ag-charts-community
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Advanced Charting / Charts supporting Javascript / Typescript / React / Angular / Vue
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JavaScript
"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
// @ts-ignore Suppress tsc error: Property 'sign' does not exist on type 'Math'
const sign = Math.sign ? Math.sign : x => {
x = +x;
if (x === 0 || isNaN(x)) {
return x;
}
return x > 0 ? 1 : -1;
};
/**
* Finds the roots of a parametric linear equation in `t`,
* where `t` lies in the interval of `[0,1]`.
*/
function linearRoot(a, b) {
const t = -b / a;
return (a !== 0 && t >= 0 && t <= 1) ? [t] : [];
}
exports.linearRoot = linearRoot;
/**
* Finds the roots of a parametric quadratic equation in `t`,
* where `t` lies in the interval of `[0,1]`.
*/
function quadraticRoots(a, b, c) {
if (a === 0) {
return linearRoot(b, c);
}
const D = b * b - 4 * a * c; // The polynomial's discriminant.
const roots = [];
if (D === 0) { // A single real root.
const t = -b / (2 * a);
if (t >= 0 && t <= 1) {
roots.push(t);
}
}
else if (D > 0) { // A pair of distinct real roots.
const rD = Math.sqrt(D);
const t1 = (-b - rD) / (2 * a);
const t2 = (-b + rD) / (2 * a);
if (t1 >= 0 && t1 <= 1) {
roots.push(t1);
}
if (t2 >= 0 && t2 <= 1) {
roots.push(t2);
}
}
// else -> Complex roots.
return roots;
}
exports.quadraticRoots = quadraticRoots;
/**
* Finds the roots of a parametric cubic equation in `t`,
* where `t` lies in the interval of `[0,1]`.
* Returns an array of parametric intersection locations along the cubic,
* excluding out-of-bounds intersections (before or after the end point
* or in the imaginary plane).
* An adaptation of http://www.particleincell.com/blog/2013/cubic-line-intersection/
*/
function cubicRoots(a, b, c, d) {
if (a === 0) {
return quadraticRoots(b, c, d);
}
const A = b / a;
const B = c / a;
const C = d / a;
const Q = (3 * B - A * A) / 9;
const R = (9 * A * B - 27 * C - 2 * A * A * A) / 54;
const D = Q * Q * Q + R * R; // The polynomial's discriminant.
const third = 1 / 3;
const roots = [];
if (D >= 0) { // Complex or duplicate roots.
const rD = Math.sqrt(D);
const S = sign(R + rD) * Math.pow(Math.abs(R + rD), third);
const T = sign(R - rD) * Math.pow(Math.abs(R - rD), third);
const Im = Math.abs(Math.sqrt(3) * (S - T) / 2); // Complex part of the root pair.
const t = -third * A + (S + T); // A real root.
if (t >= 0 && t <= 1) {
roots.push(t);
}
if (Im === 0) {
const t = -third * A - (S + T) / 2; // The real part of a complex root.
if (t >= 0 && t <= 1) {
roots.push(t);
}
}
}
else { // Distinct real roots.
const theta = Math.acos(R / Math.sqrt(-Q * Q * Q));
const thirdA = third * A;
const twoSqrtQ = 2 * Math.sqrt(-Q);
const t1 = twoSqrtQ * Math.cos(third * theta) - thirdA;
const t2 = twoSqrtQ * Math.cos(third * (theta + 2 * Math.PI)) - thirdA;
const t3 = twoSqrtQ * Math.cos(third * (theta + 4 * Math.PI)) - thirdA;
if (t1 >= 0 && t1 <= 1) {
roots.push(t1);
}
if (t2 >= 0 && t2 <= 1) {
roots.push(t2);
}
if (t3 >= 0 && t3 <= 1) {
roots.push(t3);
}
}
return roots;
}
exports.cubicRoots = cubicRoots;
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