fonteditor-core
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fonts (ttf, woff, woff2, eot, svg, otf) parse, write, transform, glyph adjust.
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JavaScript
/**
* @file 使用插值法获取椭圆弧度，以支持svg arc命令
* @author mengke01(kekee000@gmail.com)
*
* modify from:
* https://github.com/fontello/svgpath/blob/master/lib/a2c.js
* references:
* http://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
*/
import bezierCubic2Q2 from '../math/bezierCubic2Q2';
const TAU = Math.PI * 2;
function vectorAngle(ux, uy, vx, vy) {
// Calculate an angle between two vectors
const sign = (ux * vy - uy * vx < 0) ? -1 : 1;
const umag = Math.sqrt(ux * ux + uy * uy);
const vmag = Math.sqrt(ux * ux + uy * uy);
const dot = ux * vx + uy * vy;
let div = dot / (umag * vmag);
if (div > 1 || div < -1) {
// rounding errors, e.g. -1.0000000000000002 can screw up this
div = Math.max(div, -1);
div = Math.min(div, 1);
}
return sign * Math.acos(div);
}
function correctRadii(midx, midy, rx, ry) {
// Correction of out-of-range radii
rx = Math.abs(rx);
ry = Math.abs(ry);
const Λ = (midx * midx) / (rx * rx) + (midy * midy) / (ry * ry);
if (Λ > 1) {
rx *= Math.sqrt(Λ);
ry *= Math.sqrt(Λ);
}
return [rx, ry];
}
function getArcCenter(x1, y1, x2, y2, fa, fs, rx, ry, sin_φ, cos_φ) {
// Convert from endpoint to center parameterization,
// see http://www.w3.org/TR/SVG11/implnote.html#ArcImplementationNotes
// Step 1.
//
// Moving an ellipse so origin will be the middlepoint between our two
// points. After that, rotate it to line up ellipse axes with coordinate
// axes.
//
const x1p = cos_φ * (x1 - x2) / 2 + sin_φ * (y1 - y2) / 2;
const y1p = -sin_φ * (x1 - x2) / 2 + cos_φ * (y1 - y2) / 2;
const rx_sq = rx * rx;
const ry_sq = ry * ry;
const x1p_sq = x1p * x1p;
const y1p_sq = y1p * y1p;
// Step 2.
//
// Compute coordinates of the centre of this ellipse (cx', cy')
// in the new coordinate system.
//
let radicant = (rx_sq * ry_sq) - (rx_sq * y1p_sq) - (ry_sq * x1p_sq);
if (radicant < 0) {
// due to rounding errors it might be e.g. -1.3877787807814457e-17
radicant = 0;
}
radicant /= (rx_sq * y1p_sq) + (ry_sq * x1p_sq);
radicant = Math.sqrt(radicant) * (fa === fs ? -1 : 1);
const cxp = radicant * rx / ry * y1p;
const cyp = radicant * -ry / rx * x1p;
// Step 3.
//
// Transform back to get centre coordinates (cx, cy) in the original
// coordinate system.
//
const cx = cos_φ * cxp - sin_φ * cyp + (x1 + x2) / 2;
const cy = sin_φ * cxp + cos_φ * cyp + (y1 + y2) / 2;
// Step 4.
//
// Compute angles (θ1, Δθ).
//
const v1x = (x1p - cxp) / rx;
const v1y = (y1p - cyp) / ry;
const v2x = (-x1p - cxp) / rx;
const v2y = (-y1p - cyp) / ry;
const θ1 = vectorAngle(1, 0, v1x, v1y);
let Δθ = vectorAngle(v1x, v1y, v2x, v2y);
if (fs === 0 && Δθ > 0) {
Δθ -= TAU;
}
if (fs === 1 && Δθ < 0) {
Δθ += TAU;
}
return [cx, cy, θ1, Δθ];
}
function approximateUnitArc(θ1, Δθ) {
// Approximate one unit arc segment with bézier curves,
// see http://math.stackexchange.com/questions/873224/
// calculate-control-points-of-cubic-bezier-curve-approximating-a-part-of-a-circle
const α = 4 / 3 * Math.tan(Δθ / 4);
const x1 = Math.cos(θ1);
const y1 = Math.sin(θ1);
const x2 = Math.cos(θ1 + Δθ);
const y2 = Math.sin(θ1 + Δθ);
return [x1, y1, x1 - y1 * α, y1 + x1 * α, x2 + y2 * α, y2 - x2 * α, x2, y2];
}
function a2c(x1, y1, x2, y2, fa, fs, rx, ry, φ) {
const sin_φ = Math.sin(φ * TAU / 360);
const cos_φ = Math.cos(φ * TAU / 360);
// Make sure radii are valid
//
const x1p = cos_φ * (x1 - x2) / 2 + sin_φ * (y1 - y2) / 2;
const y1p = -sin_φ * (x1 - x2) / 2 + cos_φ * (y1 - y2) / 2;
if (x1p === 0 && y1p === 0) {
// we're asked to draw line to itself
return [];
}
if (rx === 0 || ry === 0) {
// one of the radii is zero
return [];
}
const radii = correctRadii(x1p, y1p, rx, ry);
rx = radii[0];
ry = radii[1];
// Get center parameters (cx, cy, θ1, Δθ)
//
const cc = getArcCenter(x1, y1, x2, y2, fa, fs, rx, ry, sin_φ, cos_φ);
const result = [];
let θ1 = cc[2];
let Δθ = cc[3];
// Split an arc to multiple segments, so each segment
// will be less than τ/4 (= 90°)
//
const segments = Math.max(Math.ceil(Math.abs(Δθ) / (TAU / 4)), 1);
Δθ /= segments;
for (let i = 0; i < segments; i++) {
result.push(approximateUnitArc(θ1, Δθ));
θ1 += Δθ;
}
// We have a bezier approximation of a unit circle,
// now need to transform back to the original ellipse
//
return result.map(curve => {
for (let i = 0; i < curve.length; i += 2) {
let x = curve[i + 0];
let y = curve[i + 1];
// scale
x *= rx;
y *= ry;
// rotate
const xp = cos_φ * x - sin_φ * y;
const yp = sin_φ * x + cos_φ * y;
// translate
curve[i + 0] = xp + cc[0];
curve[i + 1] = yp + cc[1];
}
return curve;
});
}
/**
* 获取椭圆弧度
*
* @param {number} rx 椭圆长半轴
* @param {number} ry 椭圆短半轴
* @param {number} angle 旋转角度
* @param {number} largeArc 是否大圆弧
* @param {number} sweep 是否延伸圆弧
* @param {Object} p0 分割点1
* @param {Object} p1 分割点2
* @return {Array} 分割后的路径
*/
export default function getArc(rx, ry, angle, largeArc, sweep, p0, p1) {
const result = a2c(p0.x, p0.y, p1.x, p1.y, largeArc, sweep, rx, ry, angle);
const path = [];
if (result.length) {
path.push({
x: result[0][0],
y: result[0][1],
onCurve: true
});
// 将三次曲线转换成二次曲线
result.forEach(c => {
const q2Array = bezierCubic2Q2({
x: c[0],
y: c[1]
}, {
x: c[2],
y: c[3]
}, {
x: c[4],
y: c[5]
}, {
x: c[6],
y: c[7]
});
q2Array[0][2].onCurve = true;
path.push(q2Array[0][1]);
path.push(q2Array[0][2]);
if (q2Array[1]) {
q2Array[1][2].onCurve = true;
path.push(q2Array[1][1]);
path.push(q2Array[1][2]);
}
});
}
return path;
}