Test3

const float theta_spacing = 0.07; const float phi_spacing = 0.02; const float R1 = 1; const float R2 = 2; const float K2 = 5; // Calculate K1 based on screen size: the maximum x-distance occurs // roughly at the edge of the torus, which is at x=R1+R2, z=0. we // want that to be displaced 3/8ths of the width of the screen, which // is 3/4th of the way from the center to the side of the screen. // screen_width*3/8 = K1*(R1+R2)/(K2+0) // screen_width*K2*3/(8*(R1+R2)) = K1 const float K1 = screen_width*K2*3/(8*(R1+R2)); render_frame(float A, float B) { // precompute sines and cosines of A and B float cosA = cos(A), sinA = sin(A); float cosB = cos(B), sinB = sin(B); char output[0..screen_width, 0..screen_height] = ' '; float zbuffer[0..screen_width, 0..screen_height] = 0; // theta goes around the cross-sectional circle of a torus for (float theta=0; theta < 2*pi; theta += theta_spacing) { // precompute sines and cosines of theta float costheta = cos(theta), sintheta = sin(theta); // phi goes around the center of revolution of a torus for(float phi=0; phi < 2*pi; phi += phi_spacing) { // precompute sines and cosines of phi float cosphi = cos(phi), sinphi = sin(phi); // the x,y coordinate of the circle, before revolving (factored // out of the above equations) float circlex = R2 + R1*costheta; float circley = R1*sintheta; // final 3D (x,y,z) coordinate after rotations, directly from // our math above float x = circlex*(cosB*cosphi + sinA*sinB*sinphi) - circley*cosA*sinB; float y = circlex*(sinB*cosphi - sinA*cosB*sinphi) + circley*cosA*cosB; float z = K2 + cosA*circlex*sinphi + circley*sinA; float ooz = 1/z; // "one over z" // x and y projection. note that y is negated here, because y // goes up in 3D space but down on 2D displays. int xp = (int) (screen_width/2 + K1*ooz*x); int yp = (int) (screen_height/2 - K1*ooz*y); // calculate luminance. ugly, but correct. float L = cosphi*costheta*sinB - cosA*costheta*sinphi - sinA*sintheta + cosB*(cosA*sintheta - costheta*sinA*sinphi); // L ranges from -sqrt(2) to +sqrt(2). If it's < 0, the surface // is pointing away from us, so we won't bother trying to plot it. if (L > 0) { // test against the z-buffer. larger 1/z means the pixel is // closer to the viewer than what's already plotted. if(ooz > zbuffer[xp,yp]) { zbuffer[xp, yp] = ooz; int luminance_index = L*8; // luminance_index is now in the range 0..11 (8*sqrt(2) = 11.3) // now we lookup the character corresponding to the // luminance and plot it in our output: output[xp, yp] = ".,-~:;=!*#$@"[luminance_index]; } } } } // now, dump output[] to the screen. // bring cursor to "home" location, in just about any currently-used // terminal emulation mode printf("\x1b[H"); for (int j = 0; j < screen_height; j++) { for (int i = 0; i < screen_width; i++) { putchar(output[i,j]); } putchar('\n'); } }