b-splineライブラリを使って丸みを帯びた図形を作ってみた
こんにちわ。nap5です。
b-splineライブラリを使って丸みを帯びた図形を作ってみたので紹介したいと思います。
b-splineを使った何かアウトプットをしてみたかったので、トライしてみました。
よく調べると、pythonのscipyライブラリ補間系ユーティリティにsplrepメソッドがあり、これを使うと実現したい丸みを帯びた図形を作りやすいことが分かりました。
https://stackoverflow.com/a/34807513/15972569
使用したライブラリは以下になります。
https://github.com/thibauts/b-spline
また、numpyライクに操作できるライブラリとしてnumjsを使用しました。
今回のプログラムです。
次数に3,4,5,10を指定してオリジナルなsvgコマンドパスとsvg-path-editorを用いて比較してみました。
import bspline from "b-spline";
import { samples } from "culori";
import { interpolate } from "popmotion";
import nj from "numjs";
const divmod = (n, m) => {
const quotient = Math.floor(n / m);
const remainder = n % m;
return { factor: quotient, fraction: remainder };
};
const niceBspline = ({ points = [], n = 100, degree = 3, periodic = true }) => {
let knots = [];
let count = points.length;
let weights = points.map((p) => {
return 1;
});
// If periodic, extend the point array by count+degree+1
if (periodic) {
const { factor, fraction } = divmod(count + degree + 1, count);
points = [
...[...Array(factor).keys()]
.map((_, index) => {
return points;
})
.flat(),
...points.slice(0, fraction),
];
count = points.length;
weights = points.map((p) => {
return 1;
});
// https://numpy.org/doc/stable/reference/generated/numpy.clip.html
// https://github.com/nicolaspanel/numjs
degree = nj.clip(degree, 1, degree).tolist()[0];
} else {
// If opened, prevent degree from exceeding count-1
degree = nj.clip(degree, 1, count - 1).tolist()[0];
}
// Calculate knot vector
if (periodic) {
knots.push(...nj.arange(0 - degree, count + degree + degree - 1).tolist());
knots = knots.slice(0, count + degree + 1);
} else {
knots.push(
...[...Array(degree).keys()].map((_, index) => {
return 0;
})
);
knots.push(...nj.arange(count - degree + 1).tolist());
knots.push(
...[...Array(degree).keys()].map((_, index) => {
return count - degree;
})
);
}
// do spline
const splinePoints = samples(100).map((t) => {
return bspline(t, degree, points, knots, weights);
});
return { count, degree, points, knots, splinePoints };
};
const makePath = ({ points, noZ }) => {
let path = `M ${points[0][0]},${points[0][1]}`;
for (let i = 1; i < points.length; i++) {
path = path + ` L ${points[i][0]},${points[i][1]}`;
}
path = path + (noZ ? `` : ` Z`);
return path;
};
const formatPoint = ([x, y]) => {
return { x, y };
};
const unFormatPoint = ({ x, y }) => {
return [x, y];
};
const buildPoints = ({ edgeCount }) => {
const stepSize = (Math.PI * 2) / edgeCount;
return [...Array(edgeCount)].map((_, edgeIndex) => {
return [Math.cos(edgeIndex * stepSize), Math.sin(edgeIndex * stepSize)];
});
};
const points = [
[50, 25],
[59, 12],
[50, 10],
[57, 2],
[40, 4],
[41, 12],
];
const { splinePoints: a } = niceBspline({
points,
periodic: true,
degree: 3,
});
const { splinePoints: b } = niceBspline({
points,
periodic: true,
degree: 4,
});
const { splinePoints: c } = niceBspline({
points,
periodic: true,
degree: 5,
});
const { splinePoints: d } = niceBspline({
points,
periodic: true,
degree: 10,
});
const originalPath = makePath({ points, noZ: false });
const splinePathA = makePath({ points: a, noZ: true });
const splinePathB = makePath({ points: b, noZ: true });
const splinePathC = makePath({ points: c, noZ: true });
const splinePathD = makePath({ points: d, noZ: true });
console.log(originalPath);
console.log(splinePathA);
console.log(splinePathB);
console.log(splinePathC);
console.log(splinePathD);
こちらが実行結果になります。
$ time node index.js
M 50,25 L 59,12 L 50,10 L 57,2 L 40,4 L 41,12 Z
M 56,13.833333333333334 L 55.95700775396726,13.329525915894656 L 55.836043666265084,12.874703398986636 L 55.64912671248759,12.462856294812218 L 55.408275868228934,12.087975115574341 L 55.125510109083216,11.744050373475943 L 54.81284841064455,11.425072580719963 L 54.48230974850708,11.125032249509344 L 54.1459130982649,10.837919892047022 L 53.81567743551215,10.557726020535938 L 53.50362173584294,10.27844114717903 L 53.221764974851396,9.994055784179242 L 52.98212612813163,9.698560443739506 L 52.79672417127779,9.385945638062768 L 52.677578079883965,9.050201879351967 L 52.63396128409902,8.686544044670764 L 52.65820363963412,8.297742929413166 L 52.736177886060545,7.889448853738213 L 52.85374405209116,7.467317806160781 L 52.99676216643873,7.037005775195754 L 53.15109225781606,6.604168749358015 L 53.30259435493595,6.1744627171624415 L 53.4371284865112,5.753543667123914 L 53.540554681254605,5.347067587757313 L 53.598732967878966,4.960690467577519 L 53.5975233750971,4.600068295099415 L 53.52278593162177,4.270857058837875 L 53.36038066616579,3.978712747307789 L 53.09616760744196,3.7292913490240296 L 52.717767409839645,3.52781943160476 L 52.23009711439464,3.3753049317787607 L 51.647891010915195,3.270361335354704 L 50.98599606925288,3.211574645203866 L 50.25925925925926,3.197530864197531 L 49.48252755078589,3.2268159952069757 L 48.67064791368434,3.298016041103482 L 47.83846731780616,3.4097170047583267 L 47.00083273300291,3.560504889042794 L 46.172591129126175,3.7489656968281597 L 45.368589476027495,3.973685430985706 L 44.60367474355843,4.2332500943867135 L 43.892693901570546,4.526245689902458 L 43.25049391991541,4.851258220404226 L 42.69135012334686,5.206906668288161 L 42.21993598536809,5.5923639689071765 L 41.83295767593289,6.007262709742047 L 41.52688020221945,6.45124939151059 L 41.298168571405995,6.9239705149306205 L 41.143287790670705,7.425072580719964 L 41.0587028671918,7.954202089596439 L 41.040878808147454,8.511005542277864 L 41.08628062071588,9.095129439482054 L 41.191373312075285,9.706220281926846 L 41.35262188940385,10.343924570330039 L 41.5664913598798,11.007888805409463 L 41.82944673068131,11.69775948788295 L 42.13795300898658,12.41318311846829 L 42.48848447746519,13.153667065512794 L 42.87782185353863,13.914122176085243 L 43.30311515659949,14.683919767686726 L 43.76153639239038,15.452101362569682 L 44.25025756665385,16.207708482986515 L 44.766450685132455,16.939782651189653 L 45.307287753568744,17.6373653894315 L 45.869940777705295,18.289498219964504 L 46.45158176328465,18.885222665041052 L 47.04938271604938,19.413580246913575 L 47.660515641742045,19.86361248783451 L 48.282152546105195,20.224360910056248 L 48.91146543488142,20.484867035831225 L 49.54562631381324,20.634172387411855 L 50.18179344717453,20.661411929037683 L 50.81592787377912,20.563861758076634 L 51.4418813169961,20.353141316920524 L 52.05329078974625,20.042330079010007 L 52.64379330495032,19.644507517785758 L 53.2070258755291,19.172753106688422 L 53.73662551440329,18.640146319158664 L 54.2262292344937,18.059766628637156 L 54.66947404872107,17.444693508564537 L 55.059996970006154,16.808006432381497 L 55.39143501126973,16.162784873528672 L 55.65742518543253,15.522108305446745 L 55.85160450541534,14.899056201576354 L 55.96760998413892,14.306708035358174 L 55.99908756647865,13.758134004741494 L 55.94422063027307,13.261692358060072 L 55.813098848911515,12.813377113652596 L 55.61774119798812,12.407178783721996 L 55.370166653096966,12.037087880471207 L 55.08239418983221,11.697094916103183 L 54.76644278378795,11.381190402820849 L 54.43433141055833,11.083364852827152 L 54.09807904573744,10.797608778325031 L 53.769704664919445,10.517912691517427 L 53.46122724369842,10.238267104607273 L 53.184665757668505,9.952662529797514 L 52.95203918242384,9.655089479291094 L 52.775366493558515,9.339538465290937 L 52.66666666666667,9
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real 0m0.703s
user 0m0.682s
sys 0m0.153ssvg-path-editorに張り付けて眺めてみます。
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実はよーく見ると点がダブっているのですが、これはファクターで点を増幅させているからです。simplify-jsライブラリを使ってpolygonの簡素化で調節してみたんですが、形状に違和感が出るくらいなら、まぁダブってもいいかなということで、そのままにしています。
splineしているパスに関してはZコマンドは指定せずにしています。
これはきれいな見た目を維持するためです。
fillプロパティも指定でき、カラーリングもできるので、指定しなくても問題ないかなという感じです。
なかなか難しかったんですが、なんとかワークアラウンドを見つけられることができてよかったです。
最後におまけで、三角形でもやってみました。
import bspline from "b-spline";
import { samples } from "culori";
import { interpolate } from "popmotion";
import nj from "numjs";
const divmod = (n, m) => {
const quotient = Math.floor(n / m);
const remainder = n % m;
return { factor: quotient, fraction: remainder };
};
const niceBspline = ({ points = [], n = 100, degree = 3, periodic = true }) => {
let knots = [];
let count = points.length;
let weights = points.map((p) => {
return 1;
});
// If periodic, extend the point array by count+degree+1
if (periodic) {
const { factor, fraction } = divmod(count + degree + 1, count);
points = [
...[...Array(factor).keys()]
.map((_, index) => {
return points;
})
.flat(),
...points.slice(0, fraction),
];
count = points.length;
weights = points.map((p) => {
return 1;
});
// https://numpy.org/doc/stable/reference/generated/numpy.clip.html
// https://github.com/nicolaspanel/numjs
degree = nj.clip(degree, 1, degree).tolist()[0];
} else {
// If opened, prevent degree from exceeding count-1
degree = nj.clip(degree, 1, count - 1).tolist()[0];
}
// Calculate knot vector
if (periodic) {
knots.push(...nj.arange(0 - degree, count + degree + degree - 1).tolist());
knots = knots.slice(0, count + degree + 1);
} else {
knots.push(
...[...Array(degree).keys()].map((_, index) => {
return 0;
})
);
knots.push(...nj.arange(count - degree + 1).tolist());
knots.push(
...[...Array(degree).keys()].map((_, index) => {
return count - degree;
})
);
}
// do spline
const splinePoints = samples(100).map((t) => {
return bspline(t, degree, points, knots, weights);
});
return { count, degree, points, knots, splinePoints };
};
const makePath = ({ points, noZ }) => {
let path = `M ${points[0][0]},${points[0][1]}`;
for (let i = 1; i < points.length; i++) {
path = path + ` L ${points[i][0]},${points[i][1]}`;
}
path = path + (noZ ? `` : ` Z`);
return path;
};
const formatPoint = ([x, y]) => {
return { x, y };
};
const unFormatPoint = ({ x, y }) => {
return [x, y];
};
const buildPoints = ({ edgeCount }) => {
const stepSize = (Math.PI * 2) / edgeCount;
return [...Array(edgeCount)].map((_, edgeIndex) => {
return [Math.cos(edgeIndex * stepSize), Math.sin(edgeIndex * stepSize)];
});
};
const points = buildPoints({ edgeCount: 3 });
const { splinePoints: a } = niceBspline({
points,
periodic: true,
degree: 3,
});
const { splinePoints: b } = niceBspline({
points,
periodic: true,
degree: 4,
});
const { splinePoints: c } = niceBspline({
points,
periodic: true,
degree: 5,
});
const { splinePoints: d } = niceBspline({
points,
periodic: true,
degree: 10,
});
const originalPath = makePath({ points, noZ: false });
const splinePathA = makePath({ points: a, noZ: true });
const splinePathB = makePath({ points: b, noZ: true });
const splinePathC = makePath({ points: c, noZ: true });
const splinePathD = makePath({ points: d, noZ: true });
console.log(originalPath);
console.log(splinePathA);
console.log(splinePathB);
console.log(splinePathC);
console.log(splinePathD);
以下が実行結果になります。
$ time node index.js
M 1,0 L -0.4999999999999998,0.8660254037844387 L -0.5000000000000004,-0.8660254037844385 Z
M -0.2499999999999999,0.4330127018922194 L -0.27907866544230164,0.41345369925640063 L -0.3057086011631467,0.3899961056051008 L -0.32988980716253435,0.36298265421440606 L -0.35162228344046526,0.33275607836040255 L -0.37090602999693906,0.29965911131917655 L -0.3877410468319559,0.2640344863668143 L -0.4021273339455158,0.2262249367794022 L -0.41406489133761853,0.1865731958330262 L -0.42355371900826455,0.14542199680377313 L -0.43059381695745347,0.10311407296772895 L -0.43518518518518534,0.059992157600979805 L -0.43732782369146017,0.016398983979611897 L -0.43702173247627807,-0.027322714620288235 L -0.4342669115396389,-0.07083020492263448 L -0.42906336088154284,-0.11378075365134047 L -0.42141108050198967,-0.1558316275303202 L -0.41131007040097967,-0.196640093283487 L -0.3987603305785126,-0.23586341763475505 L -0.38376186103458854,-0.2731588673080377 L -0.36631466176920746,-0.30818370902724884 L -0.34641873278236934,-0.34059520951630246 L -0.32407407407407435,-0.3700506354991119 L -0.2992806856443223,-0.39620725369959103 L -0.27203856749311317,-0.41872233084165383 L -0.24234849257806118,-0.43725447245107335 L -0.2103047617280861,-0.45162427907864844 L -0.17618332081142035,-0.46196696971220985 L -0.14028098555187654,-0.4684539109898009 L -0.10289457167326796,-0.47125646954946465 L -0.06432089489940754,-0.4705460120292442 L -0.024856770954108105,-0.4664939050671825 L 0.015200984438817185,-0.45927151530132315 L 0.05555555555555528,-0.44905020936970885 L 0.09591012667229348,-0.43600135391038297 L 0.13596788206521887,-0.4202963155613884 L 0.17543200601051825,-0.4021064609607685 L 0.21400568278437865,-0.3816031567465664 L 0.2513920966629871,-0.35895776955682523 L 0.28729443192253085,-0.3343416660295879 L 0.3214158728391968,-0.30792621280289767 L 0.353459603689172,-0.27988277651479776 L 0.3831288087486433,-0.25038272380333126 L 0.410126672293798,-0.21959742130654117 L 0.4341563786008229,-0.1876982356624709 L 0.45492111194590523,-0.15485653350916329 L 0.4721240566052319,-0.12124368148466164 L 0.48546839685499,-0.08703104622700897 L 0.4946573169713666,-0.05238999437424843 L 0.49939400123054845,-0.01749189256442328 L 0.49939400123054845,0.017491892564423513 L 0.49465731697136656,0.052389994374248516 L 0.48546839685499,0.08703104622700919 L 0.472124056605232,0.12124368148466166 L 0.45492111194590545,0.1548565335091632 L 0.43415637860082307,0.18769823566247107 L 0.4101266722937983,0.21959742130654128 L 0.38312880874864336,0.2503827238033315 L 0.3534596036891721,0.27988277651479787 L 0.32141587283919715,0.30792621280289767 L 0.2872944319225312,0.33434166602958804 L 0.2513920966629877,0.3589577695568252 L 0.21400568278437881,0.38160315674656664 L 0.17543200601051853,0.4021064609607687 L 0.135967882065219,0.4202963155613886 L 0.0959101266722939,0.43600135391038297 L 0.055555555555555844,0.44905020936970885 L 0.015200984438817254,0.45927151530132326 L -0.024856770954107835,0.46649390506718275 L -0.06432089489940734,0.47054601202924423 L -0.1028945716732676,0.47125646954946476 L -0.14028098555187601,0.46845391098980105 L -0.17618332081141994,0.4619669697122101 L -0.21030476172808565,0.4516242790786486 L -0.24234849257806107,0.4372544724510734 L -0.2720385674931129,0.41872233084165394 L -0.2992806856443218,0.3962072536995914 L -0.32407407407407407,0.370050635499112 L -0.346418732782369,0.3405952095163026 L -0.3663146617692073,0.3081837090272491 L -0.3837618610345883,0.273158867308038 L -0.3987603305785125,0.23586341763475496 L -0.41131007040097955,0.19664009328348725 L -0.4214110805019896,0.1558316275303205 L -0.42906336088154273,0.11378075365134054 L -0.4342669115396389,0.07083020492263467 L -0.43702173247627807,0.027322714620288277 L -0.43732782369146017,-0.01639898397961173 L -0.43518518518518534,-0.05999215760097932 L -0.43059381695745347,-0.10311407296772875 L -0.4235537190082646,-0.14542199680377288 L -0.4140648913376187,-0.18657319583302628 L -0.40212733394551603,-0.2262249367794019 L -0.38774104683195604,-0.2640344863668143 L -0.3709060299969393,-0.29965911131917633 L -0.3516222834404656,-0.33275607836040216 L -0.32988980716253463,-0.3629826542144059 L -0.3057086011631469,-0.38999610560510056 L -0.2790786654423019,-0.4134536992564007 L -0.2500000000000003,-0.4330127018922192
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real 0m0.697s
user 0m0.720s
sys 0m0.108s図形的には梅干しありのおにぎり🍙スケルトンですね。
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いろいろパラメータ調節してみると面白いかもしれません。
最近では、Twitterでモックアップ動画を公開しているので、こちらもよかったら、覗いてみてください。
最後に、Udemyでコースを公開しました。
良かったら覗いてみてください。
また、コースの内容紹介記事は以下になります。
簡単ですが、以上です。
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