example. varieties [ag-000F]
example. varieties [ag-000F]
\(\mathbf {V}\left (10 x^2-x^3-y^2\right )\) from [cox1997ideals, p. 24]:
\(\mathbf {V}\left (x^2-y^2 z^2+z^3\right )\) from [cox1997ideals, p. 7, p. 16]:
figure. [uts-000J]
figure. [uts-000J]
#define AS_LIB 1 int get_shape() { return int(iTime) % 52; } #include "/forest/shader/implicit.glsl" void mainImage( out vec4 fragColor, in vec2 fragCoord ) { vec2 uv = 2.*(fragCoord-iResolution.xy/2.)/iResolution.y; // contains [-1,1]^2 vec3 col = vec3(0.); // Camera rays vec3 camPos = vec3(4.,0.,0.); vec3 camDir = - normalize(camPos); vec3 rayPos, rayDir; float zoom = 1.3; // 1.8*cos(iTime); // if (checkKey(KEY_E)) zoom = 0.5; float fov = 0.4*zoom; float fov_ortho = 1.5*zoom; #if perspective // perspective cam rayPos = camPos; rayDir = normalize(camDir + fov*vec3(0., uv.x, uv.y)); #else // orthographic cam rayPos = camPos + fov_ortho*vec3(0., uv.x, uv.y); rayDir = camDir; #endif // for perspective background in orthographic mode vec3 cubemapDir = normalize(camDir + fov*vec3(0., uv.x, uv.y)); // Mouse-controlled rotation vec2 mouse = initMouse + vec2(0.015625*sin(iTime*PI), 0.0); // initMouse; // iMouse.xy == vec2(0.,0.) ? initMouse : (iMouse.xy/iResolution.xy - 0.5); float yaw = clamp(- mouse.x * 2.*PI * 1., -PI,PI); float pitch = clamp( mouse.y * PI * 1.2, -PI*0.5, PI*0.5); // pitch and yaw rotations (column-wise matrices) mat3 rot = mat3(cos(yaw), sin(yaw), 0., -sin(yaw), cos(yaw), 0., 0., 0., 1.); rot = rot * mat3(cos(pitch), 0., -sin(pitch), 0., 1., 0., sin(pitch), 0., cos(pitch)); // apply camPos = rot*camPos; camDir = rot*camDir; rayPos = rot*rayPos; rayDir = rot*rayDir; cubemapDir = rot*cubemapDir; //cubemapDir = vec3(cubemapDir.x, cubemapDir.z, cubemapDir.y); vec3 hitPoint = raycast(rayPos, rayDir); if (hitPoint == BINGO) { fragColor = vec4(BINGO,1.0); return; } //if (hitPoint == NOHIT) { fragColor = vec4(NOHIT,1.0); return; } //if (hitPoint == NOBOUNDHIT) { fragColor = vec4(NOBOUNDHIT,1.0); return; } //if (hitPoint == ESCAPEDBOUNDS) { fragColor = vec4(ESCAPEDBOUNDS,1.0); return; } //if (hitPoint == MAXDISTREACHED) { fragColor = vec4(MAXDISTREACHED,1.0); return; } //if (hitPoint == MAXITERREACHED) { fragColor = vec4(MAXITERREACHED,1.0); return; } if (hitPoint == NOBOUNDHIT || hitPoint == NOHIT || hitPoint == ESCAPEDBOUNDS || hitPoint == MAXITERREACHED) { //fragColor = vec4(vec3(0.2),1.0); return; // make background transparent fragColor = vec4(0.0,0.0,0.0,0.0); return; col = with_background(cubemapDir); #if showBoundingCube // darken bounding cube if (hitPoint != NOBOUNDHIT) { col *= vec3(0.7); } #endif fragColor = vec4(col,1.0); return; } vec3 grad = gradf(hitPoint+1.1*EPS*(-rayDir)); float s = -sign(dot(grad,rayDir)); col = with_color_mode(grad, s, hitPoint, camPos); col = clamp(col, 0., 1.); col = with_surface_pattern(col, hitPoint); col = with_shading(col, grad, s, rayDir); col = clamp(col, 0., 1.); fragColor = vec4(col,1.0); }