Write a ray-caster for inversive spheres
This commit is contained in:
Aaron Fenyes
parent
f274119da6
commit
c78a041dc7
@ -8,7 +8,6 @@
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//
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extern crate js_sys;
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use std::f64::consts::PI as PI;
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use sycamore::{prelude::*, rt::{JsCast, JsValue}};
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use web_sys::{console, WebGl2RenderingContext, WebGlShader};
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@ -71,8 +70,8 @@ fn main() {
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console_error_panic_hook::set_once();
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sycamore::render(|| {
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let turn = create_signal(0.0);
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let tip = create_signal(0.0);
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let ctrl_x = create_signal(0.0);
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let ctrl_y = create_signal(0.0);
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let display = create_node_ref();
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on_mount(move || {
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@ -93,18 +92,10 @@ fn main() {
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WebGl2RenderingContext::VERTEX_SHADER,
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r##"#version 300 es
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in vec3 position;
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in vec3 color;
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out vec4 vertexColor;
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uniform mat4 world_to_clip;
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uniform mat3 rotation;
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in vec4 position;
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void main() {
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vec3 world_pos = rotation * position - vec3(0., 0., 6.);
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gl_Position = world_to_clip * vec4(world_pos, 1.);
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vertexColor = vec4(color, 1.);
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gl_Position = position;
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}
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"##,
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);
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@ -115,12 +106,68 @@ fn main() {
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precision highp float;
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in vec4 vertexColor;
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out vec4 outColor;
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uniform vec2 resolution;
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uniform float shortdim;
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uniform vec2 ctrl;
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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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const float focal_slope = 0.3;
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const vec3 light_dir = normalize(vec3(2., 2., 1.));
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void main() {
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outColor = vertexColor;
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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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vecInv v = sphere(vec3(ctrl, -5.), 1.);
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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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float offset = sqrt(1. - adjust);
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float u_front = scale * (1. - offset);
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float u_back = scale * (1. + offset);
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vec3 color;
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if (adjust < 1. && u_front > 0.) {
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// the expression for normal needs to be checked. it's
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// supposed to give the negative gradient of the lorentz
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// product between the impact point vector and the sphere
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// vector with respect to the coordinates of the impact
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// point. i calculated it in my head and decided that
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// the result looked good enough for now
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vec3 pt_front = u_front * dir;
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vec3 normal_front = normalize(-v.sp + 2.*v.lt.s*pt_front);
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float incidence = dot(normal_front, light_dir);
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if (incidence < 0.) {
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color = mix(vec3(0.2, 0.0, 0.4), vec3(0.1, 0.0, 0.2), -incidence);
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} else {
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color = mix(vec3(0.4, 0.0, 0.2), vec3(1., 0.8, 1.), incidence);
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}
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} else {
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color = vec3(0.);
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}
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outColor = vec4(color, 1.);
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}
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"##,
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);
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@ -142,79 +189,38 @@ fn main() {
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// find indices of vertex attributes and uniforms
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let position_index = ctx.get_attrib_location(&program, "position") as u32;
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let color_index = ctx.get_attrib_location(&program, "color") as u32;
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let world_to_clip_loc = ctx.get_uniform_location(&program, "world_to_clip");
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let rotation_loc = ctx.get_uniform_location(&program, "rotation");
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let resolution_loc = ctx.get_uniform_location(&program, "resolution");
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let shortdim_loc = ctx.get_uniform_location(&program, "shortdim");
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let ctrl_loc = ctx.get_uniform_location(&program, "ctrl");
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// create a vertex array and bind it to the graphics context
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let vertex_array = ctx.create_vertex_array().unwrap();
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ctx.bind_vertex_array(Some(&vertex_array));
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// enable depth testing
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ctx.enable(WebGl2RenderingContext::DEPTH_TEST);
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// set the projection map
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let focal_length = 3.0_f32;
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let near_clip = 0.1_f32;
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let far_clip = 20_f32;
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let depth_inv = 1_f32 / (far_clip - near_clip);
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let world_to_clip: [f32; 16] = [
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focal_length, 0.0, 0.0, 0.0,
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0.0, focal_length, 0.0, 0.0,
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0.0, 0.0, -(near_clip + far_clip) * depth_inv, -1.,
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0.0, 0.0, -2. * near_clip * far_clip * depth_inv, 0.0
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// set the vertex positions
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const VERTEX_CNT: usize = 6;
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let positions: [f32; 3*VERTEX_CNT] = [
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// northwest triangle
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-1.0, -1.0, 0.0,
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-1.0, 1.0, 0.0,
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1.0, 1.0, 0.0,
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// southeast triangle
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-1.0, -1.0, 0.0,
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1.0, 1.0, 0.0,
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1.0, -1.0, 0.0
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];
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ctx.uniform_matrix4fv_with_f32_array(world_to_clip_loc.as_ref(), false, &world_to_clip);
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bind_vertex_attrib(&ctx, position_index, 3, &positions);
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// set the resolution
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let width = canvas.width() as f32;
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let height = canvas.height() as f32;
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ctx.uniform2f(resolution_loc.as_ref(), width, height);
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ctx.uniform1f(shortdim_loc.as_ref(), width.min(height));
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// set up a repainting routine
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create_effect(move || {
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const VERTEX_CNT: usize = 9;
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// set the vertex positions
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let tip_shift = 4.0/3.0 * tip.get() as f32;
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let positions: [f32; 3*VERTEX_CNT] = [
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// triangle 1
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1.0 - tip_shift, 1.0 - tip_shift, 1.0 - tip_shift,
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1.0, -1.0, -1.0,
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-1.0, 1.0, -1.0,
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// triangle 2
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1.0 - tip_shift, 1.0 - tip_shift, 1.0 - tip_shift,
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-1.0, 1.0, -1.0,
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-1.0, -1.0, 1.0,
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// triangle 3
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1.0 - tip_shift, 1.0 - tip_shift, 1.0 - tip_shift,
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-1.0, -1.0, 1.0,
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1.0, -1.0, -1.0
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];
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bind_vertex_attrib(&ctx, position_index, 3, &positions);
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// set the vertex colors
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let colors: [f32; 3*VERTEX_CNT] = [
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// triangle 1
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1.0, 0.0, 0.5,
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1.0, 0.0, 0.5,
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1.0, 0.0, 0.5,
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// triangle 2
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0.0, 0.5, 1.0,
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0.0, 0.5, 1.0,
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0.0, 0.5, 1.0,
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// triangle 3
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0.5, 0.0, 1.0,
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0.5, 0.0, 1.0,
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0.5, 0.0, 1.0
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];
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bind_vertex_attrib(&ctx, color_index, 3, &colors);
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// set the rotation
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let angle_val = (2.0*PI*turn.get()) as f32;
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let angle_cos = angle_val.cos();
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let angle_sin = angle_val.sin();
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let rotation: [f32; 9] = [
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angle_cos, 0.0, angle_sin,
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0.0, 1.0, 0.0,
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-angle_sin, 0.0, angle_cos,
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];
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ctx.uniform_matrix3fv_with_f32_array(rotation_loc.as_ref(), false, &rotation);
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// pass the control parameters
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ctx.uniform2f(ctrl_loc.as_ref(), ctrl_x.get() as f32, ctrl_y.get() as f32);
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// clear the screen and draw the scene
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ctx.clear_color(0.0, 0.0, 0.0, 1.0);
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@ -228,15 +234,17 @@ fn main() {
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canvas(ref=display, width="600", height="600")
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input(
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type="range",
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min=-1.0,
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max=1.0,
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step=0.01,
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bind:valueAsNumber=turn
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bind:valueAsNumber=ctrl_x
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)
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input(
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type="range",
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min=-1.0,
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max=1.0,
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step=0.01,
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bind:valueAsNumber=tip
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bind:valueAsNumber=ctrl_y
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)
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}
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}
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