svg-kit/lib/Path/CubicBezier.js

A SVG toolkit, with its own Vector Graphics structure, multiple renderers (svg text, DOM svg, canvas), and featuring Flowing Text.

/*
	SVG Kit

	Copyright (c) 2017 - 2024 Cédric Ronvel

	The MIT License (MIT)

	Permission is hereby granted, free of charge, to any person obtaining a copy
	of this software and associated documentation files (the "Software"), to deal
	in the Software without restriction, including without limitation the rights
	to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
	copies of the Software, and to permit persons to whom the Software is
	furnished to do so, subject to the following conditions:

	The above copyright notice and this permission notice shall be included in all
	copies or substantial portions of the Software.

	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
	AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
	LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
	OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
	SOFTWARE.
*/

"use strict" ;



/*
	Mostly derived from svg-path-properties by RogerVecianaAbzu:
	https://github.com/rveciana/svg-path-properties/blob/master/src/bezier.ts
*/



const Bezier = require( './Bezier.js' ) ;
const QuadraticBezier = require( './QuadraticBezier.js' ) ;
const BoundingBox = require( '../BoundingBox.js' ) ;
const { tValues , cValues , binomialCoefficients } = require( './bezier-values.json' ) ;



function CubicBezier( startPoint , startControl , endControl , endPoint ) {
	this.startPoint = startPoint ;
	this.startControl = startControl ;
	this.endControl = endControl ;
	this.endPoint = endPoint ;
	Bezier.call( this , startPoint , startControl , endControl , endPoint ) ;
}

module.exports = CubicBezier ;

CubicBezier.prototype = Object.create( Bezier.prototype ) ;
CubicBezier.prototype.constructor = CubicBezier ;



// The parametric formula for a given axis
function parametric( ps , t ) {
	const mt = 1 - t ;
	return ( mt * mt * mt * ps[0] ) + ( 3 * mt * mt * t * ps[1] ) + ( 3 * mt * t * t * ps[2] ) + ( t * t * t * ps[3] ) ;
}



CubicBezier.getPoint =
CubicBezier.prototype.getPoint = ( xs , ys , t ) => {
	return {
		x: parametric( xs , t ) ,
		y: parametric( ys , t )
	} ;
} ;



CubicBezier.getDerivative =
CubicBezier.prototype.getDerivative = ( xs , ys , t ) => {
	const derivative = QuadraticBezier.getPoint(
		[ 3 * ( xs[1] - xs[0] ) , 3 * ( xs[2] - xs[1] ) , 3 * ( xs[3] - xs[2] ) ] ,
		[ 3 * ( ys[1] - ys[0] ) , 3 * ( ys[2] - ys[1] ) , 3 * ( ys[3] - ys[2] ) ] ,
		t
	) ;
	return derivative ;
} ;



CubicBezier.getLength =
CubicBezier.prototype.getLength = ( xs , ys , t = 1 ) => {
	let z ;
	let sum ;
	let correctedT ;

	/*if (xs.length >= tValues.length) {
        throw new Error('too high n bezier');
      }*/

	const n = 20 ;

	z = t / 2 ;
	sum = 0 ;
	for ( let i = 0 ; i < n ; i ++ ) {
		correctedT = z * tValues[n][i] + z ;
		sum += cValues[n][i] * cubicIteration( xs , ys , correctedT ) ;
	}
	return z * sum ;
} ;



function cubicIteration( xs , ys , t ) {
	const xbase = getCurveDerivative( 1 , t , xs ) ;
	const ybase = getCurveDerivative( 1 , t , ys ) ;
	const combined = xbase * xbase + ybase * ybase ;
	return Math.sqrt( combined ) ;
}



// Compute the curve derivative (hodograph) at t.
function getCurveDerivative( derivative , t , vs ) {
	// the derivative of any 't'-less function is zero.
	const n = vs.length - 1 ;
	let _vs ;
	let value ;

	if ( n === 0 ) {
		return 0 ;
	}

	// direct values? compute!
	if ( derivative === 0 ) {
		value = 0 ;
		for ( let k = 0 ; k <= n ; k ++ ) {
			value +=
        binomialCoefficients[n][k] *
        Math.pow( 1 - t , n - k ) *
        Math.pow( t , k ) *
        vs[k] ;
		}
		return value ;
	}
	// Still some derivative? go down one order, then try
	// for the lower order curve's.
	_vs = new Array( n ) ;
	for ( let k = 0 ; k < n ; k ++ ) {
		_vs[k] = n * ( vs[k + 1] - vs[k] ) ;
	}

	return getCurveDerivative( derivative - 1 , t , _vs ) ;
}



// Derived from:For cubic bezier.
// https://stackoverflow.com/questions/24809978/calculating-the-bounding-box-of-cubic-bezier-curve
CubicBezier.getBoundingBox =
CubicBezier.prototype.getBoundingBox = function( xs , ys ) {
	let tExtrema = [] ,
		xExtrema = [ xs[0] , xs[3] ] ,
		yExtrema = [ ys[0] , ys[3] ] ;

	getTExtrema( xs , tExtrema ) ;
	getTExtrema( ys , tExtrema ) ;

	for ( let t of tExtrema ) {
		xExtrema.push( parametric( xs , t ) ) ;
		yExtrema.push( parametric( ys , t ) ) ;
	}

	return new BoundingBox(
		Math.min( ... xExtrema ) ,
		Math.min( ... yExtrema ) ,
		Math.max( ... xExtrema ) ,
		Math.max( ... yExtrema )
	) ;
} ;

/* eslint-disable camelcase */
function getTExtrema( ps , tExtrema ) {
	let b = 6 * ps[0] - 12 * ps[1] + 6 * ps[2] ,
		a = - 3 * ps[0] + 9 * ps[1] - 9 * ps[2] + 3 * ps[3] ,
		c = 3 * ps[1] - 3 * ps[0] ;

	if ( Math.abs( a ) < 1e-12 ) {
		if ( Math.abs( b ) < 1e-12 ) { return ; }
		let t = - c / b ;
		if ( 0 < t && t < 1 ) { tExtrema.push( t ) ; }
		return ;
	}

	let b2ac = b * b - 4 * c * a ;

	if ( b2ac < 0 ) {
		if ( Math.abs( b2ac ) < 1e-12 ) {
			let t = - b / ( 2 * a ) ;
			if ( 0 < t && t < 1 ) { tExtrema.push( t ) ; }
		}
		return ;
	}

	let sqrt_b2ac = Math.sqrt( b2ac ) ;
	let t1 = ( - b + sqrt_b2ac ) / ( 2 * a ) ;
	if ( 0 < t1 && t1 < 1 ) { tExtrema.push( t1 ) ; }

	let t2 = ( - b - sqrt_b2ac ) / ( 2 * a ) ;
	if ( 0 < t2 && t2 < 1 ) { tExtrema.push( t2 ) ; }
}