Compare commits
No commits in common. "8eb1ebb8d2920617d11effd25afb668732b45419" and "58a5c38e6229e6e30b9e468114c4f302140bb2eb" have entirely different histories.
8eb1ebb8d2
...
58a5c38e62
@ -1,203 +0,0 @@
|
||||
module Viewer
|
||||
|
||||
using Blink
|
||||
using Colors
|
||||
using Printf
|
||||
|
||||
export ConstructionViewer, display!, opentools!, closetools!
|
||||
|
||||
# === Blink utilities ===
|
||||
|
||||
append_to_head!(w, type, content) = @js w begin
|
||||
@var element = document.createElement($type)
|
||||
element.appendChild(document.createTextNode($content))
|
||||
document.head.appendChild(element)
|
||||
end
|
||||
|
||||
style!(w, stylesheet) = append_to_head!(w, "style", stylesheet)
|
||||
|
||||
script!(w, code) = append_to_head!(w, "script", code)
|
||||
|
||||
# === construction viewer ===
|
||||
|
||||
mutable struct ConstructionViewer
|
||||
win::Window
|
||||
|
||||
function ConstructionViewer()
|
||||
# create window and open developer console
|
||||
win = Window(Blink.Dict(:width => 620, :height => 830))
|
||||
|
||||
# set stylesheet
|
||||
style!(win, """
|
||||
body {
|
||||
background-color: #ccc;
|
||||
}
|
||||
|
||||
/* the maximum dimensions keep Ganja from blowing up the canvas */
|
||||
#view {
|
||||
display: block;
|
||||
width: 600px;
|
||||
height: 600px;
|
||||
margin-top: 10px;
|
||||
margin-left: 10px;
|
||||
border-radius: 10px;
|
||||
background-color: #f0f0f0;
|
||||
}
|
||||
|
||||
#control-panel {
|
||||
width: 600px;
|
||||
height: 200px;
|
||||
box-sizing: border-box;
|
||||
padding: 5px 10px 5px 10px;
|
||||
margin-top: 10px;
|
||||
margin-left: 10px;
|
||||
overflow-y: scroll;
|
||||
border-radius: 10px;
|
||||
background-color: #f0f0f0;
|
||||
}
|
||||
|
||||
#control-panel > div {
|
||||
margin-top: 5px;
|
||||
padding: 4px;
|
||||
border-radius: 5px;
|
||||
border: solid;
|
||||
font-family: monospace;
|
||||
}
|
||||
""")
|
||||
|
||||
# load Ganja.js
|
||||
loadjs!(win, "https://unpkg.com/ganja.js")
|
||||
|
||||
# create global functions and variables
|
||||
script!(win, """
|
||||
// create algebra
|
||||
var CGA3 = Algebra(4, 1);
|
||||
|
||||
// initialize element list and palette
|
||||
var elements = [];
|
||||
var palette = [];
|
||||
|
||||
// declare handles for the view and its options
|
||||
var view;
|
||||
var viewOpt;
|
||||
|
||||
// declare handles for the controls
|
||||
var controlPanel;
|
||||
var visToggles;
|
||||
|
||||
// create scene function
|
||||
function scene() {
|
||||
commands = [];
|
||||
for (let n = 0; n < elements.length; ++n) {
|
||||
if (visToggles[n].checked) {
|
||||
commands.push(palette[n], elements[n]);
|
||||
}
|
||||
}
|
||||
return commands;
|
||||
}
|
||||
|
||||
function updateView() {
|
||||
requestAnimationFrame(view.update.bind(view, scene));
|
||||
}
|
||||
""")
|
||||
|
||||
@js win begin
|
||||
# create view
|
||||
viewOpt = Dict(
|
||||
:conformal => true,
|
||||
:gl => true,
|
||||
:devicePixelRatio => window.devicePixelRatio
|
||||
)
|
||||
view = CGA3.graph(scene, viewOpt)
|
||||
view.setAttribute(:id, "view")
|
||||
view.removeAttribute(:style)
|
||||
document.body.replaceChildren(view)
|
||||
|
||||
# create control panel
|
||||
controlPanel = document.createElement(:div)
|
||||
controlPanel.setAttribute(:id, "control-panel")
|
||||
document.body.appendChild(controlPanel)
|
||||
end
|
||||
|
||||
new(win)
|
||||
end
|
||||
end
|
||||
|
||||
function display!(viewer::ConstructionViewer, elements::Matrix)
|
||||
# load elements
|
||||
elements_full = [
|
||||
[0; elt; fill(0, 26)]
|
||||
for elt in eachcol(elements)
|
||||
]
|
||||
@js viewer.win elements = $elements_full.map((elt) -> @new CGA3(elt))
|
||||
|
||||
# generate palette. this is Gadfly's `default_discrete_colors` palette,
|
||||
# available under the MIT license
|
||||
palette = distinguishable_colors(
|
||||
length(elements_full),
|
||||
[LCHab(70, 60, 240)],
|
||||
transform = c -> deuteranopic(c, 0.5),
|
||||
lchoices = Float64[65, 70, 75, 80],
|
||||
cchoices = Float64[0, 50, 60, 70],
|
||||
hchoices = range(0, stop=330, length=24)
|
||||
)
|
||||
palette_packed = [RGB24(c).color for c in palette]
|
||||
@js viewer.win palette = $palette_packed
|
||||
|
||||
# create visibility toggles
|
||||
@js viewer.win begin
|
||||
controlPanel.replaceChildren()
|
||||
visToggles = []
|
||||
end
|
||||
for (elt, c) in zip(eachcol(elements), palette)
|
||||
vec_str = join(map(t -> @sprintf("%.3f", t), elt), ", ")
|
||||
color_str = "#$(hex(c))"
|
||||
style_str = "background-color: $color_str; border-color: $color_str;"
|
||||
@js viewer.win begin
|
||||
@var toggle = document.createElement(:div)
|
||||
toggle.setAttribute(:style, $style_str)
|
||||
toggle.checked = true
|
||||
toggle.addEventListener(
|
||||
"click",
|
||||
() -> begin
|
||||
toggle.checked = !toggle.checked
|
||||
toggle.style.backgroundColor = toggle.checked ? $color_str : "inherit";
|
||||
updateView()
|
||||
end
|
||||
)
|
||||
toggle.appendChild(document.createTextNode($vec_str))
|
||||
visToggles.push(toggle);
|
||||
controlPanel.appendChild(toggle);
|
||||
end
|
||||
end
|
||||
|
||||
# update view
|
||||
@js viewer.win updateView()
|
||||
end
|
||||
|
||||
function opentools!(viewer::ConstructionViewer)
|
||||
size(viewer.win, 1240, 830)
|
||||
opentools(viewer.win)
|
||||
end
|
||||
|
||||
function closetools!(viewer::ConstructionViewer)
|
||||
closetools(viewer.win)
|
||||
size(viewer.win, 620, 830)
|
||||
end
|
||||
|
||||
end
|
||||
|
||||
# ~~~ sandbox setup ~~~
|
||||
|
||||
# in the default view, e4 + e5 is the point at infinity
|
||||
elements = sqrt(0.5) * BigFloat[
|
||||
1 1 -1 -1 0;
|
||||
1 -1 1 -1 0;
|
||||
1 -1 -1 1 0;
|
||||
0 0 0 0 -sqrt(6);
|
||||
1 1 1 1 2
|
||||
]
|
||||
|
||||
# show construction
|
||||
viewer = Viewer.ConstructionViewer()
|
||||
Viewer.display!(viewer, elements)
|
||||
@ -1,76 +0,0 @@
|
||||
<!DOCTYPE html>
|
||||
<html>
|
||||
<head>
|
||||
<style>
|
||||
body {
|
||||
background-color: #ffe0f0;
|
||||
}
|
||||
|
||||
/* needed to keep Ganja canvas from blowing up */
|
||||
canvas {
|
||||
min-width: 600px;
|
||||
max-width: 600px;
|
||||
min-height: 600px;
|
||||
max-height: 600px;
|
||||
}
|
||||
</style>
|
||||
<script src="https://unpkg.com/ganja.js"></script>
|
||||
</head>
|
||||
<body>
|
||||
<p><button onclick="flip()">Flip</button></p>
|
||||
<script>
|
||||
// in the default view, e4 + e5 is the point at infinity
|
||||
let CGA3 = Algebra(4, 1);
|
||||
let elements = [
|
||||
CGA3.inline(() => Math.sqrt(0.5)*( 1e1 + 1e2 + 1e3 + 1e5))(),
|
||||
CGA3.inline(() => Math.sqrt(0.5)*( 1e1 - 1e2 - 1e3 + 1e5))(),
|
||||
CGA3.inline(() => Math.sqrt(0.5)*(-1e1 + 1e2 - 1e3 + 1e5))(),
|
||||
CGA3.inline(() => Math.sqrt(0.5)*(-1e1 - 1e2 + 1e3 + 1e5))(),
|
||||
CGA3.inline(() => -Math.sqrt(3)*1e4 + Math.sqrt(2)*1e5)()
|
||||
];
|
||||
|
||||
// set up palette
|
||||
var colorIndex;
|
||||
var palette = [0xff00b0, 0x00ffb0, 0x00b0ff, 0x8040ff, 0xc0c0c0];
|
||||
function nextColor() {
|
||||
colorIndex = (colorIndex + 1) % palette.length;
|
||||
return palette[colorIndex];
|
||||
}
|
||||
function resetColorCycle() {
|
||||
colorIndex = palette.length - 1;
|
||||
}
|
||||
resetColorCycle();
|
||||
|
||||
// create scene function
|
||||
function scene() {
|
||||
commands = [];
|
||||
resetColorCycle();
|
||||
elements.forEach((elt) => commands.push(nextColor(), elt));
|
||||
return commands;
|
||||
}
|
||||
|
||||
// initialize graph
|
||||
let graph = CGA3.graph(
|
||||
scene,
|
||||
{
|
||||
conformal: true, gl: true, grid: true
|
||||
}
|
||||
)
|
||||
document.body.appendChild(graph);
|
||||
|
||||
function flip() {
|
||||
let last = elements.length - 1;
|
||||
for (let n = 0; n < last; ++n) {
|
||||
// reflect
|
||||
elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
|
||||
|
||||
// de-noise
|
||||
for (let k = 6; k < elements[n].length; ++k) {
|
||||
elements[n][k] = 0;
|
||||
}
|
||||
}
|
||||
requestAnimationFrame(graph.update.bind(graph, scene));
|
||||
}
|
||||
</script>
|
||||
</body>
|
||||
</html>
|
||||
@ -1,127 +0,0 @@
|
||||
using Blink
|
||||
using Colors
|
||||
|
||||
# === utilities ===
|
||||
|
||||
append_to_head!(w, type, content) = @js w begin
|
||||
@var element = document.createElement($type)
|
||||
element.appendChild(document.createTextNode($content))
|
||||
document.head.appendChild(element)
|
||||
end
|
||||
|
||||
style!(w, stylesheet) = append_to_head!(w, "style", stylesheet)
|
||||
|
||||
script!(w, code) = append_to_head!(w, "script", code)
|
||||
|
||||
function add_element!(vec)
|
||||
# add element
|
||||
full_vec = [0; vec; fill(0, 26)]
|
||||
n = @js win elements.push(@new CGA3($full_vec))
|
||||
|
||||
# generate palette. this is Gadfly's `default_discrete_colors` palette,
|
||||
# available under the MIT license
|
||||
palette = distinguishable_colors(
|
||||
n,
|
||||
[LCHab(70, 60, 240)],
|
||||
transform = c -> deuteranopic(c, 0.5),
|
||||
lchoices = Float64[65, 70, 75, 80],
|
||||
cchoices = Float64[0, 50, 60, 70],
|
||||
hchoices = range(0, stop=330, length=24)
|
||||
)
|
||||
palette_packed = [RGB24(c).color for c in palette]
|
||||
@js win palette = $palette_packed
|
||||
end
|
||||
|
||||
# === build page ===
|
||||
|
||||
# create window and open developer console
|
||||
win = Window()
|
||||
opentools(win)
|
||||
|
||||
# set stylesheet
|
||||
style!(win, """
|
||||
body {
|
||||
background-color: #ffe0f0;
|
||||
}
|
||||
|
||||
/* needed to keep Ganja canvas from blowing up */
|
||||
canvas {
|
||||
min-width: 600px;
|
||||
max-width: 600px;
|
||||
min-height: 600px;
|
||||
max-height: 600px;
|
||||
}
|
||||
""")
|
||||
|
||||
# load Ganja.js
|
||||
loadjs!(win, "https://unpkg.com/ganja.js")
|
||||
|
||||
# create global functions and variables
|
||||
script!(win, """
|
||||
// create algebra
|
||||
var CGA3 = Algebra(4, 1);
|
||||
|
||||
// initialize element list and palette
|
||||
var elements = [];
|
||||
var palette = [];
|
||||
|
||||
// declare visualization handle
|
||||
var graph;
|
||||
|
||||
// create scene function
|
||||
function scene() {
|
||||
commands = [];
|
||||
for (let n = 0; n < elements.length; ++n) {
|
||||
commands.push(palette[n], elements[n]);
|
||||
}
|
||||
return commands;
|
||||
}
|
||||
|
||||
function flip() {
|
||||
let last = elements.length - 1;
|
||||
for (let n = 0; n < last; ++n) {
|
||||
// reflect
|
||||
elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
|
||||
|
||||
// de-noise
|
||||
for (let k = 6; k < elements[n].length; ++k) {
|
||||
elements[n][k] = 0;
|
||||
}
|
||||
}
|
||||
requestAnimationFrame(graph.update.bind(graph, scene));
|
||||
}
|
||||
""")
|
||||
|
||||
# set up controls
|
||||
body!(win, """
|
||||
<p><button id="flip-button" onclick="flip()">Flip</button></p>
|
||||
""", async = false)
|
||||
|
||||
# === set up visualization ===
|
||||
|
||||
# list elements. in the default view, e4 + e5 is the point at infinity
|
||||
elements = sqrt(0.5) * BigFloat[
|
||||
1 1 -1 -1 0;
|
||||
1 -1 1 -1 0;
|
||||
1 -1 -1 1 0;
|
||||
0 0 0 0 -sqrt(6);
|
||||
1 1 1 1 2
|
||||
]
|
||||
|
||||
# load elements
|
||||
for vec in eachcol(elements)
|
||||
add_element!(vec)
|
||||
end
|
||||
|
||||
# initialize visualization
|
||||
@js win begin
|
||||
graph = CGA3.graph(
|
||||
scene,
|
||||
Dict(
|
||||
"conformal" => true,
|
||||
"gl" => true,
|
||||
"grid" => true
|
||||
)
|
||||
)
|
||||
document.body.appendChild(graph)
|
||||
end
|
||||
@ -10,10 +10,10 @@ using PolynomialRoots
|
||||
# the difference between the matrices `target` and `attempt`, projected onto the
|
||||
# subspace of matrices whose entries vanish at each empty index of `target`
|
||||
function proj_diff(target, attempt)
|
||||
J, K, values = findnz(target)
|
||||
I, J, values = findnz(target)
|
||||
result = zeros(size(target)...)
|
||||
for (j, k, val) in zip(J, K, values)
|
||||
result[j, k] = val - attempt[j, k]
|
||||
for (i, j, val) in zip(I, J, values)
|
||||
result[i, j] = val - attempt[i, j]
|
||||
end
|
||||
result
|
||||
end
|
||||
@ -21,24 +21,24 @@ end
|
||||
# === example ===
|
||||
|
||||
# the Lorentz form
|
||||
Q = diagm([1, 1, 1, 1, -1])
|
||||
Q = diagm([-1, 1, 1, 1, 1])
|
||||
|
||||
# initialize the partial gram matrix for an arrangement of seven spheres in
|
||||
# which spheres 1 through 5 are mutually tangent, and spheres 3 through 7 are
|
||||
# also mutually tangent
|
||||
I = Int64[]
|
||||
J = Int64[]
|
||||
K = Int64[]
|
||||
values = BigFloat[]
|
||||
for j in 1:7
|
||||
for k in 1:7
|
||||
if (j <= 5 && k <= 5) || (j >= 3 && k >= 3)
|
||||
for i in 1:7
|
||||
for j in 1:7
|
||||
if (i <= 5 && j <= 5) || (i >= 3 && j >= 3)
|
||||
push!(I, i)
|
||||
push!(J, j)
|
||||
push!(K, k)
|
||||
push!(values, j == k ? 1 : -1)
|
||||
push!(values, i == j ? 1 : -1)
|
||||
end
|
||||
end
|
||||
end
|
||||
gram = sparse(J, K, values)
|
||||
gram = sparse(I, J, values)
|
||||
|
||||
# set the independent variable
|
||||
#
|
||||
@ -54,11 +54,11 @@ gram[1, 6] = gram[6, 1]
|
||||
# in this initial guess, the mutual tangency condition is satisfied for spheres
|
||||
# 1 through 5
|
||||
guess = sqrt(0.5) * BigFloat[
|
||||
1 1 1 1 2 0.2 0.1;
|
||||
0 0 0 0 -sqrt(6) 0.3 -0.2;
|
||||
1 1 -1 -1 0 -0.1 0.3;
|
||||
1 -1 1 -1 0 -0.5 0.4;
|
||||
1 -1 -1 1 0 0.1 -0.2;
|
||||
0 0 0 0 -sqrt(6) 0.3 -0.2;
|
||||
1 1 1 1 2 0.2 0.1;
|
||||
1 -1 -1 1 0 0.1 -0.2
|
||||
]
|
||||
|
||||
# search parameters
|
||||
@ -108,11 +108,11 @@ println("\nLoss: ", loss, "\n")
|
||||
|
||||
# === algebraic check ===
|
||||
|
||||
R, gens = polynomial_ring(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
||||
R, gens = polynomial_ring(Generic.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
||||
x = gens[1]
|
||||
t = gens[2:4]
|
||||
|
||||
S, u = polynomial_ring(AbstractAlgebra.Rationals{BigInt}(), "u")
|
||||
S, u = polynomial_ring(Generic.Rationals{BigInt}(), "u")
|
||||
|
||||
M = matrix_space(R, 7, 7)
|
||||
gram_symb = M(R[
|
||||
|
||||
@ -11,7 +11,7 @@ function printbad(msg)
|
||||
println(" ", msg)
|
||||
end
|
||||
|
||||
F, gens = rational_function_field(AbstractAlgebra.Rationals{BigInt}(), ["a₁", "a₂", "b₁", "b₂", "c₁", "c₂"])
|
||||
F, gens = rational_function_field(Generic.Rationals{BigInt}(), ["a₁", "a₂", "b₁", "b₂", "c₁", "c₂"])
|
||||
a = gens[1:2]
|
||||
b = gens[3:4]
|
||||
c = gens[5:6]
|
||||
|
||||
@ -11,7 +11,7 @@ function printbad(msg)
|
||||
println(" ", msg)
|
||||
end
|
||||
|
||||
F, gens = rational_function_field(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
||||
F, gens = rational_function_field(Generic.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
|
||||
x = gens[1]
|
||||
t = gens[2:4]
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user