Published
Edited
Mar 21, 2021
Importers
md`# Svg EllipticalArc`
/**
* svg Arc to canvas 2d
*
* canvas ellipse(x, y, radiusX, radiusY, rotation, startAngle, endAngle, anticlockwise)
* svg cmd A rx ry x-axis-rotation large-arc-flag sweep-flag x y
*
*/
/**
* https://svgwg.org/svg2-draft/implnote.html#ArcConversionEndpointToCenter
* @param {*} x1
* @param {*} y1
* @param {*} x2
* @param {*} y2
* @param {*} largeArcFlag large-arc-flag
* @param {*} sweepFlag sweep-flag
* @param {*} srx 椭圆x半径
* @param {*} sry 椭圆y半径
* @param {*} xAxisRotationDeg x-axis-rotation
*/
function conversionEndPointToCenterPointParameterization(x1, y1, x2, y2, largeArcFlag, sweepFlag, srx, sry, xAxisRotationDeg) {
const xAxisRotation = degToRad(xAxisRotationDeg);
const cosphi = Math.cos(xAxisRotation);
const sinphi = Math.sin(xAxisRotation);
const [x1p, y1p] = mat2DotVec2(
[cosphi, sinphi, -sinphi, cosphi],
[(x1 - x2) / 2, (y1 - y2) / 2]
);
const [rx, ry] = correctRadii(srx, sry, x1p, y1p);
const sign = largeArcFlag !== sweepFlag ? 1 : -1;
const n = pow(rx) * pow(ry) - pow(rx) * pow(y1p) - pow(ry) * pow(x1p);
const d = pow(rx) * pow(y1p) + pow(ry) * pow(x1p);
const [cxp, cyp] = vec2Scale(
[(rx * y1p) / ry, (-ry * x1p) / rx],
sign * Math.sqrt(Math.abs(n / d))
);
const [cx, cy] = vec2Add(
mat2DotVec2([cosphi, -sinphi, sinphi, cosphi], [cxp, cyp]),
[(x1 + x2) / 2, (y1 + y2) / 2]
);
const a = [(x1p - cxp) / rx, (y1p - cyp) / ry];
const b = [(-x1p - cxp) / rx, (-y1p - cyp) / ry];
const startAngle = vec2Angle([1, 0], a);
const deltaAngle0 = vec2Angle(a, b) % (2 * Math.PI);
const deltaAngle =
!sweepFlag && deltaAngle0 > 0
? deltaAngle0 - 2 * Math.PI
: sweepFlag && deltaAngle0 < 0
? deltaAngle0 + 2 * Math.PI
: deltaAngle0;
const endAngle = startAngle + deltaAngle;
return [
cx,
cy,
rx,
ry,
xAxisRotation,
startAngle,
endAngle,
// xAxisRotation,
deltaAngle < 0
]
// return {
// cx,
// cy,
// rx,
// ry,
// startAngle,
// endAngle,
// xAxisRotation,
// anticlockwise: deltaAngle < 0
// };
}
function mat2DotVec2([m00, m01, m10, m11], [vx, vy]) {
return [m00 * vx + m01 * vy, m10 * vx + m11 * vy];
}
function vec2Add([ux, uy], [vx, vy]) {
return [ux + vx, uy + vy];
}
function vec2Scale([a0, a1], scalar) {
return [a0 * scalar, a1 * scalar];
}
function vec2Mag([ux, uy]) {
return Math.sqrt(ux ** 2 + uy ** 2);
}
function vec2Angle(u, v) {
const [ux, uy] = u;
const [vx, vy] = v;
const sign = ux * vy - uy * vx >= 0 ? 1 : -1;
return sign * Math.acos(vec2Dot(u, v) / (vec2Mag(u) * vec2Mag(v)));
}
function vec2Dot([ux, uy], [vx, vy]) {
return ux * vx + uy * vy;
}
function correctRadii(signedRx, signedRy, x1p, y1p) {
const prx = Math.abs(signedRx);
const pry = Math.abs(signedRy);
const A = pow(x1p) / pow(prx) + pow(y1p) / pow(pry);
const rx = A > 1 ? Math.sqrt(A) * prx : prx;
const ry = A > 1 ? Math.sqrt(A) * pry : pry;
return [rx, ry];
}
function pow(n) {
return Math.pow(n, 2);
}
/**
* degree to Radian
* @param {*} deg
* @returns
*/
function degToRad(deg) {
return (deg * Math.PI) / 180;
}
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