import DeveloperError from './DeveloperError.js';
|
import CesiumMath from './Math.js';
|
|
/**
|
* Defines functions for 2nd order polynomial functions of one variable with only real coefficients.
|
*
|
* @exports QuadraticRealPolynomial
|
*/
|
var QuadraticRealPolynomial = {};
|
|
/**
|
* Provides the discriminant of the quadratic equation from the supplied coefficients.
|
*
|
* @param {Number} a The coefficient of the 2nd order monomial.
|
* @param {Number} b The coefficient of the 1st order monomial.
|
* @param {Number} c The coefficient of the 0th order monomial.
|
* @returns {Number} The value of the discriminant.
|
*/
|
QuadraticRealPolynomial.computeDiscriminant = function(a, b, c) {
|
//>>includeStart('debug', pragmas.debug);
|
if (typeof a !== 'number') {
|
throw new DeveloperError('a is a required number.');
|
}
|
if (typeof b !== 'number') {
|
throw new DeveloperError('b is a required number.');
|
}
|
if (typeof c !== 'number') {
|
throw new DeveloperError('c is a required number.');
|
}
|
//>>includeEnd('debug');
|
|
var discriminant = b * b - 4.0 * a * c;
|
return discriminant;
|
};
|
|
function addWithCancellationCheck(left, right, tolerance) {
|
var difference = left + right;
|
if ((CesiumMath.sign(left) !== CesiumMath.sign(right)) &&
|
Math.abs(difference / Math.max(Math.abs(left), Math.abs(right))) < tolerance) {
|
return 0.0;
|
}
|
|
return difference;
|
}
|
|
/**
|
* Provides the real valued roots of the quadratic polynomial with the provided coefficients.
|
*
|
* @param {Number} a The coefficient of the 2nd order monomial.
|
* @param {Number} b The coefficient of the 1st order monomial.
|
* @param {Number} c The coefficient of the 0th order monomial.
|
* @returns {Number[]} The real valued roots.
|
*/
|
QuadraticRealPolynomial.computeRealRoots = function(a, b, c) {
|
//>>includeStart('debug', pragmas.debug);
|
if (typeof a !== 'number') {
|
throw new DeveloperError('a is a required number.');
|
}
|
if (typeof b !== 'number') {
|
throw new DeveloperError('b is a required number.');
|
}
|
if (typeof c !== 'number') {
|
throw new DeveloperError('c is a required number.');
|
}
|
//>>includeEnd('debug');
|
|
var ratio;
|
if (a === 0.0) {
|
if (b === 0.0) {
|
// Constant function: c = 0.
|
return [];
|
}
|
|
// Linear function: b * x + c = 0.
|
return [-c / b];
|
} else if (b === 0.0) {
|
if (c === 0.0) {
|
// 2nd order monomial: a * x^2 = 0.
|
return [0.0, 0.0];
|
}
|
|
var cMagnitude = Math.abs(c);
|
var aMagnitude = Math.abs(a);
|
|
if ((cMagnitude < aMagnitude) && (cMagnitude / aMagnitude < CesiumMath.EPSILON14)) { // c ~= 0.0.
|
// 2nd order monomial: a * x^2 = 0.
|
return [0.0, 0.0];
|
} else if ((cMagnitude > aMagnitude) && (aMagnitude / cMagnitude < CesiumMath.EPSILON14)) { // a ~= 0.0.
|
// Constant function: c = 0.
|
return [];
|
}
|
|
// a * x^2 + c = 0
|
ratio = -c / a;
|
|
if (ratio < 0.0) {
|
// Both roots are complex.
|
return [];
|
}
|
|
// Both roots are real.
|
var root = Math.sqrt(ratio);
|
return [-root, root];
|
} else if (c === 0.0) {
|
// a * x^2 + b * x = 0
|
ratio = -b / a;
|
if (ratio < 0.0) {
|
return [ratio, 0.0];
|
}
|
|
return [0.0, ratio];
|
}
|
|
// a * x^2 + b * x + c = 0
|
var b2 = b * b;
|
var four_ac = 4.0 * a * c;
|
var radicand = addWithCancellationCheck(b2, -four_ac, CesiumMath.EPSILON14);
|
|
if (radicand < 0.0) {
|
// Both roots are complex.
|
return [];
|
}
|
|
var q = -0.5 * addWithCancellationCheck(b, CesiumMath.sign(b) * Math.sqrt(radicand), CesiumMath.EPSILON14);
|
if (b > 0.0) {
|
return [q / a, c / q];
|
}
|
|
return [c / q, q / a];
|
};
|
export default QuadraticRealPolynomial;
|
