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add "pinwheel" patterns, better levo/dextro and net calculations, all…
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…ow net for impossible constructions

scale only works to resolve chirality in symmetrical cases...
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@dnanto
dnanto committed Oct 21, 2024
1 parent 887fe12 commit 12fe1d4
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2 changes: 2 additions & 0 deletions app.html
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Original file line number Diff line number Diff line change
Expand Up @@ -45,6 +45,8 @@
<option value="dualtrihex">dualtrihex</option>
<option value="dualsnubhex">dualsnubhex</option>
<option value="dualrhombitrihex">dualrhombitrihex</option>
<option value="pinwheel-1">pinwheel-1</option>
<option value="pinwheel-2">pinwheel-2</option>
</select>
</div>
<div>
Expand Down
5 changes: 2 additions & 3 deletions js/app.js
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Original file line number Diff line number Diff line change
Expand Up @@ -47,7 +47,7 @@ const DEFAULTS = Object.assign(

function params() {
const PARAMS = Object.fromEntries(Object.keys(DEFAULTS).map((k) => [k, DEFAULTS[k](document.getElementById(k))]));
PARAMS.c = PARAMS.l ? "levo" : "dextro";
PARAMS.c = PARAMS.l;
return PARAMS;
}

Expand All @@ -61,7 +61,7 @@ function params_to_tag(PARAMS) {
"R=" + PARAMS.R,
"t=" + PARAMS.t,
`s=${(PARAMS.s * 100).toFixed(2)}%`,
"c=" + PARAMS.c,
"c=" + (PARAMS.c ? "levo" : "dextro"),
"@(" + [PARAMS.θ, PARAMS.ψ, PARAMS.φ].map((e) => e + "°").join(",") + ")",
].join(",");
}
Expand Down Expand Up @@ -160,7 +160,6 @@ function update(e) {
`T-Number=(${h})²+(${h})(${k})+(${k})²=${h * h + h * k + k * k}`,
`Q-Number=(${H})²+(${H})(${K})+(${K})²=${H * H + H * K + K * K}`,
].join("\n");
if (PARAMS.c === "levo") paper.view.scale(1, -1);
} catch (e) {
console.log(e);
paper.clear();
Expand Down
251 changes: 134 additions & 117 deletions js/democapsid.js
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Original file line number Diff line number Diff line change
Expand Up @@ -446,6 +446,48 @@ function calc_tile(t, R) {
),
radius: R,
};
} else if (t === "pinwheel-1") {
tile = {
basis: [
[1.5 * r, 0.75 * R],
[0, 1.5 * R],
],
tile: (e) =>
Array.from({ length: 6 }, (_, i) =>
new paper.Path({
segments: [
[0, 0],
[0, R],
[-r / 2, 0.75 * R],
[-r / 2, 0.25 * R],
].map((f) => e.coor.add(f)),
closed: true,
data: { mer: 1 },
}).rotate(i * 60, e.coor)
),
radius: r,
};
} else if (t === "pinwheel-2") {
tile = {
basis: [
[1.5 * r, 0.75 * R],
[0, 1.5 * R],
],
tile: (e) =>
Array.from({ length: 6 }, (_, i) =>
new paper.Path({
segments: [
[0, 0],
[0, R],
[r / 2, 0.75 * R],
[r / 2, 0.25 * R],
].map((f) => e.coor.add(f)),
closed: true,
data: { mer: 1 },
}).rotate(i * 60, e.coor)
),
radius: r,
};
} else {
throw new Error("incorrect tile mode");
}
Expand All @@ -466,16 +508,29 @@ function* tile_grid(ck, basis) {
}
}

function ck_vectors(basis, h, k, H, K) {
function ck_vectors(basis, h, k, H, K, c) {
const [v1, v2] = basis;
const v3 = v2.rot(Math.PI / 3);
return [
//
v1.mul(h).add(v2.mul(k)),
v2.mul(H).add(v3.mul(K)),
v1.mul(-h - k).add(v2.mul(h)),
v1.mul(k).add(v3.mul(-h)),
];
if (c) {
return [
// levo
v1.mul(h).add(v2.mul(k)),
v2.mul(H).add(v3.mul(K)),
v3.mul(h).add(v1.mul(-k)),
v1.mul(k).add(v3.mul(-h)),
];
} else {
return [
// dextro
v1.mul(h).add(v3.mul(-k)),
v2.mul(H).add(v1.mul(K)),
v3.mul(h).add(v2.mul(k)),
v1
.mul(h)
.add(v3.mul(-k))
.rot(-Math.PI / 3),
];
}
}

function triangle_circumcircle_center(p, q, r) {
Expand Down Expand Up @@ -719,7 +774,6 @@ function ico_axis_3(ck, iter = ITER, tol = TOL) {
const [p, q] = [pB.add(o.proj(v)), pB.add(o)];
[v, k] = [q.sub(p), pB.sub(pD).uvec()];
const f = (t) => c - p.add(v.roro(k, t)).sub(pF).norm();
let br = brackets(f, 0, 2 * Math.PI, iter).next().value;
t = bisection(f, ...brackets(f, 0, 2 * Math.PI, iter).next().value, tol, iter).slice(-1);
const pG = p.add(v.roro(k, t));
return [pD, pF, pG, Math.abs(pD[1]) - pG.sub([0, 0, pG[2]]).norm()];
Expand Down Expand Up @@ -830,34 +884,38 @@ function ico_axis_2(ck, iter = ITER, tol = TOL) {
}

function model_sa_error(PARAMS) {
const tile = calc_tile(PARAMS.t, PARAMS.R);
const ck = ck_vectors(tile.basis, PARAMS.h, PARAMS.k, PARAMS.H, PARAMS.K);
const triangles = [
[ck[3], ck[0]],
[ck[0], ck[1]],
[ck[1], ck[2]],
];
// coordinates
const ico_coors = ["", "", ico_axis_2, ico_axis_3, "", ico_axis_5][PARAMS.a](ck, ITER, TOL);
const config = ico_config(PARAMS.a);

const n_tris = config.t_id.map((e) => parseInt(e[1])).reduce((a, b) => (a < b ? b : a));
const n_per_tri = Array.from({ length: n_tris }).fill(0);
config.t_id.forEach((e, i) => (n_per_tri[e[1] - 1] += config.t_rep[i]));
const sa_net = triangles
.slice(0, n_tris)
.map((e, i) => ([...e[0], 0].cross([...e[1], 0]).norm() / 2) * n_per_tri[i])
.sum();
const sa_capsid = config.v_idx
.map((e) => e.map((i) => ico_coors[i]))
.map((e, i) => (e[1].sub(e[0]).cross(e[2].sub(e[0])).norm() / 2) * config.t_rep[i])
.sum();
return (sa_net - sa_capsid) / sa_net;
try {
const tile = calc_tile(PARAMS.t, PARAMS.R);
const ck = ck_vectors(tile.basis, PARAMS.h, PARAMS.k, PARAMS.H, PARAMS.K, PARAMS.c);
const triangles = [
[ck[3], ck[0]],
[ck[0], ck[1]],
[ck[1], ck[2]],
];
// coordinates
const ico_coors = ["", "", ico_axis_2, ico_axis_3, "", ico_axis_5][PARAMS.a](ck, ITER, TOL);
const config = ico_config(PARAMS.a);

const n_tris = config.t_id.map((e) => parseInt(e[1])).reduce((a, b) => (a < b ? b : a));
const n_per_tri = Array.from({ length: n_tris }).fill(0);
config.t_id.forEach((e, i) => (n_per_tri[e[1] - 1] += config.t_rep[i]));
const sa_net = triangles
.slice(0, n_tris)
.map((e, i) => ([...e[0], 0].cross([...e[1], 0]).norm() / 2) * n_per_tri[i])
.sum();
const sa_capsid = config.v_idx
.map((e) => e.map((i) => ico_coors[i]))
.map((e, i) => (e[1].sub(e[0]).cross(e[2].sub(e[0])).norm() / 2) * config.t_rep[i])
.sum();
return (sa_net - sa_capsid) / sa_net;
} catch (_) {
return NaN;
}
}

function lattice_config(h, k, H, K, R, t) {
function lattice_config(h, k, H, K, c, R, t) {
const tile = calc_tile(t, R);
const ck = ck_vectors(tile.basis, h, k, H, K);
const ck = ck_vectors(tile.basis, h, k, H, K, c);

// grid
//// calculate
Expand Down Expand Up @@ -926,9 +984,9 @@ function calc_facets(lat_cfg, PARAMS) {

function draw_lattice(PARAMS) {
// unpack
const [h, k, H, K, R, t] = ["h", "k", "H", "K", "R", "t"].map((e) => PARAMS[e]);
const [h, k, H, K, c, R, t] = ["h", "k", "H", "K", "c", "R", "t"].map((e) => PARAMS[e]);
// lattice
const lat_cfg = lattice_config(h, k, H, K, R, t);
const lat_cfg = lattice_config(h, k, H, K, c, R, t);
lat_cfg.lattice.flat().forEach((e) => (e.style.fillColor = PARAMS["mer_color_" + e.data.offset] + PARAMS["mer_alpha_" + e.data.offset]));
return new paper.Group(
new paper.Group({
Expand All @@ -941,16 +999,16 @@ function draw_lattice(PARAMS) {
strokeJoin: "round",
},
})
);
).scale(1, -1);
}

function draw_facets(PARAMS) {
// unpack
const [h, k, H, K, R, t] = ["h", "k", "H", "K", "R", "t"].map((e) => PARAMS[e]);
const [h, k, H, K, c, R, t] = ["h", "k", "H", "K", "c", "R", "t"].map((e) => PARAMS[e]);

// lattice
const lat_cfg = lattice_config(h, k, H, K, R, t);
const g = new paper.Group({ children: calc_facets(lat_cfg, PARAMS), position: paper.view.center });
const lat_cfg = lattice_config(h, k, H, K, c, R, t);
const g = new paper.Group({ children: calc_facets(lat_cfg, PARAMS), position: paper.view.center }).scale(1, -1);

lat_cfg.lattice.forEach((e) => e.forEach((f) => f.remove()));

Expand Down Expand Up @@ -984,87 +1042,46 @@ function draw_facets(PARAMS) {

function draw_net(PARAMS) {
// unpack
const [h, k, H, K, R, t] = ["h", "k", "H", "K", "R", "t"].map((e) => PARAMS[e]);
const [h, k, H, K, c, R, t] = ["h", "k", "H", "K", "c", "R", "t"].map((e) => PARAMS[e]);

// lattice
const lat_cfg = lattice_config(h, k, H, K, R, t);
const lat_cfg = lattice_config(h, k, H, K, c, R, t);
const ck = lat_cfg.ck;
const facets = calc_facets(lat_cfg, PARAMS);

let g;
/****/ if (PARAMS.a === 5) {
const unit1 = new paper.Group(facets.slice(0, 2)).rotate(-degrees(ck[0].angle([1, 0]))).scale(-1, 1);
const unit2 = unit1.clone().rotate(180);
const top_center = unit2.children[1].children
.flatMap((e) => e.segments)
.map((e) => e.point)
.reduce((a, b) => (a.y < b.y ? a : b));
unit2.position.x += unit1.children[0].bounds.right - top_center.x;
unit2.position.y += unit1.children[0].bounds.height;
if (PARAMS.a == 5) {
const u = new paper.Group(facets.slice(0, 2).map((e) => e.clone()));
const v = u
.clone()
.rotate(180, ck[0])
.translate(ck[1].sub(ck[0].mul(2)));
g = new paper.Group({
children: Array.from({ length: 5 })
.flatMap((_, i) => {
const [u1, u2] = [unit1.clone(), unit2.clone()];
u1.position.x += i * unit1.children[0].bounds.width;
u2.position.x += i * unit1.children[0].bounds.width;
return [u1, u2];
})
.flatMap((e) => e.children),
children: [u, v].flatMap((e) => Array.from({ length: 5 }, (_, i) => e.clone().translate(ck[0].mul(i)))).flatMap((e) => e.children),
position: paper.view.center,
});
// clean-up
[unit1, unit2].forEach((e) => e.remove());
} else if (PARAMS.a === 3) {
const angle = ck[0].angle([1, 0]);
const unit1 = new paper.Group(facets).rotate(-degrees(angle)).scale(-1, 1);
const unit0 = facets[0].clone().rotate(180);
unit0.position.x += ck[0].norm() / 2;
const centroid = [unit0.bounds.topLeft, unit0.bounds.topRight, unit0.bounds.bottomCenter].reduce((a, b) => a.add(b)).divide(3);
const center1 = unit0.bounds.topRight.add(new paper.Point([1, 0].mul(ck[1].norm()).rot(-(Math.PI / 3 - ck[1].angle(ck[2])))));
const center2 = unit0.bounds.topRight.add(new paper.Point([1, 0].mul(ck[2].norm()).rot(-(Math.PI / 3 - ck[1].angle(ck[2]) + ck[1].angle(ck[2])))));
const f = new paper.Group([...[1, 2, 3].map((_, i) => unit1.clone().rotate(i * 120, centroid))]);
f.children.slice(0, -1).forEach((e) => e.children[1].remove());
const unit2 = f.clone().rotate(180);
unit2.bounds.left = Math.min(center1.x, center2.x);
unit2.bounds.bottom = unit0.bounds.topRight.y;
unit2.position.y -= unit2.children[1].children[0].bounds.bottom - center1.y;
unit2.children.forEach((e) => f.addChild(e.clone()));
f.position = paper.view.center;
}).rotate(-degrees(Math.atan2(ck[0].dot([0, 1]), ck[0][0] * 1 - ck[0][1] * 0)));
[u, v].forEach((e) => e.remove());
} else if (PARAMS.a == 3) {
const centroid = [[0, 0], ck[0], ck[3]].centroid();
const u = new paper.Group(facets.slice(0, 1).map((e) => e.clone()));
const v = new paper.Group(facets.slice(0, 3).map((e) => e.clone())).translate(ck[0]).rotate(-60, ck[0]);
const w = new paper.Group([u.clone(), ...Array.from({ length: 3 }, (_, i) => v.clone().rotate(i * 120, centroid))]);
const p = ck[0].add(ck[1].rot(Math.PI / 3).rot((4 * Math.PI) / 3));
g = new paper.Group({
children: f.children.flatMap((e) => e.children.flat()),
});
// clean-up
[unit0, unit1, unit2].forEach((e) => e.remove());
} else if (PARAMS.a === 2) {
const angle = ck[0].angle([1, 0]);
const unit1 = new paper.Group(facets).rotate(-degrees(angle)).rotate(-60).scale(-1, 1);
const unit2 = unit1.children[1].clone();
const vector = unit1.children[0].bounds.topLeft.subtract(unit1.children[0].bounds.bottomCenter);
unit2.position = unit2.position.add(vector);
const unit3 = new paper.Group([unit1.clone(), unit1.children[0].clone().rotate(60, unit1.children[0].bounds.topRight), unit2.clone()]);
const unit4 = unit3.clone().rotate(180, unit3.children[0].children[0].bounds.topRight);
unit4.position = unit4.position.add(vector.rotate(240));
const unit5 = new paper.Group([unit3, unit4]);
const point1 = unit5.children[0].children[2].children
.filter((e) => e.data.offset === 1)
.flatMap((e) => e.segments.map((e) => e.point))
.filter((e) => Math.abs(e.getDistance(unit5.children[0].children[1].bounds.bottomLeft) - ck[1].norm()) < 1e-5)
.reduce((a, b) => (a.y < b.y ? b : a));
const unit6 = unit5.clone();
unit6.position = unit6.position.add(unit5.children[1].children[0].children[0].bounds.bottomRight.subtract(point1));
const f = new paper.Group([unit5, unit6]);
f.position = paper.view.center;
const children = f.children.flatMap((e) => e.children).flatMap((e) => e.children);
children: [w.clone(), w.clone().translate(ck[0].add(p)).rotate(60, p)].flatMap((e) => e.children).flatMap((e) => e.children),
position: paper.view.center,
}).rotate(-degrees(Math.atan2(ck[0].dot([0, 1]), ck[0][0] * 1 - ck[0][1] * 0)) - 30);
[u, v, w].forEach((e) => e.remove());
} else if (PARAMS.a == 2) {
const u = new paper.Group(facets.slice(0, 3).map((e) => e.clone()));
const v = new paper.Group([...u.clone().children, u.children[0].clone().rotate(60, ck[0]), u.children[2].clone().translate(ck[0])]);
const w = new paper.Group([v.clone(), v.clone().rotate(180, ck[3]).translate(ck[3].mul(-1))]);
g = new paper.Group({
children: [...children.filter((_, i) => i % 3 === 0).flatMap((e) => e.children), ...children.filter((_, i) => i % 3 !== 0)],
});
// clean-up
[2, 5, 8, 11].forEach((e) => g.children[e].remove());
[unit1, unit2, unit3, unit4, unit5, unit6].forEach((e) => e.remove());
} else {
throw new Error("invalid symmetry mode!");
children: [w.clone(), w.clone().translate(ck[1].mul(-1).add(ck[0].mul(-2)).add(ck[3]))].flatMap((e) => e.children).flatMap((e) => e.children),
position: paper.view.center,
}).rotate(-degrees(Math.atan2(ck[0].dot([0, 1]), ck[0][0] * 1 - ck[0][1] * 0)) - 30);
[u, v, w].forEach((e) => e.remove());
}
g.scale(-1, 1);

// clean-up
facets.forEach((e) => e.remove());
Expand All @@ -1075,11 +1092,11 @@ function draw_net(PARAMS) {
g.style.strokeWidth = PARAMS.line_size;
g.style.strokeCap = "round";
g.style.strokeJoin = "round";
return g;
return g.scale(1, -1);
}
g.remove();
return new paper.Group({
children: g.children.map(
children: g.children.flatMap(
(e) =>
new paper.Group(
e.children.map((e) => {
Expand All @@ -1095,15 +1112,15 @@ function draw_net(PARAMS) {
strokeCap: "round",
strokeJoin: "round",
},
});
}).scale(1, -1);
}

function draw_capsid(PARAMS) {
// unpack
const [h, k, H, K, R, t] = ["h", "k", "H", "K", "R", "t"].map((e) => PARAMS[e]);
const [h, k, H, K, c, R, t] = ["h", "k", "H", "K", "c", "R", "t"].map((e) => PARAMS[e]);

// lattice
const lat_cfg = lattice_config(h, k, H, K, R, t);
const lat_cfg = lattice_config(h, k, H, K, c, R, t);
const facets = calc_facets(lat_cfg, PARAMS);

// coordinates
Expand Down Expand Up @@ -1233,7 +1250,7 @@ function draw_capsid(PARAMS) {
});
g.style.strokeCap = "round";
g.style.strokeJoin = "round";
return g;
return g.scale(-1, 1);
}
g.remove();
return new paper.Group({
Expand All @@ -1259,7 +1276,7 @@ function draw_capsid(PARAMS) {
strokeCap: "round",
strokeJoin: "round",
},
});
}).scale(-1, 1);
}

if (typeof exports !== "undefined") {
Expand Down

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