上面是使用javascript实现的互动曲线，核心代码如下
class QuadBezierLine {
constructor(_p0, _p1, _p2, _step, _uniformSpeed) {
this.step=_step;
this.points=[];
this.uniformSpeed=_uniformSpeed;
this.updatePoints(_p0, _p1, _p2);
}
//Speed(t_) = Sqrt[A*t*t+B*t+C]
speed(t) {
return Math.sqrt(this.A * t * t + this.B * t + this.C);
}
//Length(t) = Integrate[Speed[t], t]
//Length(t_)=((2*Sqrt[A]*(2*A*t*Sqrt[C+t*(B+A*t)]+B*(Sqrt[C + t*(B + A*t)]-Sqrt[C])) +
// (B^2-4*A*C)(Log[B+2*Sqrt[A]*Sqrt[C]]-Log[B+2*A*t+2*Sqrt[A]*Sqrt[C+t*(B+A*t)]]))/
// (8* A^(3/2)));
length(t) {
let temp1 = Math.sqrt(this.C + t * (this.B + this.A * t));
let temp2 = (2 * this.A * t * temp1 + this.B * (temp1 - Math.sqrt(this.C)));
let temp3 = Math.log(this.B + 2 * Math.sqrt(this.A) * Math.sqrt(this.C));
let temp4 = Math.log(this.B + 2 * this.A * t + 2 * Math.sqrt(this.A) * temp1);
let temp5 = 2 * Math.sqrt(this.A) * temp2;
let temp6 = (this.B * this.B - 4 * this.A * this.C) * (temp3 - temp4);
return (temp5 + temp6) / (8 * Math.pow(this.A, 1.5));
}
//X(n+1) = Xn - F(Xn)/F'(Xn)
invertLength(t, len) {
let t1 = t, t2;
do {
t2 = t1 - (this.length(t1) - len) / this.speed(t1);
if (Math.abs(t1 - t2) < 0.000001)
break;
t1 = t2;
} while (true);
return t2;
}
updatePoints(_p0, _p1, _p2) {
this.p0=_p0;
this.p1=_p1;
this.p2=_p2;
let ax = this.p0.x - 2 * this.p1.x + this.p2.x;
let ay = this.p0.y - 2 * this.p1.y + this.p2.y;
let bx = 2 * this.p1.x - 2 * this.p0.x;
let by = 2 * this.p1.y - 2 * this.p0.y;
this.A = 4 * (ax * ax + ay *ay);
this.B = 4 * (ax * bx + ay *by);
this.C = bx * bx + by * by;
this.points.length = 0;
let totalLength = this.length(1);
for (let index = 1; index < this.step; index++) {
let t = index / this.step;
if(this.uniformSpeed) {
//根据 L 函数的反函数，求得 l 对应的 t 值
t = this.invertLength(t, totalLength*t);
}
let x = (1-t)*(1-t)*this.p0.x+2*(1-t)*t*this.p1.x+t*t*this.p2.x;
let y = (1-t)*(1-t)*this.p0.y+2*(1-t)*t*this.p1.y+t*t*this.p2.y;
this.points.push({x:x, y:y});
}
}
draw() {
this.points.forEach(pt => {
fill('green');
ellipse(pt.x, pt.y, 5, 5);
});
}
}