// Copyright © 2020 IWBTShyGuy // Attribution 4.0 International (CC BY 4.0) precision highp float; uniform vec2 resolution; uniform float time; uniform vec2 mouse; // ------ Configures ------ // const vec3 RED = vec3(230.0, 0.0, 18.0) / 255.0; const vec3 GREEN = vec3(0.0, 167.0, 60.0) / 255.0; const vec3 BLUE = vec3(0.0, 100.0, 180.0) / 255.0; const int N_SPHERE = 8; const float SPHERE_RADIUS = 0.5; const float ORBIT_RADIUS = 2.0; const float ORBIT_VELO = 1.0; const float ROTATION_VELO = 1.5; const vec3 ROTATION_AXIS = normalize(vec3(1.0, 2.0, 0.0)); const float SPHERE_DOT_RADIUS = 0.07; const float BACK_DOT_RADIUS = 0.21; const float BACK_DOT_INTERVAL = 0.12; const float BACK_DOT_VELO = 1.5; // ------ 3D utilities ------ // const float PI = 3.141592653; struct Camera { vec3 position; vec3 direction; vec3 up_direction; float fov; float aspect; // x / y }; struct Ray { vec3 origin; vec3 direction; }; Camera newCamera(vec3 position, vec3 direction, vec3 up_direction, float fov, float aspect) { Camera camera; camera.position = position; camera.direction = direction; camera.up_direction = up_direction; camera.fov = fov; camera.aspect = aspect; return camera; } // perspective camera ray // cf: https://qiita.com/aa_debdeb/items/301dfc54788f1219b554 Ray cameraRay(in Camera camera, in vec2 uv) { uv = uv * 2.0 - 1.0; float radian = camera.fov; float h = tan(radian * 0.5); float w = h * camera.aspect; vec3 right = normalize(cross(camera.direction, camera.up_direction)); vec3 up = normalize(cross(right, camera.direction)); vec3 direction = normalize(right * w * uv.x + up * h * uv.y + camera.direction); Ray ray; ray.origin = camera.position; ray.direction = direction; return ray; } // Rodrigues' rotation formula mat3 rot(vec3 axis, float angle) { return mat3( axis[0] * axis[0] * (1.0 - cos(angle)) + cos(angle), axis[0] * axis[1] * (1.0 - cos(angle)) + axis[2] * sin(angle), axis[0] * axis[2] * (1.0 - cos(angle)) - axis[1] * sin(angle), axis[0] * axis[1] * (1.0 - cos(angle)) - axis[2] * sin(angle), axis[1] * axis[1] * (1.0 - cos(angle)) + cos(angle), axis[1] * axis[2] * (1.0 - cos(angle)) + axis[0] * sin(angle), axis[0] * axis[2] * (1.0 - cos(angle)) + axis[1] * sin(angle), axis[1] * axis[2] * (1.0 - cos(angle)) - axis[0] * sin(angle), axis[2] * axis[2] * (1.0 - cos(angle)) + cos(angle) ); } bool depthTest(in Ray ray, in vec3 current_position, in vec3 new_position) { float dist0 = distance(ray.origin, current_position); float dist1 = distance(ray.origin, new_position); return dist0 > dist1; } // ------ sphere ------ // struct Sphere { vec3 center; float radius; }; Sphere newSphere(in vec3 center, in float radius) { Sphere sphere; sphere.center = center; sphere.radius = radius; return sphere; } const float A = (sqrt(5.0) + 1.0) / 2.0; const float B = (sqrt(5.0) - 1.0) / 2.0; const int N = 32; // the number of vertices. void setVertices(out vec3 vertices[N]) { vertices[0] = normalize(vec3(1.0, 1.0, 1.0)); vertices[1] = normalize(vec3(1.0, 1.0, -1.0)); vertices[2] = normalize(vec3(1.0, -1.0, 1.0)); vertices[3] = normalize(vec3(1.0, -1.0, -1.0)); vertices[4] = normalize(vec3(-1.0, 1.0, 1.0)); vertices[5] = normalize(vec3(-1.0, 1.0, -1.0)); vertices[6] = normalize(vec3(-1.0, -1.0, 1.0)); vertices[7] = normalize(vec3(-1.0, -1.0, -1.0)); vertices[8] = normalize(vec3(0.0, A, B)); vertices[9] = normalize(vec3(0.0, A, -B)); vertices[10] = normalize(vec3(0.0, -A, B)); vertices[11] = normalize(vec3(0.0, -A, -B)); vertices[12] = normalize(vec3(A, B, 0.0)); vertices[13] = normalize(vec3(A, -B, 0.0)); vertices[14] = normalize(vec3(-A, B, 0.0)); vertices[15] = normalize(vec3(-A, -B, 0.0)); vertices[16] = normalize(vec3(B, 0.0, A)); vertices[17] = normalize(vec3(B, 0.0, -A)); vertices[18] = normalize(vec3(-B, 0.0, A)); vertices[19] = normalize(vec3(-B, 0.0, -A)); vertices[20] = normalize(vec3(0.0, 1.0, A)); vertices[21] = normalize(vec3(0.0, 1.0, -A)); vertices[22] = normalize(vec3(0.0, -1.0, A)); vertices[23] = normalize(vec3(0.0, -1.0, -A)); vertices[24] = normalize(vec3(1.0, A, 0.0)); vertices[25] = normalize(vec3(1.0, -A, 0.0)); vertices[26] = normalize(vec3(-1.0, A, 0.0)); vertices[27] = normalize(vec3(-1.0, -A, 0.0)); vertices[28] = normalize(vec3(A, 0.0, 1.0)); vertices[29] = normalize(vec3(A, 0.0, -1.0)); vertices[30] = normalize(vec3(-A, 0.0, 1.0)); vertices[31] = normalize(vec3(-A, 0.0, -1.0)); } bool onSphere(in Ray ray, in Sphere sphere, out vec3 intersection) { vec3 to_center = sphere.center - ray.origin; vec3 h = to_center - dot(to_center, ray.direction) * ray.direction; float d2 = sphere.radius * sphere.radius - dot(h, h); if (d2 < 0.0) return false; intersection = ray.origin + (dot(to_center, ray.direction) - sqrt(d2)) * ray.direction; return true; } // ------ basis function for gradation ------ // float parab(float t) { return 2.0 * t * t; } vec3 nowColor(float t) { t = fract(t / 3.0) * 3.0; float r0 = t < 1.0 ? (t < 0.5 ? 1.0 - parab(t) : parab(1.0 - t)) : 0.0; float g = t < 2.0 ? (t < 1.0 ? 1.0 - r0 : (t < 1.5 ? 1.0 - parab(t - 1.0) : parab(2.0 - t))) : 0.0; float r1 = 2.0 < t ? (t < 2.5 ? parab(t - 2.0) : 1.0 - parab(3.0 - t)) : 0.0; float b = 1.0 < t ? 1.0 - g - r1 : 0.0; return (r0 + r1) * RED + g * GREEN + b * BLUE; } void createSpheres(out Sphere sphere[N_SPHERE], float t) { for (int i = 0; i < N_SPHERE; i++) { float theta = t + 2.0 * PI * float(i) / float(N_SPHERE); sphere[i] = newSphere(vec3(sin(theta), 0.0, cos(theta)) * ORBIT_RADIUS, SPHERE_RADIUS); } } vec4 backGroundPolka(in vec2 fragCoord) { vec2 uv = fragCoord / resolution.y / BACK_DOT_INTERVAL + BACK_DOT_VELO * time; vec2 lattice = uv + 0.5; lattice = vec2(floor(lattice.x), floor(lattice.y)); if (distance(uv, lattice) < BACK_DOT_RADIUS) return vec4(nowColor(time), 1.0); else return vec4(0.0, 0.0, 0.0, 1.0); } vec3 rotOnSphere(in Sphere sphere, in vec3 position, mat3 rotation) { return rotation * (position - sphere.center) + sphere.center; } vec4 spherePolka(in Sphere sphere, in vec3 position) { vec3 vertices[N]; setVertices(vertices); for (int i = 0; i < N; i++) { vec3 dot_center = sphere.radius * vertices[i] + sphere.center; if (distance(position, dot_center) < SPHERE_DOT_RADIUS) { return vec4(nowColor(-time), 1.0); } } return vec4(0.0, 0.0, 0.0, 1.0); } void main() { vec2 uv = gl_FragCoord.xy / resolution.xy; vec3 unit = normalize(vec3(0.0, -0.5, 1.0)); Camera camera = newCamera( -5.0 * unit - vec3(0.0, 0.5, 0.0), unit, vec3(0.0, 1.0, 0.0), PI / 4.0, resolution.x / resolution.y ); Ray ray = cameraRay(camera, uv); Sphere sphere[N_SPHERE]; createSpheres(sphere, ORBIT_VELO * time); bool onOneSphere = false; vec3 position = vec3(100.0); Sphere on_sphere; for (int i = 0; i < N_SPHERE; i++) { vec3 tmp_position; if (onSphere(ray, sphere[i], tmp_position)) { if (depthTest(ray, position, tmp_position)) { position = tmp_position; on_sphere = sphere[i]; } onOneSphere = true; } } if (onOneSphere) { mat3 rotation = rot(ROTATION_AXIS, ROTATION_VELO * time); position = rotOnSphere(on_sphere, position, rotation); gl_FragColor = spherePolka(on_sphere, position); } else { gl_FragColor = backGroundPolka(gl_FragCoord.xy); } }

Polka de Sphère