187 lines
5.5 KiB
GLSL
187 lines
5.5 KiB
GLSL
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#version 300 es
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precision highp float;
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out vec4 outColor;
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// view
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uniform vec2 resolution;
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uniform float shortdim;
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// controls
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uniform vec2 ctrl;
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uniform vec2 radius;
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uniform float opacity;
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uniform float highlight;
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uniform int layer_threshold;
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// light and camera
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const float focal_slope = 0.3;
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const vec3 light_dir = normalize(vec3(2., 2., 1.));
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const float ixn_threshold = 0.005;
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// --- sRGB ---
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// map colors from RGB space to sRGB space, as specified in the sRGB standard
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// (IEC 61966-2-1:1999)
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//
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// https://www.color.org/sRGB.pdf
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// https://www.color.org/chardata/rgb/srgb.xalter
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//
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// in RGB space, color value is proportional to light intensity, so linear
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// color-vector interpolation corresponds to physical light mixing. in sRGB
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// space, the color encoding used by many monitors, we use more of the value
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// interval to represent low intensities, and less of the interval to represent
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// high intensities. this improves color quantization
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float sRGB(float t) {
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if (t <= 0.0031308) {
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return 12.92*t;
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} else {
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return 1.055*pow(t, 5./12.) - 0.055;
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}
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}
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vec3 sRGB(vec3 color) {
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return vec3(sRGB(color.r), sRGB(color.g), sRGB(color.b));
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}
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// --- inversive geometry ---
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struct vecInv {
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vec3 sp;
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vec2 lt;
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};
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vecInv sphere(vec3 center, float radius) {
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return vecInv(
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center / radius,
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vec2(
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0.5 / radius,
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0.5 * (dot(center, center) / radius - radius)
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)
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);
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}
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// --- shading ---
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struct taggedFrag {
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int id;
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vec4 color;
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vec3 pt;
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vec3 normal;
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};
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taggedFrag[2] sort(taggedFrag a, taggedFrag b) {
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taggedFrag[2] result;
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if (a.pt.z > b.pt.z) {
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result[0] = a;
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result[1] = b;
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} else {
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result[0] = b;
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result[1] = a;
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}
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return result;
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}
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taggedFrag sphere_shading(vecInv v, vec3 pt, vec3 base_color, int id) {
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// the expression for normal needs to be checked. it's supposed to give the
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// negative gradient of the lorentz product between the impact point vector
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// and the sphere vector with respect to the coordinates of the impact
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// point. i calculated it in my head and decided that the result looked good
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// enough for now
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vec3 normal = normalize(-v.sp + 2.*v.lt.s*pt);
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float incidence = dot(normal, light_dir);
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float illum = mix(0.4, 1.0, max(incidence, 0.0));
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return taggedFrag(id, vec4(illum * base_color, opacity), pt, normal);
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}
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// --- ray-casting ---
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vec2 sphere_cast(vecInv v, vec3 dir) {
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float a = -v.lt.s * dot(dir, dir);
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float b = dot(v.sp, dir);
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float c = -v.lt.t;
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float scale = -b/(2.*a);
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float adjust = 4.*a*c/(b*b);
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if (adjust < 1.) {
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float offset = sqrt(1. - adjust);
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return vec2(
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scale * (1. - offset),
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scale * (1. + offset)
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);
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} else {
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// these parameters describe points behind the camera, so the
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// corresponding fragments won't be drawn
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return vec2(-1., -1.);
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}
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}
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void main() {
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vec2 scr = (2.*gl_FragCoord.xy - resolution) / shortdim;
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vec3 dir = vec3(focal_slope * scr, -1.);
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// initialize two spheres
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vecInv v [2];
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v[0] = sphere(vec3(0.5, 0.5, -5. + ctrl.x), radius.x);
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v[1] = sphere(vec3(-0.5, -0.5, -5. + ctrl.y), radius.y);
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vec3 color0 = vec3(1., 0.214, 0.);
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vec3 color1 = vec3(0., 0.214, 1.);
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// cast rays through the spheres
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vec2 u0 = sphere_cast(v[0], dir);
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vec2 u1 = sphere_cast(v[1], dir);
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// shade and depth-sort the impact points
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taggedFrag front_hits[2] = sort(
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sphere_shading(v[0], u0[0] * dir, color0, 0),
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sphere_shading(v[1], u1[0] * dir, color1, 1)
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);
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taggedFrag back_hits[2] = sort(
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sphere_shading(v[0], u0[1] * dir, color0, 0),
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sphere_shading(v[1], u1[1] * dir, color1, 1)
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);
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taggedFrag middle_frags[2] = sort(front_hits[1], back_hits[0]);
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// finish depth sorting
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taggedFrag frags_by_depth[4];
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frags_by_depth[0] = front_hits[0];
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frags_by_depth[1] = middle_frags[0];
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frags_by_depth[2] = middle_frags[1];
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frags_by_depth[3] = back_hits[1];
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// highlight intersections and cusps
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for (int i = 3; i >= 1; --i) {
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// intersections
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taggedFrag frag0 = frags_by_depth[i];
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taggedFrag frag1 = frags_by_depth[i-1];
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float ixn_sin = length(cross(frag0.normal, frag1.normal));
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vec3 disp = frag0.pt - frag1.pt;
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float ixn_dist = max(
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abs(dot(frag1.normal, disp)),
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abs(dot(frag0.normal, disp))
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) / ixn_sin;
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float ixn_highlight = 0.5 * highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
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frags_by_depth[i].color = mix(frags_by_depth[i].color, vec4(1.), ixn_highlight);
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frags_by_depth[i-1].color = mix(frags_by_depth[i-1].color, vec4(1.), ixn_highlight);
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// cusps
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float cusp_cos = abs(dot(dir, frag0.normal));
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float cusp_threshold = 2.*sqrt(ixn_threshold * v[frag0.id].lt.s);
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float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
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frags_by_depth[i].color = mix(frags_by_depth[i].color, vec4(1.), cusp_highlight);
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}
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// composite the sphere fragments
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vec3 color = vec3(0.);
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for (int i = 3; i >= layer_threshold; --i) {
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if (frags_by_depth[i].pt.z < 0.) {
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vec4 frag_color = frags_by_depth[i].color;
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color = mix(color, frag_color.rgb, frag_color.a);
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}
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}
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outColor = vec4(sRGB(color), 1.);
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}
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