app-proto/inversive-display/src/identity.vert

@@ -1,7 +0,0 @@
-#version 300 es
-
-in vec4 position;
-
-void main() {
-    gl_Position = position;
-}

app-proto/inversive-display/src/inversive.frag

@@ -1,187 +0,0 @@
-#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.);
-}

app-proto/inversive-display/src/main.rs

@@ -8,6 +8,7 @@
 //
 
 extern crate js_sys;
+use std::f64::consts::PI as PI;
 use sycamore::{prelude::*, rt::{JsCast, JsValue}};
 use web_sys::{console, WebGl2RenderingContext, WebGlShader};
 
@@ -70,13 +71,8 @@ fn main() {
     console_error_panic_hook::set_once();
     
     sycamore::render(|| {
-        let ctrl_x = create_signal(0.0);
+        let turn = create_signal(0.0);
-        let ctrl_y = create_signal(0.0);
+        let tip = 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 || {
@@ -95,12 +91,38 @@ fn main() {
             let vertex_shader = compile_shader(
                 &ctx,
                 WebGl2RenderingContext::VERTEX_SHADER,
-                include_str!("identity.vert"),
+                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.);
+                }
+                "##,
             );
             let fragment_shader = compile_shader(
                 &ctx,
                 WebGl2RenderingContext::FRAGMENT_SHADER,
-                include_str!("inversive.frag"),
+                r##"#version 300 es
+            
+                precision highp float;
+                
+                in vec4 vertexColor;
+                
+                out vec4 outColor;
+                
+                void main() {
+                    outColor = vertexColor;
+                }
+                "##,
             );
             let program = ctx.create_program().unwrap();
             ctx.attach_shader(&program, &vertex_shader);
@@ -120,48 +142,80 @@ fn main() {
             
             // find indices of vertex attributes and uniforms
             let position_index = ctx.get_attrib_location(&program, "position") as u32;
-            let resolution_loc = ctx.get_uniform_location(&program, "resolution");
+            let color_index = ctx.get_attrib_location(&program, "color") as u32;
-            let shortdim_loc = ctx.get_uniform_location(&program, "shortdim");
+            let world_to_clip_loc = ctx.get_uniform_location(&program, "world_to_clip");
-            let ctrl_loc = ctx.get_uniform_location(&program, "ctrl");
+            let rotation_loc = ctx.get_uniform_location(&program, "rotation");
-            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 vertex positions
+            // set the projection map
-            const VERTEX_CNT: usize = 6;
+            let focal_length = 3.0_f32;
-            let positions: [f32; 3*VERTEX_CNT] = [
+            let near_clip = 0.1_f32;
-                // northwest triangle
+            let far_clip = 20_f32;
-                -1.0, -1.0, 0.0,
+            let depth_inv = 1_f32 / (far_clip - near_clip);
-                -1.0,  1.0, 0.0,
+            let world_to_clip: [f32; 16] = [
-                 1.0,  1.0, 0.0,
+                focal_length, 0.0, 0.0, 0.0,
-                // southeast triangle
+                0.0, focal_length, 0.0, 0.0,
-                -1.0, -1.0, 0.0,
+                0.0, 0.0, (near_clip + far_clip) * depth_inv, -1.,
-                 1.0,  1.0, 0.0,
+                0.0, 0.0, 2. * near_clip * far_clip * depth_inv, 0.0
-                 1.0, -1.0, 0.0
             ];
-            bind_vertex_attrib(&ctx, position_index, 3, &positions);
+            ctx.uniform_matrix4fv_with_f32_array(world_to_clip_loc.as_ref(), false, &world_to_clip);
             
             // set up a repainting routine
             create_effect(move || {
-                // set the resolution
+                const VERTEX_CNT: usize = 9;
-                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));
                 
-                // pass the control parameters
+                // set the vertex positions
-                ctx.uniform2f(ctrl_loc.as_ref(), ctrl_x.get() as f32, ctrl_y.get() as f32);
+                let tip_shift = 4.0/3.0 * tip.get() as f32;
-                ctx.uniform2f(radius_loc.as_ref(), radius_x.get() as f32, radius_y.get() as f32);
+                let positions: [f32; 3*VERTEX_CNT] = [
-                ctx.uniform1f(opacity_loc.as_ref(), opacity.get() as f32);
+                    // triangle 1
-                ctx.uniform1f(highlight_loc.as_ref(), highlight.get() as f32);
+                    1.0 - tip_shift, 1.0 - tip_shift, 1.0 - tip_shift,
-                ctx.uniform1i(layer_threshold_loc.as_ref(), layer_threshold.get() as i32);
+                    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);
                 
-                // draw the scene
+                // 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);
                 ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
             });
         });
@@ -171,49 +225,15 @@ fn main() {
                 canvas(ref=display, width="600", height="600")
                 input(
                     type="range",
-                    min=-1.0,
                     max=1.0,
-                    step=0.001,
+                    step=0.01,
-                    bind:valueAsNumber=ctrl_x
+                    bind:valueAsNumber=turn
-                )
-                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=0.001,
+                    step=0.01,
-                    bind:valueAsNumber=opacity
+                    bind:valueAsNumber=tip
-                )
-                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
                 )
             }
         }