRATIO!=MRATIO/2))||(j%MRATIO!=MRATIO/2)) && (((i/MRATIO!=MRATIO/2))||(j/MRATIO!=MRATIO/2)) )
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)mr2);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)mr2);
|
|
draw_rotated_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
break;
|
|
}
|
|
case (D_ANNULUS_HEATED):
|
|
{
|
|
draw_circle(MU, 0.0, LAMBDA, NSEG);
|
|
draw_circle(0.0, 0.0, 1.0, NSEG);
|
|
break;
|
|
}
|
|
case (D_MENGER_HEATED):
|
|
{
|
|
glLineWidth(3);
|
|
draw_rectangle(-1.0, -1.0, 1.0, 1.0);
|
|
|
|
/* level 1 */
|
|
if (MDEPTH > 0)
|
|
{
|
|
glLineWidth(2);
|
|
x = 1.0/((double)MRATIO);
|
|
draw_rectangle(x, x, -x, -x);
|
|
}
|
|
|
|
/* level 2 */
|
|
if (MDEPTH > 1)
|
|
{
|
|
glLineWidth(1);
|
|
mr2 = MRATIO*MRATIO;
|
|
l = 2.0/((double)mr2);
|
|
|
|
for (i=0; i<MRATIO; i++)
|
|
for (j=0; j<MRATIO; j++)
|
|
if ((i!=MRATIO/2)||(j!=MRATIO/2))
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)MRATIO);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)MRATIO);
|
|
draw_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
/* level 3 */
|
|
if (MDEPTH > 2)
|
|
{
|
|
glLineWidth(1);
|
|
l = 2.0/((double)(mr2*MRATIO));
|
|
|
|
for (i=0; i<mr2; i++)
|
|
for (j=0; j<mr2; j++)
|
|
if ( (((i%MRATIO!=MRATIO/2))||(j%MRATIO!=MRATIO/2)) && (((i/MRATIO!=MRATIO/2))||(j/MRATIO!=MRATIO/2)) )
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)mr2);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)mr2);
|
|
draw_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
break;
|
|
}
|
|
case (D_MENGER_H_OPEN):
|
|
{
|
|
glLineWidth(3);
|
|
// draw_rectangle(XMIN, -1.0, XMAX, 1.0);
|
|
|
|
/* level 1 */
|
|
if (MDEPTH > 0)
|
|
{
|
|
glLineWidth(2);
|
|
x = 1.0/((double)MRATIO);
|
|
draw_rectangle(x, x, -x, -x);
|
|
}
|
|
|
|
/* level 2 */
|
|
if (MDEPTH > 1)
|
|
{
|
|
glLineWidth(1);
|
|
mr2 = MRATIO*MRATIO;
|
|
l = 2.0/((double)mr2);
|
|
|
|
for (i=0; i<MRATIO; i++)
|
|
for (j=0; j<MRATIO; j++)
|
|
if ((i!=MRATIO/2)||(j!=MRATIO/2))
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)MRATIO);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)MRATIO);
|
|
draw_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
/* level 3 */
|
|
if (MDEPTH > 2)
|
|
{
|
|
glLineWidth(1);
|
|
l = 2.0/((double)(mr2*MRATIO));
|
|
|
|
for (i=0; i<mr2; i++)
|
|
for (j=0; j<mr2; j++)
|
|
if ( (((i%MRATIO!=MRATIO/2))||(j%MRATIO!=MRATIO/2)) && (((i/MRATIO!=MRATIO/2))||(j/MRATIO!=MRATIO/2)) )
|
|
{
|
|
x = -1.0 - 0.5*l + 2.0*((double)i + 0.5)/((double)mr2);
|
|
y = -1.0 - 0.5*l + 2.0*((double)j + 0.5)/((double)mr2);
|
|
draw_rectangle(x, y, x+l, y+l);
|
|
}
|
|
}
|
|
|
|
break;
|
|
}
|
|
case (D_MANDELBROT):
|
|
{
|
|
/* Do nothing */
|
|
break;
|
|
}
|
|
case (D_MANDELBROT_CIRCLE):
|
|
{
|
|
/* Do nothing */
|
|
break;
|
|
}
|
|
case (D_JULIA):
|
|
{
|
|
/* Do nothing */
|
|
break;
|
|
}
|
|
default:
|
|
{
|
|
printf("Function draw_billiard not defined for this billiard \n");
|
|
}
|
|
}
|
|
}
|