three
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JavaScript 3D library
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JavaScript
// Bezier Curves formulas obtained from: https://en.wikipedia.org/wiki/B%C3%A9zier_curve
/**
* Computes a point on a Catmull-Rom spline.
*
* @param {number} t - The interpolation factor.
* @param {number} p0 - The first control point.
* @param {number} p1 - The second control point.
* @param {number} p2 - The third control point.
* @param {number} p3 - The fourth control point.
* @return {number} The calculated point on a Catmull-Rom spline.
*/
function CatmullRom( t, p0, p1, p2, p3 ) {
const v0 = ( p2 - p0 ) * 0.5;
const v1 = ( p3 - p1 ) * 0.5;
const t2 = t * t;
const t3 = t * t2;
return ( 2 * p1 - 2 * p2 + v0 + v1 ) * t3 + ( - 3 * p1 + 3 * p2 - 2 * v0 - v1 ) * t2 + v0 * t + p1;
}
//
function QuadraticBezierP0( t, p ) {
const k = 1 - t;
return k * k * p;
}
function QuadraticBezierP1( t, p ) {
return 2 * ( 1 - t ) * t * p;
}
function QuadraticBezierP2( t, p ) {
return t * t * p;
}
/**
* Computes a point on a Quadratic Bezier curve.
*
* @param {number} t - The interpolation factor.
* @param {number} p0 - The first control point.
* @param {number} p1 - The second control point.
* @param {number} p2 - The third control point.
* @return {number} The calculated point on a Quadratic Bezier curve.
*/
function QuadraticBezier( t, p0, p1, p2 ) {
return QuadraticBezierP0( t, p0 ) + QuadraticBezierP1( t, p1 ) +
QuadraticBezierP2( t, p2 );
}
//
function CubicBezierP0( t, p ) {
const k = 1 - t;
return k * k * k * p;
}
function CubicBezierP1( t, p ) {
const k = 1 - t;
return 3 * k * k * t * p;
}
function CubicBezierP2( t, p ) {
return 3 * ( 1 - t ) * t * t * p;
}
function CubicBezierP3( t, p ) {
return t * t * t * p;
}
/**
* Computes a point on a Cubic Bezier curve.
*
* @param {number} t - The interpolation factor.
* @param {number} p0 - The first control point.
* @param {number} p1 - The second control point.
* @param {number} p2 - The third control point.
* @param {number} p3 - The fourth control point.
* @return {number} The calculated point on a Cubic Bezier curve.
*/
function CubicBezier( t, p0, p1, p2, p3 ) {
return CubicBezierP0( t, p0 ) + CubicBezierP1( t, p1 ) + CubicBezierP2( t, p2 ) +
CubicBezierP3( t, p3 );
}
export { CatmullRom, QuadraticBezier, CubicBezier };