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Branches Tags
glen:main
glen:aroundLineInEightyChars
glen:noTrailingWhitespace
glen:pointCoordRegulators
glen:study554
glen:readme-toplevel
glen:kaleidocycle-example
glen:outline-update-fix
glen:lang-trials
glen:seed-problem
StudioInfinity:main
StudioInfinity:readme-toplevel
StudioInfinity:kaleidocycle-example
StudioInfinity:outline-update-fix
StudioInfinity:lang-trials
StudioInfinity:seed-problem
glen:0.3pre
glen:0.2
glen:v0.1.1
glen:v0.1.0
StudioInfinity:0.3pre
StudioInfinity:0.2
StudioInfinity:v0.1.1
StudioInfinity:v0.1.0
..
compare: StudioInfinity:main
Branches Tags
StudioInfinity:main
StudioInfinity:readme-toplevel
StudioInfinity:kaleidocycle-example
StudioInfinity:outline-update-fix
StudioInfinity:lang-trials
StudioInfinity:seed-problem
glen:main
glen:aroundLineInEightyChars
glen:noTrailingWhitespace
glen:pointCoordRegulators
glen:study554
glen:readme-toplevel
glen:kaleidocycle-example
glen:outline-update-fix
glen:lang-trials
glen:seed-problem
StudioInfinity:0.3pre
StudioInfinity:0.2
StudioInfinity:v0.1.1
StudioInfinity:v0.1.0
glen:0.3pre
glen:0.2
glen:v0.1.1
glen:v0.1.0

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aroundLine ... main

21 changed files with 487 additions and 644 deletions
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53
app-proto/src/assembly.rs
View file

@ -261,8 +261,7 @@ impl ProblemPoser for Sphere {
let index = self.column_index().expect(
indexing_error("Sphere", &self.id, "it").as_str());
problem.gram.push_sym(index, index, 1.0);
problem.guess.set_column(
index, &self.representation.get_clone_untracked());
problem.guess.set_column(index, &self.representation.get_clone_untracked());
}
}
@ -368,8 +367,7 @@ impl ProblemPoser for Point {
indexing_error("Point", &self.id, "it").as_str());
problem.gram.push_sym(index, index, 0.0);
problem.frozen.push(Self::WEIGHT_COMPONENT, index, 0.5);
problem.guess.set_column(
index, &self.representation.get_clone_untracked());
problem.guess.set_column(index, &self.representation.get_clone_untracked());
}
}
@ -414,8 +412,7 @@ pub struct InversiveDistanceRegulator {
impl InversiveDistanceRegulator {
pub fn new(subjects: [Rc<dyn Element>; 2]) -> Self {
let representations = subjects.each_ref().map(
|subj| subj.representation());
let representations = subjects.each_ref().map(|subj| subj.representation());
let measurement = create_memo(move || {
representations[0].with(|rep_0|
representations[1].with(|rep_1|
@ -548,9 +545,7 @@ impl PointCoordinateRegulator {
move |rep| rep[axis as usize]
);
let set_point = create_signal(SpecifiedValue::from_empty_spec());
Self {
subject, axis, measurement, set_point, serial: Self::next_serial()
}
Self { subject, axis, measurement, set_point, serial: Self::next_serial() }
}
}
@ -584,8 +579,8 @@ impl ProblemPoser for PointCoordinateRegulator {
}
if nset == Axis::CARDINALITY {
let [x, y, z] = coords;
problem.frozen.push(Point::NORM_COMPONENT,
col, point(x,y,z)[Point::NORM_COMPONENT]);
problem.frozen.push(
Point::NORM_COMPONENT, col, point(x,y,z)[Point::NORM_COMPONENT]);
}
}
});
@ -684,8 +679,7 @@ impl Assembly {
let id = elt.id().clone();
let elt_rc = Rc::new(elt);
self.elements.update(|elts| elts.insert(elt_rc.clone()));
self.elements_by_id.update(
|elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
// create and insert the element's default regulators
for reg in elt_rc.default_regulators() {
@ -761,8 +755,7 @@ impl Assembly {
pub fn load_config(&self, config: &DMatrix<f64>) {
for elt in self.elements.get_clone_untracked() {
elt.representation().update(
|rep| rep.set_column(
0, &config.column(elt.column_index().unwrap()))
|rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
);
}
}
@ -907,8 +900,7 @@ impl Assembly {
if column_index < realized_dim {
// this element had a column index when we started, so by
// invariant (1), it's reflected in the tangent space
let mut target_columns =
motion_proj.columns_mut(0, realized_dim);
let mut target_columns = motion_proj.columns_mut(0, realized_dim);
target_columns += self.tangent.with(
|tan| tan.proj(&elt_motion.velocity, column_index)
);
@ -916,10 +908,9 @@ impl Assembly {
// this element didn't have a column index when we started, so
// by invariant (2), it's unconstrained
let mut target_column = motion_proj.column_mut(column_index);
let unif_to_std =
elt_motion.element.representation().with_untracked(
|rep| local_unif_to_std(rep.as_view())
);
let unif_to_std = elt_motion.element.representation().with_untracked(
|rep| local_unif_to_std(rep.as_view())
);
target_column += unif_to_std * elt_motion.velocity;
}
}
@ -936,10 +927,7 @@ impl Assembly {
elt.project_to_normalized(rep);
},
None => {
console_log!(
"No velocity to unpack for fresh element \"{}\"",
elt.id()
)
console_log!("No velocity to unpack for fresh element \"{}\"", elt.id())
},
};
});
@ -974,15 +962,13 @@ mod tests {
fn unindexed_subject_test_inversive_distance() {
let _ = create_root(|| {
let subjects = [0, 1].map(
|k| Rc::new(
Sphere::default(format!("sphere{k}"), k)) as Rc<dyn Element>
|k| Rc::new(Sphere::default(format!("sphere{k}"), k)) as Rc<dyn Element>
);
subjects[0].set_column_index(0);
InversiveDistanceRegulator {
subjects: subjects,
measurement: create_memo(|| 0.0),
set_point: create_signal(
SpecifiedValue::try_from("0.0".to_string()).unwrap()),
set_point: create_signal(SpecifiedValue::try_from("0.0".to_string()).unwrap()),
serial: InversiveDistanceRegulator::next_serial()
}.pose(&mut ConstraintProblem::new(2));
});
@ -1011,10 +997,8 @@ mod tests {
// nudge the sphere repeatedly along the `z` axis
const STEP_SIZE: f64 = 0.0025;
const STEP_CNT: usize = 400;
let sphere = assembly.elements_by_id.with(
|elts_by_id| elts_by_id[sphere_id].clone());
let velocity =
DVector::from_column_slice(&[0.0, 0.0, STEP_SIZE, 0.0]);
let sphere = assembly.elements_by_id.with(|elts_by_id| elts_by_id[sphere_id].clone());
let velocity = DVector::from_column_slice(&[0.0, 0.0, STEP_SIZE, 0.0]);
for _ in 0..STEP_CNT {
assembly.deform(
vec![
@ -1032,8 +1016,7 @@ mod tests {
let final_half_curv = sphere.representation().with_untracked(
|rep| rep[Sphere::CURVATURE_COMPONENT]
);
assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs()
< DRIFT_TOL);
assert!((final_half_curv / INITIAL_HALF_CURV - 1.0).abs() < DRIFT_TOL);
});
}
}

4
app-proto/src/components/add_remove.rs
View file

@ -39,9 +39,7 @@ pub fn AddRemove() -> View {
}
) { "Add point" }
button(
/* KLUDGE */ // for convenience, we're using an emoji as an
// icon for this button
class = "emoji",
class = "emoji", /* KLUDGE */ // for convenience, we're using an emoji as a temporary icon for this button
disabled = {
let state = use_context::<AppState>();
state.selection.with(|sel| sel.len() != 2)

120
app-proto/src/components/display.rs
View file

@ -50,8 +50,7 @@ impl SceneSpheres {
}
fn len_i32(&self) -> i32 {
self.representations.len().try_into().expect(
"Number of spheres must fit in a 32-bit integer")
self.representations.len().try_into().expect("Number of spheres must fit in a 32-bit integer")
}
fn push(
@ -128,12 +127,8 @@ impl DisplayItem for Sphere {
const HIGHLIGHT: f32 = 0.2;
let representation = self.representation.get_clone_untracked();
let color =
if selected { self.color.map(|channel| 0.2 + 0.8*channel) }
else { self.color };
let opacity =
if self.ghost.get() { GHOST_OPACITY }
else { DEFAULT_OPACITY };
let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
let opacity = if self.ghost.get() { GHOST_OPACITY } else { DEFAULT_OPACITY };
let highlight = if selected { 1.0 } else { HIGHLIGHT };
scene.spheres.push(representation, color, opacity, highlight);
}
@ -150,8 +145,7 @@ impl DisplayItem for Sphere {
// `a*u^2 + b*u + c` by the linear function `b*u + c`
const DEG_THRESHOLD: f64 = 1e-9;
let rep = self.representation.with_untracked(
|rep| assembly_to_world * rep);
let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
let a = -rep[3] * dir.norm_squared();
let b = rep.rows_range(..3).dot(&dir);
let c = -rep[4];
@ -192,9 +186,7 @@ impl DisplayItem for Point {
const HIGHLIGHT: f32 = 0.5;
let representation = self.representation.get_clone_untracked();
let color =
if selected { self.color.map(|channel| 0.2 + 0.8*channel) }
else { self.color };
let color = if selected { self.color.map(|channel| 0.2 + 0.8*channel) } else { self.color };
let opacity = if self.ghost.get() { GHOST_OPACITY } else { 1.0 };
let highlight = if selected { 1.0 } else { HIGHLIGHT };
scene.points.push(representation, color, opacity, highlight, selected);
@ -207,8 +199,7 @@ impl DisplayItem for Point {
assembly_to_world: &DMatrix<f64>,
pixel_size: f64,
) -> Option<f64> {
let rep = self.representation.with_untracked(
|rep| assembly_to_world * rep);
let rep = self.representation.with_untracked(|rep| assembly_to_world * rep);
if rep[2] < 0.0 {
// this constant should be kept synchronized with `point.frag`
const POINT_RADIUS_PX: f64 = 4.0;
@ -366,12 +357,11 @@ fn event_dir(event: &MouseEvent) -> (Vector3<f64>, f64) {
// this constant should be kept synchronized with `spheres.frag` and
// `point.vert`
const FOCAL_SLOPE: f64 = 0.3;
let horizontal = f64::from(event.client_x()) - rect.left();
let vertical = rect.bottom() - f64::from(event.client_y());
(
Vector3::new(
FOCAL_SLOPE * (2.0*horizontal - width) / shortdim,
FOCAL_SLOPE * (2.0*vertical - height) / shortdim,
FOCAL_SLOPE * (2.0*(f64::from(event.client_x()) - rect.left()) - width) / shortdim,
FOCAL_SLOPE * (2.0*(rect.bottom() - f64::from(event.client_y())) - height) / shortdim,
-1.0,
),
FOCAL_SLOPE * 2.0 / shortdim,
@ -455,8 +445,7 @@ pub fn Display() -> View {
let performance = window().unwrap().performance().unwrap();
// get the display canvas
let canvas =
display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
let canvas = display.get().unchecked_into::<web_sys::HtmlCanvasElement>();
let ctx = canvas
.get_context("webgl2")
.unwrap()
@ -469,8 +458,7 @@ pub fn Display() -> View {
// set blend mode
ctx.enable(WebGl2RenderingContext::BLEND);
ctx.blend_func(WebGl2RenderingContext::SRC_ALPHA,
WebGl2RenderingContext::ONE_MINUS_SRC_ALPHA);
ctx.blend_func(WebGl2RenderingContext::SRC_ALPHA, WebGl2RenderingContext::ONE_MINUS_SRC_ALPHA);
// set up the sphere rendering program
let sphere_program = set_up_program(
@ -499,20 +487,16 @@ pub fn Display() -> View {
// machine, the the length of a float or genType array seems to be
// capped at 1024 elements
console::log_2(
&ctx.get_parameter(
WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
&ctx.get_parameter(WebGl2RenderingContext::MAX_FRAGMENT_UNIFORM_VECTORS).unwrap(),
&JsValue::from("uniform vectors available"),
);
// find the sphere program's vertex attribute
let viewport_position_attr =
ctx.get_attrib_location(&sphere_program, "position") as u32;
let viewport_position_attr = ctx.get_attrib_location(&sphere_program, "position") as u32;
// find the sphere program's uniforms
const SPHERE_MAX: usize = 200;
let sphere_cnt_loc = ctx.get_uniform_location(
&sphere_program, "sphere_cnt"
);
let sphere_cnt_loc = ctx.get_uniform_location(&sphere_program, "sphere_cnt");
let sphere_sp_locs = get_uniform_array_locations::<SPHERE_MAX>(
&ctx, &sphere_program, "sphere_list", Some("sp")
);
@ -525,18 +509,10 @@ pub fn Display() -> View {
let sphere_highlight_locs = get_uniform_array_locations::<SPHERE_MAX>(
&ctx, &sphere_program, "highlight_list", None
);
let resolution_loc = ctx.get_uniform_location(
&sphere_program, "resolution"
);
let shortdim_loc = ctx.get_uniform_location(
&sphere_program, "shortdim"
);
let layer_threshold_loc = ctx.get_uniform_location(
&sphere_program, "layer_threshold"
);
let debug_mode_loc = ctx.get_uniform_location(
&sphere_program, "debug_mode"
);
let resolution_loc = ctx.get_uniform_location(&sphere_program, "resolution");
let shortdim_loc = ctx.get_uniform_location(&sphere_program, "shortdim");
let layer_threshold_loc = ctx.get_uniform_location(&sphere_program, "layer_threshold");
let debug_mode_loc = ctx.get_uniform_location(&sphere_program, "debug_mode");
// load the viewport vertex positions into a new vertex buffer object
const VERTEX_CNT: usize = 6;
@ -550,18 +526,13 @@ pub fn Display() -> View {
1.0, 1.0, 0.0,
1.0, -1.0, 0.0,
];
let viewport_position_buffer =
load_new_buffer(&ctx, &viewport_positions);
let viewport_position_buffer = load_new_buffer(&ctx, &viewport_positions);
// find the point program's vertex attributes
let point_position_attr =
ctx.get_attrib_location(&point_program, "position") as u32;
let point_color_attr =
ctx.get_attrib_location(&point_program, "color") as u32;
let point_highlight_attr =
ctx.get_attrib_location(&point_program, "highlight") as u32;
let point_selection_attr =
ctx.get_attrib_location(&point_program, "selected") as u32;
let point_position_attr = ctx.get_attrib_location(&point_program, "position") as u32;
let point_color_attr = ctx.get_attrib_location(&point_program, "color") as u32;
let point_highlight_attr = ctx.get_attrib_location(&point_program, "highlight") as u32;
let point_selection_attr = ctx.get_attrib_location(&point_program, "selected") as u32;
// set up a repainting routine
let (_, start_animation_loop, _) = create_raf(move || {
@ -625,8 +596,7 @@ pub fn Display() -> View {
let realization_successful = state.assembly.realization_status.with(
|status| status.is_ok()
);
let step_val =
state.assembly.step.with_untracked(|step| step.value);
let step_val = state.assembly.step.with_untracked(|step| step.value);
let on_init_step = step_val.is_some_and(|n| n == 0.0);
let on_last_step = step_val.is_some_and(
|n| state.assembly.descent_history.with_untracked(
@ -636,8 +606,7 @@ pub fn Display() -> View {
let on_manipulable_step =
!realization_successful && on_init_step
|| realization_successful && on_last_step;
if on_manipulable_step
&& state.selection.with(|sel| sel.len() == 1) {
if on_manipulable_step && state.selection.with(|sel| sel.len() == 1) {
let sel = state.selection.with(
|sel| sel.into_iter().next().unwrap().clone()
);
@ -682,8 +651,7 @@ pub fn Display() -> View {
// measure mean frame interval
frames_since_last_sample += 1;
if frames_since_last_sample >= SAMPLE_PERIOD {
mean_frame_interval.set(
(time - last_sample_time) / (SAMPLE_PERIOD as f64));
mean_frame_interval.set((time - last_sample_time) / (SAMPLE_PERIOD as f64));
last_sample_time = time;
frames_since_last_sample = 0;
}
@ -708,8 +676,7 @@ pub fn Display() -> View {
// set up the scene
state.assembly.elements.with_untracked(
|elts| for elt in elts {
let selected =
state.selection.with(|sel| sel.contains(elt));
let selected = state.selection.with(|sel| sel.contains(elt));
elt.show(&mut scene, selected);
}
);
@ -724,10 +691,9 @@ pub fn Display() -> View {
ctx.enable_vertex_attrib_array(viewport_position_attr);
// write the spheres in world coordinates
let sphere_reps_world: Vec<_> =
scene.spheres.representations.into_iter().map(
|rep| (&asm_to_world * rep).cast::<f32>()
).collect();
let sphere_reps_world: Vec<_> = scene.spheres.representations.into_iter().map(
|rep| (&asm_to_world * rep).cast::<f32>()
).collect();
// set the resolution
let width = canvas.width() as f32;
@ -763,12 +729,10 @@ pub fn Display() -> View {
// bind the viewport vertex position buffer to the position
// attribute in the vertex shader
bind_to_attribute(&ctx, viewport_position_attr,
SPACE_DIM as i32, &viewport_position_buffer);
bind_to_attribute(&ctx, viewport_position_attr, SPACE_DIM as i32, &viewport_position_buffer);
// draw the scene
ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0,
VERTEX_CNT as i32);
ctx.draw_arrays(WebGl2RenderingContext::TRIANGLES, 0, VERTEX_CNT as i32);
// disable the sphere program's vertex attribute
ctx.disable_vertex_attrib_array(viewport_position_attr);
@ -796,19 +760,13 @@ pub fn Display() -> View {
// load the point positions and colors into new buffers and
// bind them to the corresponding attributes in the vertex
// shader
bind_new_buffer_to_attribute(&ctx, point_position_attr,
SPACE_DIM as i32, point_positions.as_slice());
bind_new_buffer_to_attribute(&ctx, point_color_attr,
(COLOR_SIZE + 1) as i32,
scene.points.colors_with_opacity.concat().as_slice());
bind_new_buffer_to_attribute(&ctx, point_highlight_attr,
1i32, scene.points.highlights.as_slice());
bind_new_buffer_to_attribute(&ctx, point_selection_attr,
1i32, scene.points.selections.as_slice());
bind_new_buffer_to_attribute(&ctx, point_position_attr, SPACE_DIM as i32, point_positions.as_slice());
bind_new_buffer_to_attribute(&ctx, point_color_attr, (COLOR_SIZE + 1) as i32, scene.points.colors_with_opacity.concat().as_slice());
bind_new_buffer_to_attribute(&ctx, point_highlight_attr, 1 as i32, scene.points.highlights.as_slice());
bind_new_buffer_to_attribute(&ctx, point_selection_attr, 1 as i32, scene.points.selections.as_slice());
// draw the scene
ctx.draw_arrays(WebGl2RenderingContext::POINTS, 0,
point_positions.ncols() as i32);
ctx.draw_arrays(WebGl2RenderingContext::POINTS, 0, point_positions.ncols() as i32);
// disable the point program's vertex attributes
ctx.disable_vertex_attrib_array(point_position_attr);
@ -957,9 +915,7 @@ pub fn Display() -> View {
.into_iter()
.filter(|elt| !elt.ghost().get());
for elt in tangible_elts {
let target = assembly_to_world.with(
|asm_to_world| elt.cast(dir, asm_to_world, pixel_size));
match target {
match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world, pixel_size)) {
Some(depth) => match clicked {
Some((_, best_depth)) => {
if depth < best_depth {

21
app-proto/src/components/outline.rs
View file

@ -63,10 +63,8 @@ fn RegulatorInput(regulator: Rc<dyn Regulator>) -> View {
placeholder = measurement.with(|result| result.to_string()),
bind:value = value,
on:change = move |_| {
let specification =
SpecifiedValue::try_from(value.get_clone_untracked());
valid.set(
match specification {
match SpecifiedValue::try_from(value.get_clone_untracked()) {
Ok(set_pt) => {
set_point.set(set_pt);
true
@ -143,9 +141,7 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
let class = {
let element_for_class = element.clone();
state.selection.map(
move |sel|
if sel.contains(&element_for_class) { "selected" }
else { "" }
move |sel| if sel.contains(&element_for_class) { "selected" } else { "" }
)
};
let label = element.label().clone();
@ -179,8 +175,7 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
move |event: KeyboardEvent| {
match event.key().as_str() {
"Enter" => {
state.select(&element_for_handler,
event.shift_key());
state.select(&element_for_handler, event.shift_key());
event.prevent_default();
},
"ArrowRight" if regulated.get() => {
@ -210,22 +205,18 @@ fn ElementOutlineItem(element: Rc<dyn Element>) -> View {
let state_for_handler = state.clone();
let element_for_handler = element.clone();
move |event: MouseEvent| {
state_for_handler.select(&element_for_handler,
event.shift_key());
state_for_handler.select(&element_for_handler, event.shift_key());
event.stop_propagation();
event.prevent_default();
}
}
) {
div(class = "element-label") { (label) }
div(class = "element-representation") {
(rep_components)
}
div(class = "element-representation") { (rep_components) }
input(
r#type = "checkbox",
bind:checked = element.ghost(),
on:click =
|event: MouseEvent| event.stop_propagation()
on:click = |event: MouseEvent| event.stop_propagation()
)
}
}

14
app-proto/src/components/spheres.frag
View file

@ -175,9 +175,8 @@ void main() {
if (debug_mode) {
// at the bottom of the screen, show the color scale instead of the
// layer count
if (gl_FragCoord.y < 10.) {
layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
}
if (gl_FragCoord.y < 10.) layer_cnt = int(16. * gl_FragCoord.x / resolution.x);
// convert number to color
ivec3 bits = layer_cnt / ivec3(1, 2, 4);
vec3 color = mod(vec3(bits), 2.);
@ -218,17 +217,14 @@ void main() {
// highlight intersections
float ixn_dist = intersection_dist(frag, frag_next);
float max_highlight = max(highlight, highlight_next);
float ixn_highlight = 0.5 * max_highlight * (1. - smoothstep(
2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
float ixn_highlight = 0.5 * max_highlight * (1. - smoothstep(2./3.*ixn_threshold, 1.5*ixn_threshold, ixn_dist));
frag.color = mix(frag.color, vec4(1.), ixn_highlight);
frag_next.color = mix(frag_next.color, vec4(1.), ixn_highlight);
// highlight cusps
float cusp_cos = abs(dot(dir, frag.normal));
float cusp_threshold = 2.*sqrt(
ixn_threshold * sphere_list[hit.id].lt.s);
float cusp_highlight = highlight * (1. - smoothstep(
2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
float cusp_threshold = 2.*sqrt(ixn_threshold * sphere_list[hit.id].lt.s);
float cusp_highlight = highlight * (1. - smoothstep(2./3.*cusp_threshold, 1.5*cusp_threshold, cusp_cos));
frag.color = mix(frag.color, vec4(1.), cusp_highlight);
// composite the current fragment

129
app-proto/src/components/test_assembly_chooser.rs
View file

@ -167,36 +167,29 @@ fn load_low_curvature(assembly: &Assembly) {
let curvature = plane.regulators().with_untracked(
|regs| regs.first().unwrap().clone()
);
curvature.set_point().set(
SpecifiedValue::try_from("0".to_string()).unwrap());
curvature.set_point().set(SpecifiedValue::try_from("0".to_string()).unwrap());
}
let all_perpendicular = [central.clone()].into_iter()
.chain(sides.clone())
.chain(corners.clone());
for sphere in all_perpendicular {
// make each side and packed sphere perpendicular to the assembly plane
let right_angle = InversiveDistanceRegulator::new(
[sphere, assemb_plane.clone()]);
right_angle.set_point.set(
SpecifiedValue::try_from("0".to_string()).unwrap());
let right_angle = InversiveDistanceRegulator::new([sphere, assemb_plane.clone()]);
right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
assembly.insert_regulator(Rc::new(right_angle));
}
for sphere in sides.clone().chain(corners.clone()) {
// make each side and corner sphere tangent to the central sphere
let tangency = InversiveDistanceRegulator::new(
[sphere.clone(), central.clone()]);
tangency.set_point.set(
SpecifiedValue::try_from("-1".to_string()).unwrap());
let tangency = InversiveDistanceRegulator::new([sphere.clone(), central.clone()]);
tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
assembly.insert_regulator(Rc::new(tangency));
}
for (side_index, side) in sides.enumerate() {
// make each side tangent to the two adjacent corner spheres
for (corner_index, corner) in corners.clone().enumerate() {
if side_index != corner_index {
let tangency = InversiveDistanceRegulator::new(
[side.clone(), corner]);
tangency.set_point.set(
SpecifiedValue::try_from("-1".to_string()).unwrap());
let tangency = InversiveDistanceRegulator::new([side.clone(), corner]);
tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
assembly.insert_regulator(Rc::new(tangency));
}
}
@ -224,15 +217,12 @@ fn load_pointed(assembly: &Assembly) {
for index_y in 0..=1 {
let x = index_x as f64 - 0.5;
let y = index_y as f64 - 0.5;
let x32 = x as f32;
let y32 = y as f32;
let coords =
[0.5*(1.0 + x32), 0.5*(1.0 + y32), 0.5*(1.0 - x32*y32)];
let _ = assembly.try_insert_element(
Sphere::new(
format!("sphere{index_x}{index_y}"),
format!("Sphere {index_x}{index_y}"),
coords,
[0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
engine::sphere(x, y, 0.0, 1.0),
)
);
@ -241,7 +231,7 @@ fn load_pointed(assembly: &Assembly) {
Point::new(
format!("point{index_x}{index_y}"),
format!("Point {index_x}{index_y}"),
coords,
[0.5*(1.0 + x) as f32, 0.5*(1.0 + y) as f32, 0.5*(1.0 - x*y) as f32],
engine::point(x, y, 0.0),
)
);
@ -330,25 +320,19 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
"face1".to_string(),
"Face 1".to_string(),
COLOR_FACE,
engine::sphere_with_offset(
frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6,
-frac_1_sqrt_6, 0.0),
engine::sphere_with_offset(frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
),
Sphere::new(
"face2".to_string(),
"Face 2".to_string(),
COLOR_FACE,
engine::sphere_with_offset(
-frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6,
-frac_1_sqrt_6, 0.0),
engine::sphere_with_offset(-frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, -frac_1_sqrt_6, 0.0),
),
Sphere::new(
"face3".to_string(),
"Face 3".to_string(),
COLOR_FACE,
engine::sphere_with_offset(
-frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6,
-frac_1_sqrt_6, 0.0),
engine::sphere_with_offset(-frac_1_sqrt_6, -frac_1_sqrt_6, frac_2_sqrt_6, -frac_1_sqrt_6, 0.0),
),
];
for face in faces {
@ -373,10 +357,8 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
let vertex_a = assembly.elements_by_id.with_untracked(
|elts_by_id| elts_by_id[&format!("a{j}")].clone()
);
let incidence_a = InversiveDistanceRegulator::new(
[face.clone(), vertex_a.clone()]);
incidence_a.set_point.set(
SpecifiedValue::try_from("0".to_string()).unwrap());
let incidence_a = InversiveDistanceRegulator::new([face.clone(), vertex_a.clone()]);
incidence_a.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
assembly.insert_regulator(Rc::new(incidence_a));
// regulate the B-C vertex distances
@ -398,16 +380,13 @@ fn load_tridiminished_icosahedron(assembly: &Assembly) {
let vertex = assembly.elements_by_id.with_untracked(
|elts_by_id| elts_by_id[&format!("{series}{k}")].clone()
);
let incidence = InversiveDistanceRegulator::new(
[face.clone(), vertex.clone()]);
incidence.set_point.set(
SpecifiedValue::try_from("0".to_string()).unwrap());
let incidence = InversiveDistanceRegulator::new([face.clone(), vertex.clone()]);
incidence.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
assembly.insert_regulator(Rc::new(incidence));
// regulate the A-B and A-C vertex distances
assembly.insert_regulator(
Rc::new(InversiveDistanceRegulator::new(
[vertex_a.clone(), vertex]))
Rc::new(InversiveDistanceRegulator::new([vertex_a.clone(), vertex]))
);
}
}
@ -455,8 +434,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
const COLOR_A: ElementColor = [1.00_f32, 0.25_f32, 0.00_f32];
const COLOR_B: ElementColor = [1.00_f32, 0.00_f32, 0.25_f32];
const COLOR_C: ElementColor = [0.25_f32, 0.00_f32, 1.00_f32];
/* TO DO */ // replace with std::f64::consts::PHI when that gets stabilized
let phi = 0.5 + 1.25_f64.sqrt();
let phi = 0.5 + 1.25_f64.sqrt(); /* TO DO */ // replace with std::f64::consts::PHI when that gets stabilized
let phi_inv = 1.0 / phi;
let coord_scale = (phi + 2.0).sqrt();
let face_scales = [phi_inv, (13.0 / 12.0) / coord_scale];
@ -523,16 +501,13 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
// make each face sphere perpendicular to the substrate
for face in faces {
let right_angle = InversiveDistanceRegulator::new(
[face, substrate.clone()]);
right_angle.set_point.set(
SpecifiedValue::try_from("0".to_string()).unwrap());
let right_angle = InversiveDistanceRegulator::new([face, substrate.clone()]);
right_angle.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
assembly.insert_regulator(Rc::new(right_angle));
}
// set up the tangencies that define the packing
for [long_edge_plane, short_edge_plane]
in [["a", "b"], ["b", "c"], ["c", "a"]] {
for [long_edge_plane, short_edge_plane] in [["a", "b"], ["b", "c"], ["c", "a"]] {
for k in 0..2 {
let long_edge_ids = [
format!("{long_edge_plane}{k}0"),
@ -551,11 +526,9 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
);
// set up the short-edge tangency
let short_tangency = InversiveDistanceRegulator::new(
short_edge.clone());
let short_tangency = InversiveDistanceRegulator::new(short_edge.clone());
if k == 0 {
short_tangency.set_point.set(
SpecifiedValue::try_from("-1".to_string()).unwrap());
short_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
}
assembly.insert_regulator(Rc::new(short_tangency));
@ -566,9 +539,7 @@ fn load_dodecahedral_packing(assembly: &Assembly) {
[long_edge[i].clone(), short_edge[j].clone()]
);
if i == 0 && k == 0 {
side_tangency.set_point.set(
SpecifiedValue::try_from("-1".to_string()).unwrap()
);
side_tangency.set_point.set(SpecifiedValue::try_from("-1".to_string()).unwrap());
}
assembly.insert_regulator(Rc::new(side_tangency));
}
@ -633,8 +604,7 @@ fn load_balanced(assembly: &Assembly) {
// initial configuration deliberately violates these constraints
for inner in [a, b] {
let tangency = InversiveDistanceRegulator::new([outer.clone(), inner]);
tangency.set_point.set(
SpecifiedValue::try_from("1".to_string()).unwrap());
tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
assembly.insert_regulator(Rc::new(tangency));
}
}
@ -742,14 +712,10 @@ fn load_radius_ratio(assembly: &Assembly) {
[0.25_f32, 0.00_f32, 1.00_f32],
].into_iter(),
[
engine::sphere_with_offset(
base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
engine::sphere_with_offset(
base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
engine::sphere_with_offset(
-base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
engine::sphere_with_offset(
-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0),
engine::sphere_with_offset(base_dir[0], base_dir[1], base_dir[2], offset, 0.0),
engine::sphere_with_offset(base_dir[0], -base_dir[1], -base_dir[2], offset, 0.0),
engine::sphere_with_offset(-base_dir[0], base_dir[1], -base_dir[2], offset, 0.0),
engine::sphere_with_offset(-base_dir[0], -base_dir[1], base_dir[2], offset, 0.0),
].into_iter()
).map(
|(k, color, representation)| {
@ -799,10 +765,8 @@ fn load_radius_ratio(assembly: &Assembly) {
}
// put the vertices on the faces
let incidence_regulator = InversiveDistanceRegulator::new(
[face_j.clone(), vertex_k.clone()]);
incidence_regulator.set_point.set(
SpecifiedValue::try_from("0".to_string()).unwrap());
let incidence_regulator = InversiveDistanceRegulator::new([face_j.clone(), vertex_k.clone()]);
incidence_regulator.set_point.set(SpecifiedValue::try_from("0".to_string()).unwrap());
assembly.insert_regulator(Rc::new(incidence_regulator));
}
}
@ -896,33 +860,25 @@ fn load_irisawa_hexlet(assembly: &Assembly) {
|elts_by_id| elts_by_id[&format!("chain{k}")].clone()
)
);
for (chain_sphere, chain_sphere_next)
in chain.clone().zip(chain.cycle().skip(1)) {
for (chain_sphere, chain_sphere_next) in chain.clone().zip(chain.cycle().skip(1)) {
for (other_sphere, inversive_distance) in [
(outer.clone(), "1"),
(sun.clone(), "-1"),
(moon.clone(), "-1"),
(chain_sphere_next.clone(), "-1"),
] {
let tangency = InversiveDistanceRegulator::new(
[chain_sphere.clone(), other_sphere]);
tangency.set_point.set(
SpecifiedValue::try_from(
inversive_distance.to_string()).unwrap());
let tangency = InversiveDistanceRegulator::new([chain_sphere.clone(), other_sphere]);
tangency.set_point.set(SpecifiedValue::try_from(inversive_distance.to_string()).unwrap());
assembly.insert_regulator(Rc::new(tangency));
}
}
let outer_sun_tangency = InversiveDistanceRegulator::new(
[outer.clone(), sun]);
outer_sun_tangency.set_point.set(
SpecifiedValue::try_from("1".to_string()).unwrap());
let outer_sun_tangency = InversiveDistanceRegulator::new([outer.clone(), sun]);
outer_sun_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
assembly.insert_regulator(Rc::new(outer_sun_tangency));
let outer_moon_tangency = InversiveDistanceRegulator::new(
[outer.clone(), moon]);
outer_moon_tangency.set_point.set(
SpecifiedValue::try_from("1".to_string()).unwrap());
let outer_moon_tangency = InversiveDistanceRegulator::new([outer.clone(), moon]);
outer_moon_tangency.set_point.set(SpecifiedValue::try_from("1".to_string()).unwrap());
assembly.insert_regulator(Rc::new(outer_moon_tangency));
}
@ -956,8 +912,7 @@ pub fn TestAssemblyChooser() -> View {
"general" => load_general(assembly),
"low-curvature" => load_low_curvature(assembly),
"pointed" => load_pointed(assembly),
"tridiminished-icosahedron" =>
load_tridiminished_icosahedron(assembly),
"tridiminished-icosahedron" => load_tridiminished_icosahedron(assembly),
"dodecahedral-packing" => load_dodecahedral_packing(assembly),
"balanced" => load_balanced(assembly),
"off-center" => load_off_center(assembly),
@ -974,9 +929,7 @@ pub fn TestAssemblyChooser() -> View {
option(value = "general") { "General" }
option(value = "low-curvature") { "Low-curvature" }
option(value = "pointed") { "Pointed" }
option(value = "tridiminished-icosahedron") {
"Tridiminished icosahedron"
}
option(value = "tridiminished-icosahedron") { "Tridiminished icosahedron" }
option(value = "dodecahedral-packing") { "Dodecahedral packing" }
option(value = "balanced") { "Balanced" }
option(value = "off-center") { "Off-center" }

119
app-proto/src/engine.rs
View file

@ -9,11 +9,8 @@ pub fn point(x: f64, y: f64, z: f64) -> DVector<f64> {
}
// 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;
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,
@ -26,9 +23,7 @@ pub fn sphere(center_x: f64, center_y: f64, center_z: f64, radius: f64)
// 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>
{
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,
@ -205,9 +200,7 @@ impl ConfigSubspace {
// with the given column index has velocity `v`. the velocity is given in
// projection coordinates, and the projection is done with respect to the
// projection inner product
pub fn proj(&self, v: &DVectorView<f64>, column_index: usize)
-> DMatrix<f64>
{
pub fn proj(&self, v: &DVectorView<f64>, column_index: usize) -> DMatrix<f64> {
if self.dim() == 0 {
const ELEMENT_DIM: usize = 5;
DMatrix::zeros(ELEMENT_DIM, self.assembly_dim)
@ -298,9 +291,7 @@ impl SearchState {
}
}
fn basis_matrix(index: (usize, usize), nrows: usize, ncols: usize)
-> DMatrix<f64>
{
fn basis_matrix(index: (usize, usize), nrows: usize, ncols: usize) -> DMatrix<f64> {
let mut result = DMatrix::<f64>::zeros(nrows, ncols);
result[index] = 1.0;
result
@ -423,8 +414,7 @@ pub fn realize_gram(
for _ in 0..max_descent_steps {
// find the negative gradient of the loss function
let neg_grad = 4.0 * &*Q * &state.config * &state.err_proj;
let mut neg_grad_stacked =
neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
let mut neg_grad_stacked = neg_grad.clone().reshape_generic(Dyn(total_dim), Const::<1>);
history.neg_grad.push(neg_grad.clone());
// find the negative Hessian of the loss function
@ -441,8 +431,7 @@ pub fn realize_gram(
-&basis_mat * &state.err_proj
+ &state.config * &neg_d_err_proj
);
hess_cols.push(
deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
hess_cols.push(deriv_grad.reshape_generic(Dyn(total_dim), Const::<1>));
}
}
hess = DMatrix::from_columns(hess_cols.as_slice());
@ -451,8 +440,7 @@ pub fn realize_gram(
let hess_eigvals = hess.symmetric_eigenvalues();
let min_eigval = hess_eigvals.min();
if min_eigval <= 0.0 {
hess -= reg_scale * min_eigval
* DMatrix::identity(total_dim, total_dim);
hess -= reg_scale * min_eigval * DMatrix::identity(total_dim, total_dim);
}
history.hess_eigvals.push(hess_eigvals);
@ -489,8 +477,7 @@ pub fn realize_gram(
},
};
let base_step_stacked = hess_cholesky.solve(&neg_grad_stacked);
let base_step = base_step_stacked.reshape_generic(
Dyn(element_dim), Dyn(assembly_dim));
let base_step = base_step_stacked.reshape_generic(Dyn(element_dim), Dyn(assembly_dim));
history.base_step.push(base_step.clone());
// use backtracking line search to find a better configuration
@ -520,12 +507,9 @@ pub fn realize_gram(
}
// find the kernel of the Hessian. give it the uniform inner product
let tangent =
ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
let tangent = ConfigSubspace::symmetric_kernel(hess, unif_to_std, assembly_dim);
Ok(ConfigNeighborhood {
#[cfg(feature = "dev")] config: state.config, nbhd: tangent
})
Ok(ConfigNeighborhood { #[cfg(feature = "dev")] config: state.config, nbhd: tangent })
} else {
Err("Failed to reach target accuracy".to_string())
};
@ -624,8 +608,7 @@ pub mod examples {
for j in 0..2 {
// diagonal and hinge edges
for k in j..2 {
problem.gram.push_sym(
block + j, block + k, if j == k { 0.0 } else { -0.5 });
problem.gram.push_sym(block + j, block + k, if j == k { 0.0 } else { -0.5 });
}
// non-hinge edges
@ -719,8 +702,7 @@ mod tests {
]);
for j in 0..2 {
for k in j..2 {
problem.gram.push_sym(
j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
problem.gram.push_sym(j, k, if (j, k) == (1, 1) { 1.0 } else { 0.0 });
}
}
problem.frozen.push(3, 0, problem.guess[(3, 0)]);
@ -747,8 +729,7 @@ mod tests {
// check against Irisawa's solution
let entry_tol = SCALED_TOL.sqrt();
let solution_diams =
[30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
let solution_diams = [30.0, 10.0, 6.0, 5.0, 15.0, 10.0, 3.75, 2.5, 2.0 + 8.0/11.0];
for (k, diam) in solution_diams.into_iter().enumerate() {
assert!((config[(3, k)] - 1.0 / diam).abs() < entry_tol);
}
@ -813,29 +794,22 @@ mod tests {
// confirm that the tangent space contains all the motions we expect it
// to. since we've already bounded the dimension of the tangent space,
// this confirms that the tangent space is what we expect it to be
let tol_sq = ((element_dim * assembly_dim) as f64)
* SCALED_TOL * SCALED_TOL;
for (motion_unif, motion_std)
in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
let motion_proj: DMatrix<_> =
motion_unif.column_iter().enumerate().map(
|(k, v)| tangent.proj(&v, k)
).sum();
let tol_sq = ((element_dim * assembly_dim) as f64) * SCALED_TOL * SCALED_TOL;
for (motion_unif, motion_std) in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
let motion_proj: DMatrix<_> = motion_unif.column_iter().enumerate().map(
|(k, v)| tangent.proj(&v, k)
).sum();
assert!((motion_std - motion_proj).norm_squared() < tol_sq);
}
}
fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize)
-> Vec<DVector<f64>>
{
fn translation_motion_unif(vel: &Vector3<f64>, assembly_dim: usize) -> Vec<DVector<f64>> {
let mut elt_motion = DVector::zeros(4);
elt_motion.fixed_rows_mut::<3>(0).copy_from(vel);
iter::repeat(elt_motion).take(assembly_dim).collect()
}
fn rotation_motion_unif(
ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>
) -> Vec<DVector<f64>> {
fn rotation_motion_unif(ang_vel: &Vector3<f64>, points: Vec<DVectorView<f64>>) -> Vec<DVector<f64>> {
points.into_iter().map(
|pt| {
let vel = ang_vel.cross(&pt.fixed_rows::<3>(0));
@ -866,12 +840,9 @@ mod tests {
translation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), assembly_dim),
// the rotations about the coordinate axes
rotation_motion_unif(
&Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
rotation_motion_unif(
&Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
rotation_motion_unif(
&Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
rotation_motion_unif(&Vector3::new(1.0, 0.0, 0.0), config.column_iter().collect()),
rotation_motion_unif(&Vector3::new(0.0, 1.0, 0.0), config.column_iter().collect()),
rotation_motion_unif(&Vector3::new(0.0, 0.0, 1.0), config.column_iter().collect()),
// the twist motion. more precisely: a motion that keeps the center
// of mass stationary and preserves the distances between the
@ -888,10 +859,8 @@ mod tests {
[
DVector::from_column_slice(&[0.0, 0.0, 5.0, 0.0]),
DVector::from_column_slice(&[0.0, 0.0, 1.0, 0.0]),
DVector::from_column_slice(
&[-vel_vert_x, -vel_vert_y, -3.0, 0.0]),
DVector::from_column_slice(
&[vel_vert_x, vel_vert_y, -3.0, 0.0]),
DVector::from_column_slice(&[-vel_vert_x, -vel_vert_y, -3.0, 0.0]),
DVector::from_column_slice(&[vel_vert_x, vel_vert_y, -3.0, 0.0]),
]
}
).collect::<Vec<_>>(),
@ -911,14 +880,11 @@ mod tests {
// confirm that the tangent space contains all the motions we expect it
// to. since we've already bounded the dimension of the tangent space,
// this confirms that the tangent space is what we expect it to be
let tol_sq = ((element_dim * assembly_dim) as f64)
* SCALED_TOL * SCALED_TOL;
for (motion_unif, motion_std)
in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
let motion_proj: DMatrix<_> =
motion_unif.into_iter().enumerate().map(
|(k, v)| tangent.proj(&v.as_view(), k)
).sum();
let tol_sq = ((element_dim * assembly_dim) as f64) * SCALED_TOL * SCALED_TOL;
for (motion_unif, motion_std) in tangent_motions_unif.into_iter().zip(tangent_motions_std) {
let motion_proj: DMatrix<_> = motion_unif.into_iter().enumerate().map(
|(k, v)| tangent.proj(&v.as_view(), k)
).sum();
assert!((motion_std - motion_proj).norm_squared() < tol_sq);
}
}
@ -947,10 +913,10 @@ mod tests {
problem_orig.gram.push_sym(0, 0, 1.0);
problem_orig.gram.push_sym(1, 1, 1.0);
problem_orig.gram.push_sym(0, 1, 0.5);
let Realization { result: result_orig, history: history_orig } =
realize_gram(&problem_orig, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110);
let ConfigNeighborhood { config: config_orig, nbhd: tangent_orig } =
result_orig.unwrap();
let Realization { result: result_orig, history: history_orig } = realize_gram(
&problem_orig, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
);
let ConfigNeighborhood { config: config_orig, nbhd: tangent_orig } = result_orig.unwrap();
assert_eq!(config_orig, problem_orig.guess);
assert_eq!(history_orig.scaled_loss.len(), 1);
@ -968,10 +934,10 @@ mod tests {
frozen: problem_orig.frozen,
guess: guess_tfm,
};
let Realization { result: result_tfm, history: history_tfm } =
realize_gram(&problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110);
let ConfigNeighborhood { config: config_tfm, nbhd: tangent_tfm } =
result_tfm.unwrap();
let Realization { result: result_tfm, history: history_tfm } = realize_gram(
&problem_tfm, SCALED_TOL, 0.5, 0.9, 1.1, 200, 110
);
let ConfigNeighborhood { config: config_tfm, nbhd: tangent_tfm } = result_tfm.unwrap();
assert_eq!(config_tfm, problem_tfm.guess);
assert_eq!(history_tfm.scaled_loss.len(), 1);
@ -982,8 +948,7 @@ mod tests {
// project the equivalent nudge to the tangent space of the solution
// variety at the transformed solution
let motion_tfm = DVector::from_column_slice(
&[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
let motion_tfm = DVector::from_column_slice(&[FRAC_1_SQRT_2, 0.0, FRAC_1_SQRT_2, 0.0]);
let motion_tfm_proj = tangent_tfm.proj(&motion_tfm.as_view(), 0);
// take the transformation that sends the original solution to the
@ -1004,9 +969,7 @@ mod tests {
// the comparison tolerance because the transformation seems to
// introduce some numerical error
const SCALED_TOL_TFM: f64 = 1.0e-9;
let tol_sq = ((problem_orig.guess.nrows()
* problem_orig.guess.ncols()) as f64)
* SCALED_TOL_TFM * SCALED_TOL_TFM;
let tol_sq = ((problem_orig.guess.nrows() * problem_orig.guess.ncols()) as f64) * SCALED_TOL_TFM * SCALED_TOL_TFM;
assert!((motion_proj_tfm - motion_tfm_proj).norm_squared() < tol_sq);
}
}

7
notes/theory.md
View file

@ -22,10 +22,9 @@ Jürgen also emphasized the need for an intuitive user interface. Notes on that
His final mathematical advice was reasonably encouraging, however:
"But still I would consider it all more or less doable. One should very precisely think about a doable scope.
I think three things are essential for the math no matter what you exactly
plan.
I think three things are essential for the math no matter what you exactly plan.
1. Think projectively.
1. Think projectively,
Use Projective Geometry, Homogeneous Coordinates (or to a certain extent Quaternions, and Clifford Algebras, which are more or less an elegant way to merge Complex numbers with projective concepts.)
2. Consider ambient complex spaces.
The true nature of the objects can only be understood if embedded into a complex ambient space.
@ -43,3 +42,5 @@ CindyJS uses very concrete basic objects: 2D points are represented via projecti
Lines are given by explicit coordinates as well (not sure of the internal details/exact coordinatization, or of how a "LineThrough" is represented).
Was unclear to me how the complex parametrization for preserving continuity was handled in the code, even though Jürgen harps on complex ambient spaces; where are the complex numbers? Perhaps that part of Cinderella was never re-implemented?

2
src/index.html
View file

@ -7,3 +7,5 @@
<body><script type="module" src="dyna3.js"></script>
</body>
</html>