@ionic/core
Version:
Base components for Ionic
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JavaScript
/*!
* (C) Ionic http://ionicframework.com - MIT License
*/
/**
* Based on:
* https://stackoverflow.com/questions/7348009/y-coordinate-for-a-given-x-cubic-bezier
* https://math.stackexchange.com/questions/26846/is-there-an-explicit-form-for-cubic-b%C3%A9zier-curves
*/
/**
* EXPERIMENTAL
* Given a cubic-bezier curve, get the x value (time) given
* the y value (progression).
* Ex: cubic-bezier(0.32, 0.72, 0, 1);
* P0: (0, 0)
* P1: (0.32, 0.72)
* P2: (0, 1)
* P3: (1, 1)
*
* If you give a cubic bezier curve that never reaches the
* provided progression, this function will return an empty array.
*/
const getTimeGivenProgression = (p0, p1, p2, p3, progression) => {
return solveCubicBezier(p0[1], p1[1], p2[1], p3[1], progression).map((tValue) => {
return solveCubicParametricEquation(p0[0], p1[0], p2[0], p3[0], tValue);
});
};
/**
* Solve a cubic equation in one dimension (time)
*/
const solveCubicParametricEquation = (p0, p1, p2, p3, t) => {
const partA = 3 * p1 * Math.pow(t - 1, 2);
const partB = -3 * p2 * t + 3 * p2 + p3 * t;
const partC = p0 * Math.pow(t - 1, 3);
return t * (partA + t * partB) - partC;
};
/**
* Find the `t` value for a cubic bezier using Cardano's formula
*/
const solveCubicBezier = (p0, p1, p2, p3, refPoint) => {
p0 -= refPoint;
p1 -= refPoint;
p2 -= refPoint;
p3 -= refPoint;
const roots = solveCubicEquation(p3 - 3 * p2 + 3 * p1 - p0, 3 * p2 - 6 * p1 + 3 * p0, 3 * p1 - 3 * p0, p0);
return roots.filter((root) => root >= 0 && root <= 1);
};
const solveQuadraticEquation = (a, b, c) => {
const discriminant = b * b - 4 * a * c;
if (discriminant < 0) {
return [];
}
else {
return [(-b + Math.sqrt(discriminant)) / (2 * a), (-b - Math.sqrt(discriminant)) / (2 * a)];
}
};
const solveCubicEquation = (a, b, c, d) => {
if (a === 0) {
return solveQuadraticEquation(b, c, d);
}
b /= a;
c /= a;
d /= a;
const p = (3 * c - b * b) / 3;
const q = (2 * b * b * b - 9 * b * c + 27 * d) / 27;
if (p === 0) {
return [Math.pow(-q, 1 / 3)];
}
else if (q === 0) {
return [Math.sqrt(-p), -Math.sqrt(-p)];
}
const discriminant = Math.pow(q / 2, 2) + Math.pow(p / 3, 3);
if (discriminant === 0) {
return [Math.pow(q / 2, 1 / 2) - b / 3];
}
else if (discriminant > 0) {
return [
Math.pow(-(q / 2) + Math.sqrt(discriminant), 1 / 3) - Math.pow(q / 2 + Math.sqrt(discriminant), 1 / 3) - b / 3,
];
}
const r = Math.sqrt(Math.pow(-(p / 3), 3));
const phi = Math.acos(-(q / (2 * Math.sqrt(Math.pow(-(p / 3), 3)))));
const s = 2 * Math.pow(r, 1 / 3);
return [
s * Math.cos(phi / 3) - b / 3,
s * Math.cos((phi + 2 * Math.PI) / 3) - b / 3,
s * Math.cos((phi + 4 * Math.PI) / 3) - b / 3,
];
};
export { getTimeGivenProgression as g };