From W3C SVG 1.1 spec: Conversion from endpoint to center parameterization
You can take a look at the detailed explanation.
This is a javascript implementation.
// svg : [A | a] (rx ry x-axis-rotation large-arc-flag sweep-flag x y)+
function radian( ux, uy, vx, vy ) {
var dot = ux * vx + uy * vy;
var mod = Math.sqrt( ( ux * ux + uy * uy ) * ( vx * vx + vy * vy ) );
var rad = Math.acos( dot / mod );
if( ux * vy - uy * vx < 0.0 ) {
rad = -rad;
}
return rad;
}
//conversion_from_endpoint_to_center_parameterization
//sample : svgArcToCenterParam(200,200,50,50,0,1,1,300,200)
// x1 y1 rx ry φ fA fS x2 y2
// phi, startAngle, deltaAngle, endAngle are radians not degrees.
// SVG use degrees, convert it to radians by:
// phi = degree * Math.PI / 180;
function svgArcToCenterParam(x1, y1, rx, ry, phi, fA, fS, x2, y2) {
var cx, cy, startAngle, deltaAngle, endAngle;
var PIx2 = Math.PI * 2.0;
if (rx < 0) {
rx = -rx;
}
if (ry < 0) {
ry = -ry;
}
if (rx == 0.0 || ry == 0.0) { // invalid arguments
throw Error('rx and ry can not be 0');
}
// SVG use degrees, if your input is degree from svg,
// you should convert degree to radian as following line.
// phi = phi * Math.PI / 180;
var s_phi = Math.sin(phi);
var c_phi = Math.cos(phi);
var hd_x = (x1 - x2) / 2.0; // half diff of x
var hd_y = (y1 - y2) / 2.0; // half diff of y
var hs_x = (x1 + x2) / 2.0; // half sum of x
var hs_y = (y1 + y2) / 2.0; // half sum of y
// F6.5.1
var x1_ = c_phi * hd_x + s_phi * hd_y;
var y1_ = c_phi * hd_y - s_phi * hd_x;
// F.6.6 Correction of out-of-range radii
// Step 3: Ensure radii are large enough
var lambda = (x1_ * x1_) / (rx * rx) + (y1_ * y1_) / (ry * ry);
if (lambda > 1) {
rx = rx * Math.sqrt(lambda);
ry = ry * Math.sqrt(lambda);
}
var rxry = rx * ry;
var rxy1_ = rx * y1_;
var ryx1_ = ry * x1_;
var sum_of_sq = rxy1_ * rxy1_ + ryx1_ * ryx1_; // sum of square
if (!sum_of_sq) {
throw Error('start point can not be same as end point');
}
var coe = Math.sqrt(Math.abs((rxry * rxry - sum_of_sq) / sum_of_sq));
if (fA == fS) { coe = -coe; }
// F6.5.2
var cx_ = coe * rxy1_ / ry;
var cy_ = -coe * ryx1_ / rx;
// F6.5.3
cx = c_phi * cx_ - s_phi * cy_ + hs_x;
cy = s_phi * cx_ + c_phi * cy_ + hs_y;
var xcr1 = (x1_ - cx_) / rx;
var xcr2 = (x1_ + cx_) / rx;
var ycr1 = (y1_ - cy_) / ry;
var ycr2 = (y1_ + cy_) / ry;
// F6.5.5
startAngle = radian(1.0, 0.0, xcr1, ycr1);
// F6.5.6
deltaAngle = radian(xcr1, ycr1, -xcr2, -ycr2);
while (deltaAngle > PIx2) { deltaAngle -= PIx2; }
while (deltaAngle < 0.0) { deltaAngle += PIx2; }
if (fS == false || fS == 0) { deltaAngle -= PIx2; }
endAngle = startAngle + deltaAngle;
while (endAngle > PIx2) { endAngle -= PIx2; }
while (endAngle < 0.0) { endAngle += PIx2; }
var outputObj = { /* cx, cy, startAngle, deltaAngle */
cx: cx,
cy: cy,
startAngle: startAngle,
deltaAngle: deltaAngle,
endAngle: endAngle,
clockwise: (fS == true || fS == 1)
}
return outputObj;
}
Usage example:
svg
<path d="M 0 100 A 60 60 0 0 0 100 0"/>
js
var result = svgArcToCenterParam(0, 100, 60, 60, 0, 0, 0, 100, 0);
console.log(result);
/* will output:
{
cx: 49.99999938964844,
cy: 49.99999938964844,
startAngle: 2.356194477985314,
deltaAngle: -3.141592627780225,
endAngle: 5.497787157384675,
clockwise: false
}
*/
