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Use circles in triangle as low-curvature construction

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In the process, add a way to build a sphere by offset and curvature.
This commit is contained in:
Aaron Fenyes 2024-09-06 18:57:59 -07:00
parent 3493a798d1
commit ab830b194e
2 changed files with 121 additions and 29 deletions
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15
app-proto/inversive-display/src/engine.rs
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@ -1,5 +1,6 @@
use nalgebra::DVector;
// the sphere with the given center and radius, with inward-pointing normals
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(&[
@ -9,4 +10,18 @@ pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64) -> DVect
0.5 / radius,
0.5 * (center_norm_sq / radius - radius)
])
}
// the sphere of curvature `curv` whose closest point to the origin has position
// `off * dir` and normal `dir`, where `dir` is a unit vector. setting the
// curvature to zero gives a plane
pub fn sphere_with_offset(dir_x: f64, dir_y: f64, dir_z: f64, off: f64, curv: f64) -> DVector<f64> {
let norm_sp = 1.0 + off * curv;
DVector::from_column_slice(&[
norm_sp * dir_x,
norm_sp * dir_y,
norm_sp * dir_z,
0.5 * curv,
off * (1.0 + 0.5 * off * curv)
])
}

135
app-proto/inversive-display/src/main.rs
View File

@ -10,7 +10,6 @@
extern crate js_sys;
use core::array;
use nalgebra::{DMatrix, DVector};
use std::f64::consts::FRAC_1_SQRT_2;
use sycamore::{prelude::*, motion::create_raf, rt::{JsCast, JsValue}};
use web_sys::{console, window, WebGl2RenderingContext, WebGlProgram, WebGlShader, WebGlUniformLocation};
@ -86,30 +85,59 @@ fn bind_vertex_attrib(
fn push_gen_construction(
sphere_vec: &mut Vec<DVector<f64>>,
color_vec: &mut Vec<[f32; 3]>,
construction_to_world: &DMatrix<f64>,
ctrl_x: f64,
ctrl_y: f64,
radius_x: f64,
radius_y: f64
) {
// push spheres
sphere_vec.push(construction_to_world * engine::sphere(0.5, 0.5, ctrl_x, radius_x));
sphere_vec.push(construction_to_world * engine::sphere(-0.5, -0.5, ctrl_y, radius_y));
sphere_vec.push(construction_to_world * engine::sphere(-0.5, 0.5, 0.0, 0.75));
sphere_vec.push(construction_to_world * engine::sphere(0.5, -0.5, 0.0, 0.5));
sphere_vec.push(construction_to_world * engine::sphere(0.0, 0.15, 1.0, 0.25));
sphere_vec.push(construction_to_world * engine::sphere(0.0, -0.15, -1.0, 0.25));
// push colors
color_vec.push([1.00_f32, 0.25_f32, 0.00_f32]);
color_vec.push([0.00_f32, 0.25_f32, 1.00_f32]);
color_vec.push([0.25_f32, 0.00_f32, 1.00_f32]);
color_vec.push([0.25_f32, 1.00_f32, 0.00_f32]);
color_vec.push([0.75_f32, 0.75_f32, 0.00_f32]);
color_vec.push([0.00_f32, 0.75_f32, 0.50_f32]);
}
fn push_low_curv_construction(
sphere_vec: &mut Vec<DVector<f64>>,
color_vec: &mut Vec<[f32; 3]>,
construction_to_world: &DMatrix<f64>,
curv_x: f64,
curv_y: f64
off1: f64,
off2: f64,
off3: f64,
curv1: f64,
curv2: f64,
curv3: f64,
) {
sphere_vec.push(construction_to_world * DVector::from_column_slice(&[0.0, -1.0, 0.0, 0.5*curv_x, 0.0]));
sphere_vec.push(construction_to_world * DVector::from_column_slice(&[-FRAC_1_SQRT_2, 0.0, -FRAC_1_SQRT_2, 0.5*curv_y, 0.0]));
sphere_vec.push(construction_to_world * engine::sphere(0.5, 0.0, 0.5, FRAC_1_SQRT_2));
sphere_vec.push(construction_to_world * engine::sphere(-0.5, 0.0, -0.5, FRAC_1_SQRT_2));
// push spheres
let a = 0.75_f64.sqrt();
sphere_vec.push(construction_to_world * engine::sphere(0.0, 0.0, 0.0, 1.0));
sphere_vec.push(construction_to_world * engine::sphere_with_offset(1.0, 0.0, 0.0, off1, curv1));
sphere_vec.push(construction_to_world * engine::sphere_with_offset(-0.5, a, 0.0, off2, curv2));
sphere_vec.push(construction_to_world * engine::sphere_with_offset(-0.5, -a, 0.0, off3, curv3));
sphere_vec.push(construction_to_world * engine::sphere(-4.0/3.0, 0.0, 0.0, 1.0/3.0));
sphere_vec.push(construction_to_world * engine::sphere(2.0/3.0, -4.0/3.0 * a, 0.0, 1.0/3.0));
sphere_vec.push(construction_to_world * engine::sphere(2.0/3.0, 4.0/3.0 * a, 0.0, 1.0/3.0));
// push colors
color_vec.push([0.75_f32, 0.75_f32, 0.75_f32]);
color_vec.push([1.00_f32, 0.00_f32, 0.25_f32]);
color_vec.push([0.25_f32, 1.00_f32, 0.00_f32]);
color_vec.push([0.00_f32, 0.25_f32, 1.00_f32]);
color_vec.push([0.75_f32, 0.75_f32, 0.75_f32]);
color_vec.push([0.75_f32, 0.75_f32, 0.75_f32]);
color_vec.push([0.75_f32, 0.75_f32, 0.75_f32]);
}
#[derive(Clone, Copy, PartialEq)]
@ -136,8 +164,12 @@ fn main() {
// controls for low-curvature example
let low_curv_controls = create_node_ref();
let curv_x = create_signal(0.0);
let curv_y = create_signal(0.0);
let curv1 = create_signal(0.0);
let curv2 = create_signal(0.0);
let curv3 = create_signal(0.0);
let off1 = create_signal(1.0);
let off2 = create_signal(1.0);
let off3 = create_signal(1.0);
// shared controls
let opacity = create_signal(0.5);
@ -168,8 +200,12 @@ fn main() {
radius_y.track();
// track controls for low-curvature example
curv_x.track();
curv_y.track();
curv1.track();
curv2.track();
curv3.track();
off1.track();
off2.track();
off3.track();
// track shared controls
opacity.track();
@ -199,17 +235,10 @@ fn main() {
}
});
// list construction elements
// create list of construction elements
const SPHERE_MAX: usize = 200;
let mut sphere_vec = Vec::<DVector<f64>>::new();
let color_vec = vec![
[1.00_f32, 0.25_f32, 0.00_f32],
[0.00_f32, 0.25_f32, 1.00_f32],
[0.25_f32, 0.00_f32, 1.00_f32],
[0.25_f32, 1.00_f32, 0.00_f32],
[0.75_f32, 0.75_f32, 0.00_f32],
[0.00_f32, 0.75_f32, 0.50_f32],
];
let mut color_vec = Vec::<[f32; 3]>::new();
// timing
let mut last_time = 0.0;
@ -365,17 +394,21 @@ fn main() {
// update the construction
sphere_vec.clear();
color_vec.clear();
match tab_selection.get() {
Tab::GenTab => push_gen_construction(
&mut sphere_vec,
&mut color_vec,
&construction_to_world,
ctrl_x.get(), ctrl_y.get(),
radius_x.get(), radius_y.get()
),
Tab::LowCurvTab => push_low_curv_construction(
&mut sphere_vec,
&mut color_vec,
&construction_to_world,
curv_x.get(), curv_y.get()
off1.get(), off2.get(), off3.get(),
curv1.get(), curv2.get(), curv3.get(),
)
};
@ -496,25 +529,69 @@ fn main() {
}
div(ref=low_curv_controls) {
div(class="control") {
label(for="curv-x") { "Sphere 0 curvature" }
label(for="off-1") { "Sphere 1 offset" }
input(
type="range",
id="curv-x",
min=0.0,
max=2.0,
id="off-1",
min=-1.0,
max=1.0,
step=0.001,
bind:valueAsNumber=curv_x
bind:valueAsNumber=off1
)
}
div(class="control") {
label(for="curv-y") { "Sphere 1 curvature" }
label(for="off-2") { "Sphere 2 offset" }
input(
type="range",
id="curv-y",
id="off-2",
min=-1.0,
max=1.0,
step=0.001,
bind:valueAsNumber=off2
)
}
div(class="control") {
label(for="off-3") { "Sphere 3 offset" }
input(
type="range",
id="off-3",
min=-1.0,
max=1.0,
step=0.001,
bind:valueAsNumber=off3
)
}
div(class="control") {
label(for="curv-1") { "Sphere 1 curvature" }
input(
type="range",
id="curv-1",
min=0.0,
max=2.0,
step=0.001,
bind:valueAsNumber=curv_y
bind:valueAsNumber=curv1
)
}
div(class="control") {
label(for="curv-2") { "Sphere 2 curvature" }
input(
type="range",
id="curv-2",
min=0.0,
max=2.0,
step=0.001,
bind:valueAsNumber=curv2
)
}
div(class="control") {
label(for="curv-3") { "Sphere 3 curvature" }
input(
type="range",
id="curv-3",
min=0.0,
max=2.0,
step=0.001,
bind:valueAsNumber=curv3
)
}
}