app-proto/inversive-display/Cargo.toml

@@ -9,6 +9,7 @@ default = ["console_error_panic_hook"]
 
 [dependencies]
 js-sys = "0.3.70"
+nalgebra = "0.33.0"
 sycamore = "0.9.0-beta.2"
 
 # The `console_error_panic_hook` crate provides better debugging of panics by

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

@@ -0,0 +1,12 @@
+use nalgebra::DVector;
+
+pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVector<f64> {
+    let center_norm_sq = center_x * center_x + center_y * center_y + center_z * center_z;
+    DVector::from_column_slice(&[
+        center_x / radius,
+        center_y / radius,
+        center_z / radius,
+        0.5 / radius,
+        0.5 * (center_norm_sq / radius - radius)
+    ])
+}

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

@@ -4,6 +4,29 @@ precision highp float;
 
 out vec4 outColor;
 
+// --- 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)
+        )
+    );
+}
+
+// --- uniforms ---
+
+// construction
+const int SPHERE_MAX = 256;
+uniform vecInv sphere_list[SPHERE_MAX];
+
 // view
 uniform vec2 resolution;
 uniform float shortdim;
@@ -14,6 +37,7 @@ uniform vec2 radius;
 uniform float opacity;
 uniform float highlight;
 uniform int layer_threshold;
+uniform bool use_test_construction;
 
 // light and camera
 const float focal_slope = 0.3;
@@ -46,23 +70,6 @@ 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 {
@@ -127,10 +134,21 @@ void main() {
     vec3 dir = vec3(focal_slope * scr, -1.);
     
     // initialize two spheres
-    vecInv sphere_list [sphere_cnt];
+    vecInv sphere_list_internal [sphere_cnt];
-    sphere_list[0] = sphere(vec3(0.5, 0.5, -5. + ctrl.x), radius.x);
+    if (use_test_construction) {
-    sphere_list[1] = sphere(vec3(-0.5, -0.5, -5. + ctrl.y), radius.y);
+        /* DEBUG */
-    sphere_list[2] = sphere(vec3(-0.5, 0.5, -5.), 0.75);
+        // spheres 0 and 1 are identical in the test construction hard-coded
+        // here and the construction passed in through uniforms. sphere 2 has
+        // a different radius in the construction; we can use that to show that
+        // the switch is working
+        sphere_list_internal[0] = sphere(vec3(0.5, 0.5, -5. + ctrl.x), radius.x);
+        sphere_list_internal[1] = sphere(vec3(-0.5, -0.5, -5. + ctrl.y), radius.y);
+        sphere_list_internal[2] = sphere(vec3(-0.5, 0.5, -5.), 0.5);
+    } else {
+        for (int i = 0; i < sphere_cnt; ++i) {
+            sphere_list_internal[i] = sphere_list[i];
+        }
+    }
     vec3 color_list [sphere_cnt];
     color_list[0] = vec3(1., 0.25, 0.);
     color_list[1] = vec3(0., 0.25, 1.);
@@ -141,13 +159,13 @@ void main() {
     taggedFrag frags [2*sphere_cnt];
     int frag_cnt = 0;
     for (int i = 0; i < sphere_cnt; ++i) {
-        vec2 hit_depths = sphere_cast(sphere_list[i], dir);
+        vec2 hit_depths = sphere_cast(sphere_list_internal[i], dir);
         if (!isnan(hit_depths[0])) {
-            frags[frag_cnt] = sphere_shading(sphere_list[i], hit_depths[0] * dir, color_list[i], i);
+            frags[frag_cnt] = sphere_shading(sphere_list_internal[i], hit_depths[0] * dir, color_list[i], i);
             ++frag_cnt;
         }
         if (!isnan(hit_depths[1])) {
-            frags[frag_cnt] = sphere_shading(sphere_list[i], hit_depths[1] * dir, color_list[i], i);
+            frags[frag_cnt] = sphere_shading(sphere_list_internal[i], hit_depths[1] * dir, color_list[i], i);
             ++frag_cnt;
         }
     }
@@ -182,7 +200,7 @@ void main() {
         
         // cusps
         float cusp_cos = abs(dot(dir, frag0.normal));
-        float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[frag0.id].lt.s);
+        float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list_internal[frag0.id].lt.s);
         float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
         frags[i].color = mix(frags[i].color, vec4(1.), cusp_highlight);
     }

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

@@ -8,9 +8,13 @@
 //
 
 extern crate js_sys;
+use core::array;
+use nalgebra::DVector;
 use sycamore::{prelude::*, rt::{JsCast, JsValue}};
 use web_sys::{console, WebGl2RenderingContext, WebGlShader};
 
+mod engine;
+
 fn compile_shader(
     context: &WebGl2RenderingContext,
     shader_type: u32,
@@ -70,6 +74,7 @@ fn main() {
     console_error_panic_hook::set_once();
     
     sycamore::render(|| {
+        // controls
         let ctrl_x = create_signal(0.0);
         let ctrl_y = create_signal(0.0);
         let radius_x = create_signal(1.0);
@@ -77,9 +82,16 @@ fn main() {
         let opacity = create_signal(0.5);
         let highlight = create_signal(0.2);
         let layer_threshold = create_signal(0.0);
+        let use_test_construction = create_signal(false);
+        
+        // display
         let display = create_node_ref();
         
         on_mount(move || {
+            // list construction elements
+            const SPHERE_MAX: usize = 256;
+            let mut sphere_vec = Vec::<DVector<f64>>::new();
+            
             // get the display canvas
             let canvas = display
                 .get::<DomNode>()
@@ -119,14 +131,21 @@ fn main() {
             ctx.use_program(Some(&program));
             
             // find indices of vertex attributes and uniforms
+            let sphere_sp_locs = array::from_fn::<_, SPHERE_MAX, _>(
+                |n| ctx.get_uniform_location(&program, format!("sphere_list[{}].sp", n).as_str())
+            );
+            let sphere_lt_locs = array::from_fn::<_, SPHERE_MAX, _>(
+                |n| ctx.get_uniform_location(&program, format!("sphere_list[{}].lt", n).as_str())
+            );
             let position_index = ctx.get_attrib_location(&program, "position") as u32;
             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 ctrl_loc = ctx.get_uniform_location(&program, "ctrl"); /* DEBUG */
-            let radius_loc = ctx.get_uniform_location(&program, "radius");
+            let radius_loc = ctx.get_uniform_location(&program, "radius"); /* DEBUG */
             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");
+            let use_test_construction_loc = ctx.get_uniform_location(&program, "use_test_construction");
             
             // create a vertex array and bind it to the graphics context
             let vertex_array = ctx.create_vertex_array().unwrap();
@@ -148,18 +167,38 @@ fn main() {
             
             // set up a repainting routine
             create_effect(move || {
+                // update the construction
+                sphere_vec.clear();
+                sphere_vec.push(engine::sphere(0.5, 0.5, -5.0 + ctrl_x.get(), radius_x.get()));
+                sphere_vec.push(engine::sphere(-0.5, -0.5, -5.0 + ctrl_y.get(), radius_y.get()));
+                sphere_vec.push(engine::sphere(-0.5, 0.5, -5.0, 0.75));
+                
                 // 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));
                 
+                // pass the construction
+                for n in 0..sphere_vec.len() {
+                    let v = &sphere_vec[n];
+                    ctx.uniform3f(
+                        sphere_sp_locs[n].as_ref(),
+                        v[0] as f32, v[1] as f32, v[2] as f32
+                    );
+                    ctx.uniform2f(
+                        sphere_lt_locs[n].as_ref(),
+                        v[3] as f32, v[4] as f32
+                    );
+                }
+                
                 // pass the control parameters
-                ctx.uniform2f(ctrl_loc.as_ref(), ctrl_x.get() as f32, ctrl_y.get() as f32);
+                ctx.uniform2f(ctrl_loc.as_ref(), ctrl_x.get() as f32, ctrl_y.get() as f32); /* DEBUG */
-                ctx.uniform2f(radius_loc.as_ref(), radius_x.get() as f32, radius_y.get() as f32);
+                ctx.uniform2f(radius_loc.as_ref(), radius_x.get() as f32, radius_y.get() as f32); /* DEBUG */
                 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);
+                ctx.uniform1i(use_test_construction_loc.as_ref(), use_test_construction.get() as i32);
                 
                 // draw the scene
                 ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
@@ -215,6 +254,10 @@ fn main() {
                     step=1.0,
                     bind:valueAsNumber=layer_threshold
                 )
+                input(
+                    type="checkbox",
+                    bind:checked=use_test_construction
+                )
             }
         }
     });