Engine prototype #13
@ -21,43 +21,55 @@
|
|||||||
<script>
|
<script>
|
||||||
// in the default view, e4 + e5 is the point at infinity
|
// in the default view, e4 + e5 is the point at infinity
|
||||||
let CGA3 = Algebra(4, 1);
|
let CGA3 = Algebra(4, 1);
|
||||||
let v = [
|
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(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)()
|
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
|
// create scene function
|
||||||
let scene = () => [
|
function scene() {
|
||||||
0xff00b0, v[0],
|
commands = [];
|
||||||
0x00ffb0, v[1],
|
resetColorCycle();
|
||||||
0x00b0ff, v[2],
|
elements.forEach((elt) => commands.push(nextColor(), elt));
|
||||||
0x8040ff, v[3],
|
return commands;
|
||||||
0xc0c0c0, v[4]
|
}
|
||||||
];
|
|
||||||
|
|
||||||
// initialize graph
|
// initialize graph
|
||||||
let gr = CGA3.graph(
|
let graph = CGA3.graph(
|
||||||
scene,
|
scene,
|
||||||
{
|
{
|
||||||
conformal: true, gl: true, grid: true
|
conformal: true, gl: true, grid: true
|
||||||
}
|
}
|
||||||
)
|
)
|
||||||
document.body.appendChild(gr);
|
document.body.appendChild(graph);
|
||||||
|
|
||||||
function flip() {
|
function flip() {
|
||||||
for (let n = 0; n < 4; ++n) {
|
let last = elements.length - 1;
|
||||||
|
for (let n = 0; n < last; ++n) {
|
||||||
// reflect
|
// reflect
|
||||||
v[n] = CGA3.Mul(CGA3.Mul(v[4], v[n]), v[4]);
|
elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
|
||||||
|
|
||||||
// de-noise
|
// de-noise
|
||||||
for (let k = 6; k < v[n].length; ++k) {
|
for (let k = 6; k < elements[n].length; ++k) {
|
||||||
v[n][k] = 0;
|
elements[n][k] = 0;
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
requestAnimationFrame(gr.update.bind(gr, scene));
|
requestAnimationFrame(graph.update.bind(graph, scene));
|
||||||
}
|
}
|
||||||
</script>
|
</script>
|
||||||
</body>
|
</body>
|
||||||
|
@ -1,4 +1,5 @@
|
|||||||
using Blink
|
using Blink
|
||||||
|
using Colors
|
||||||
|
|
||||||
# === utilities ===
|
# === utilities ===
|
||||||
|
|
||||||
@ -13,8 +14,22 @@ style!(w, stylesheet) = append_to_head!(w, "style", stylesheet)
|
|||||||
script!(w, code) = append_to_head!(w, "script", code)
|
script!(w, code) = append_to_head!(w, "script", code)
|
||||||
|
|
||||||
function add_element!(vec)
|
function add_element!(vec)
|
||||||
|
# add element
|
||||||
full_vec = [0; vec; fill(0, 26)]
|
full_vec = [0; vec; fill(0, 26)]
|
||||||
@js win elements.push(@new CGA3($full_vec))
|
n = @js win elements.push(@new CGA3($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
|
end
|
||||||
|
|
||||||
# === build page ===
|
# === build page ===
|
||||||
@ -45,26 +60,28 @@ loadjs!(win, "https://unpkg.com/ganja.js")
|
|||||||
script!(win, """
|
script!(win, """
|
||||||
// create algebra
|
// create algebra
|
||||||
var CGA3 = Algebra(4, 1);
|
var CGA3 = Algebra(4, 1);
|
||||||
|
|
||||||
// in the default view, e4 + e5 is the point at infinity
|
// initialize element list and palette
|
||||||
var elements = [];
|
var elements = [];
|
||||||
|
var palette = [];
|
||||||
// create scene function
|
|
||||||
let scene = () => [
|
|
||||||
0xff00b0, elements[0],
|
|
||||||
0x00ffb0, elements[1],
|
|
||||||
0x00b0ff, elements[2],
|
|
||||||
0x8040ff, elements[3],
|
|
||||||
0xc0c0c0, elements[4]
|
|
||||||
];
|
|
||||||
|
|
||||||
// declare visualization handle
|
// declare visualization handle
|
||||||
var graph;
|
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() {
|
function flip() {
|
||||||
for (let n = 0; n < 4; ++n) {
|
let last = elements.length - 1;
|
||||||
|
for (let n = 0; n < last; ++n) {
|
||||||
// reflect
|
// reflect
|
||||||
elements[n] = CGA3.Mul(CGA3.Mul(elements[4], elements[n]), elements[4]);
|
elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
|
||||||
|
|
||||||
// de-noise
|
// de-noise
|
||||||
for (let k = 6; k < elements[n].length; ++k) {
|
for (let k = 6; k < elements[n].length; ++k) {
|
||||||
@ -78,7 +95,7 @@ script!(win, """
|
|||||||
# set up controls
|
# set up controls
|
||||||
body!(win, """
|
body!(win, """
|
||||||
<p><button id="flip-button" onclick="flip()">Flip</button></p>
|
<p><button id="flip-button" onclick="flip()">Flip</button></p>
|
||||||
""", async=false)
|
""", async = false)
|
||||||
|
|
||||||
# === set up visualization ===
|
# === set up visualization ===
|
||||||
|
|
||||||
@ -106,5 +123,5 @@ end
|
|||||||
"grid" => true
|
"grid" => true
|
||||||
)
|
)
|
||||||
)
|
)
|
||||||
document.body.appendChild(graph);
|
document.body.appendChild(graph)
|
||||||
end
|
end
|
Loading…
Reference in New Issue
Block a user