diff --git a/app-proto/inversive-display/src/identity.vert b/app-proto/inversive-display/src/identity.vert new file mode 100644 index 0000000..183a65f --- /dev/null +++ b/app-proto/inversive-display/src/identity.vert @@ -0,0 +1,7 @@ +#version 300 es + +in vec4 position; + +void main() { + gl_Position = position; +} \ No newline at end of file diff --git a/app-proto/inversive-display/src/inversive.frag b/app-proto/inversive-display/src/inversive.frag new file mode 100644 index 0000000..a4cbe8d --- /dev/null +++ b/app-proto/inversive-display/src/inversive.frag @@ -0,0 +1,187 @@ +#version 300 es + +precision highp float; + +out vec4 outColor; + +// view +uniform vec2 resolution; +uniform float shortdim; + +// controls +uniform vec2 ctrl; +uniform vec2 radius; +uniform float opacity; +uniform float highlight; +uniform int layer_threshold; + +// light and camera +const float focal_slope = 0.3; +const vec3 light_dir = normalize(vec3(2., 2., 1.)); +const float ixn_threshold = 0.005; + +// --- sRGB --- + +// map colors from RGB space to sRGB space, as specified in the sRGB standard +// (IEC 61966-2-1:1999) +// +// https://www.color.org/sRGB.pdf +// https://www.color.org/chardata/rgb/srgb.xalter +// +// in RGB space, color value is proportional to light intensity, so linear +// color-vector interpolation corresponds to physical light mixing. in sRGB +// space, the color encoding used by many monitors, we use more of the value +// interval to represent low intensities, and less of the interval to represent +// high intensities. this improves color quantization + +float sRGB(float t) { + if (t <= 0.0031308) { + return 12.92*t; + } else { + return 1.055*pow(t, 5./12.) - 0.055; + } +} + +vec3 sRGB(vec3 color) { + return vec3(sRGB(color.r), sRGB(color.g), sRGB(color.b)); +} + +// --- inversive geometry --- + +struct vecInv { + vec3 sp; + vec2 lt; +}; + +vecInv sphere(vec3 center, float radius) { + return vecInv( + center / radius, + vec2( + 0.5 / radius, + 0.5 * (dot(center, center) / radius - radius) + ) + ); +} + +// --- shading --- + +struct taggedFrag { + int id; + vec4 color; + vec3 pt; + vec3 normal; +}; + +taggedFrag[2] sort(taggedFrag a, taggedFrag b) { + taggedFrag[2] result; + if (a.pt.z > b.pt.z) { + result[0] = a; + result[1] = b; + } else { + result[0] = b; + result[1] = a; + } + return result; +} + +taggedFrag sphere_shading(vecInv v, vec3 pt, vec3 base_color, int id) { + // the expression for normal needs to be checked. it's supposed to give the + // negative gradient of the lorentz product between the impact point vector + // and the sphere vector with respect to the coordinates of the impact + // point. i calculated it in my head and decided that the result looked good + // enough for now + vec3 normal = normalize(-v.sp + 2.*v.lt.s*pt); + + float incidence = dot(normal, light_dir); + float illum = mix(0.4, 1.0, max(incidence, 0.0)); + return taggedFrag(id, vec4(illum * base_color, opacity), pt, normal); +} + +// --- ray-casting --- + +vec2 sphere_cast(vecInv v, vec3 dir) { + float a = -v.lt.s * dot(dir, dir); + float b = dot(v.sp, dir); + float c = -v.lt.t; + + float scale = -b/(2.*a); + float adjust = 4.*a*c/(b*b); + + if (adjust < 1.) { + float offset = sqrt(1. - adjust); + return vec2( + scale * (1. - offset), + scale * (1. + offset) + ); + } else { + // these parameters describe points behind the camera, so the + // corresponding fragments won't be drawn + return vec2(-1., -1.); + } +} + +void main() { + vec2 scr = (2.*gl_FragCoord.xy - resolution) / shortdim; + vec3 dir = vec3(focal_slope * scr, -1.); + + // initialize two spheres + vecInv v [2]; + v[0] = sphere(vec3(0.5, 0.5, -5. + ctrl.x), radius.x); + v[1] = sphere(vec3(-0.5, -0.5, -5. + ctrl.y), radius.y); + vec3 color0 = vec3(1., 0.214, 0.); + vec3 color1 = vec3(0., 0.214, 1.); + + // cast rays through the spheres + vec2 u0 = sphere_cast(v[0], dir); + vec2 u1 = sphere_cast(v[1], dir); + + // shade and depth-sort the impact points + taggedFrag front_hits[2] = sort( + sphere_shading(v[0], u0[0] * dir, color0, 0), + sphere_shading(v[1], u1[0] * dir, color1, 1) + ); + taggedFrag back_hits[2] = sort( + sphere_shading(v[0], u0[1] * dir, color0, 0), + sphere_shading(v[1], u1[1] * dir, color1, 1) + ); + taggedFrag middle_frags[2] = sort(front_hits[1], back_hits[0]); + + // finish depth sorting + taggedFrag frags_by_depth[4]; + frags_by_depth[0] = front_hits[0]; + frags_by_depth[1] = middle_frags[0]; + frags_by_depth[2] = middle_frags[1]; + frags_by_depth[3] = back_hits[1]; + + // highlight intersections and cusps + for (int i = 3; i >= 1; --i) { + // intersections + taggedFrag frag0 = frags_by_depth[i]; + taggedFrag frag1 = frags_by_depth[i-1]; + float ixn_sin = length(cross(frag0.normal, frag1.normal)); + vec3 disp = frag0.pt - frag1.pt; + float ixn_dist = max( + abs(dot(frag1.normal, disp)), + abs(dot(frag0.normal, disp)) + ) / ixn_sin; + float ixn_highlight = 0.5 * highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist)); + frags_by_depth[i].color = mix(frags_by_depth[i].color, vec4(1.), ixn_highlight); + frags_by_depth[i-1].color = mix(frags_by_depth[i-1].color, vec4(1.), ixn_highlight); + + // cusps + float cusp_cos = abs(dot(dir, frag0.normal)); + float cusp_threshold = 2.*sqrt(ixn_threshold * v[frag0.id].lt.s); + float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos)); + frags_by_depth[i].color = mix(frags_by_depth[i].color, vec4(1.), cusp_highlight); + } + + // composite the sphere fragments + vec3 color = vec3(0.); + for (int i = 3; i >= layer_threshold; --i) { + if (frags_by_depth[i].pt.z < 0.) { + vec4 frag_color = frags_by_depth[i].color; + color = mix(color, frag_color.rgb, frag_color.a); + } + } + outColor = vec4(sRGB(color), 1.); +} \ No newline at end of file diff --git a/app-proto/inversive-display/src/main.rs b/app-proto/inversive-display/src/main.rs index 72846fc..186facf 100644 --- a/app-proto/inversive-display/src/main.rs +++ b/app-proto/inversive-display/src/main.rs @@ -8,7 +8,6 @@ // extern crate js_sys; -use std::f64::consts::PI as PI; use sycamore::{prelude::*, rt::{JsCast, JsValue}}; use web_sys::{console, WebGl2RenderingContext, WebGlShader}; @@ -71,8 +70,13 @@ fn main() { console_error_panic_hook::set_once(); sycamore::render(|| { - let turn = create_signal(0.0); - let tip = create_signal(0.0); + let ctrl_x = create_signal(0.0); + let ctrl_y = create_signal(0.0); + let radius_x = create_signal(1.0); + let radius_y = create_signal(1.0); + let opacity = create_signal(0.5); + let highlight = create_signal(0.2); + let layer_threshold = create_signal(0.0); let display = create_node_ref(); on_mount(move || { @@ -91,38 +95,12 @@ fn main() { let vertex_shader = compile_shader( &ctx, WebGl2RenderingContext::VERTEX_SHADER, - r##"#version 300 es - - in vec3 position; - in vec3 color; - - out vec4 vertexColor; - - uniform mat4 world_to_clip; - uniform mat3 rotation; - - void main() { - vec3 world_pos = rotation * position - vec3(0., 0., 6.); - gl_Position = world_to_clip * vec4(world_pos, 1.); - vertexColor = vec4(color, 1.); - } - "##, + include_str!("identity.vert"), ); let fragment_shader = compile_shader( &ctx, WebGl2RenderingContext::FRAGMENT_SHADER, - r##"#version 300 es - - precision highp float; - - in vec4 vertexColor; - - out vec4 outColor; - - void main() { - outColor = vertexColor; - } - "##, + include_str!("inversive.frag"), ); let program = ctx.create_program().unwrap(); ctx.attach_shader(&program, &vertex_shader); @@ -142,80 +120,48 @@ fn main() { // find indices of vertex attributes and uniforms let position_index = ctx.get_attrib_location(&program, "position") as u32; - let color_index = ctx.get_attrib_location(&program, "color") as u32; - let world_to_clip_loc = ctx.get_uniform_location(&program, "world_to_clip"); - let rotation_loc = ctx.get_uniform_location(&program, "rotation"); + let resolution_loc = ctx.get_uniform_location(&program, "resolution"); + let shortdim_loc = ctx.get_uniform_location(&program, "shortdim"); + let ctrl_loc = ctx.get_uniform_location(&program, "ctrl"); + let radius_loc = ctx.get_uniform_location(&program, "radius"); + let opacity_loc = ctx.get_uniform_location(&program, "opacity"); + let highlight_loc = ctx.get_uniform_location(&program, "highlight"); + let layer_threshold_loc = ctx.get_uniform_location(&program, "layer_threshold"); // create a vertex array and bind it to the graphics context let vertex_array = ctx.create_vertex_array().unwrap(); ctx.bind_vertex_array(Some(&vertex_array)); - // set the projection map - let focal_length = 3.0_f32; - let near_clip = 0.1_f32; - let far_clip = 20_f32; - let depth_inv = 1_f32 / (far_clip - near_clip); - let world_to_clip: [f32; 16] = [ - focal_length, 0.0, 0.0, 0.0, - 0.0, focal_length, 0.0, 0.0, - 0.0, 0.0, (near_clip + far_clip) * depth_inv, -1., - 0.0, 0.0, 2. * near_clip * far_clip * depth_inv, 0.0 + // set the vertex positions + const VERTEX_CNT: usize = 6; + let positions: [f32; 3*VERTEX_CNT] = [ + // northwest triangle + -1.0, -1.0, 0.0, + -1.0, 1.0, 0.0, + 1.0, 1.0, 0.0, + // southeast triangle + -1.0, -1.0, 0.0, + 1.0, 1.0, 0.0, + 1.0, -1.0, 0.0 ]; - ctx.uniform_matrix4fv_with_f32_array(world_to_clip_loc.as_ref(), false, &world_to_clip); + bind_vertex_attrib(&ctx, position_index, 3, &positions); // set up a repainting routine create_effect(move || { - const VERTEX_CNT: usize = 9; + // set the resolution + let width = canvas.width() as f32; + let height = canvas.height() as f32; + ctx.uniform2f(resolution_loc.as_ref(), width, height); + ctx.uniform1f(shortdim_loc.as_ref(), width.min(height)); - // set the vertex positions - let tip_shift = 4.0/3.0 * tip.get() as f32; - let positions: [f32; 3*VERTEX_CNT] = [ - // triangle 1 - 1.0 - tip_shift, 1.0 - tip_shift, 1.0 - tip_shift, - 1.0, -1.0, -1.0, - -1.0, 1.0, -1.0, - // triangle 2 - 1.0 - tip_shift, 1.0 - tip_shift, 1.0 - tip_shift, - -1.0, 1.0, -1.0, - -1.0, -1.0, 1.0, - // triangle 3 - 1.0 - tip_shift, 1.0 - tip_shift, 1.0 - tip_shift, - -1.0, -1.0, 1.0, - 1.0, -1.0, -1.0 - ]; - bind_vertex_attrib(&ctx, position_index, 3, &positions); + // pass the control parameters + ctx.uniform2f(ctrl_loc.as_ref(), ctrl_x.get() as f32, ctrl_y.get() as f32); + ctx.uniform2f(radius_loc.as_ref(), radius_x.get() as f32, radius_y.get() as f32); + ctx.uniform1f(opacity_loc.as_ref(), opacity.get() as f32); + ctx.uniform1f(highlight_loc.as_ref(), highlight.get() as f32); + ctx.uniform1i(layer_threshold_loc.as_ref(), layer_threshold.get() as i32); - // set the vertex colors - let colors: [f32; 3*VERTEX_CNT] = [ - // triangle 1 - 1.0, 0.0, 0.5, - 1.0, 0.0, 0.5, - 1.0, 0.0, 0.5, - // triangle 2 - 0.0, 0.5, 1.0, - 0.0, 0.5, 1.0, - 0.0, 0.5, 1.0, - // triangle 3 - 0.5, 0.0, 1.0, - 0.5, 0.0, 1.0, - 0.5, 0.0, 1.0 - ]; - bind_vertex_attrib(&ctx, color_index, 3, &colors); - - // set the rotation - let angle_val = (2.0*PI*turn.get()) as f32; - let angle_cos = angle_val.cos(); - let angle_sin = angle_val.sin(); - let rotation: [f32; 9] = [ - angle_cos, 0.0, angle_sin, - 0.0, 1.0, 0.0, - -angle_sin, 0.0, angle_cos, - ]; - ctx.uniform_matrix3fv_with_f32_array(rotation_loc.as_ref(), false, &rotation); - - // clear the screen and draw the scene - ctx.clear_color(0.0, 0.0, 0.0, 1.0); - ctx.clear(WebGl2RenderingContext::COLOR_BUFFER_BIT); + // draw the scene ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32); }); }); @@ -225,15 +171,49 @@ fn main() { canvas(ref=display, width="600", height="600") input( type="range", + min=-1.0, max=1.0, - step=0.01, - bind:valueAsNumber=turn + step=0.001, + bind:valueAsNumber=ctrl_x + ) + input( + type="range", + min=-1.0, + max=1.0, + step=0.001, + bind:valueAsNumber=ctrl_y + ) + input( + type="range", + min=0.5, + max=1.5, + step=0.001, + bind:valueAsNumber=radius_x + ) + input( + type="range", + min=0.5, + max=1.5, + step=0.001, + bind:valueAsNumber=radius_y ) input( type="range", max=1.0, - step=0.01, - bind:valueAsNumber=tip + step=0.001, + bind:valueAsNumber=opacity + ) + input( + type="range", + max=1.0, + step=0.001, + bind:valueAsNumber=highlight + ) + input( + type="range", + max=3.0, + step=1.0, + bind:valueAsNumber=layer_threshold ) } }