rotationMatrix.js (6541B)
1 import { isBigNumber } from '../../utils/is.js'; 2 import { factory } from '../../utils/factory.js'; 3 var name = 'rotationMatrix'; 4 var dependencies = ['typed', 'config', 'multiplyScalar', 'addScalar', 'unaryMinus', 'norm', 'matrix', 'BigNumber', 'DenseMatrix', 'SparseMatrix', 'cos', 'sin']; 5 export var createRotationMatrix = /* #__PURE__ */factory(name, dependencies, _ref => { 6 var { 7 typed, 8 config, 9 multiplyScalar, 10 addScalar, 11 unaryMinus, 12 norm, 13 BigNumber, 14 matrix, 15 DenseMatrix, 16 SparseMatrix, 17 cos, 18 sin 19 } = _ref; 20 21 /** 22 * Create a 2-dimensional counter-clockwise rotation matrix (2x2) for a given angle (expressed in radians). 23 * Create a 2-dimensional counter-clockwise rotation matrix (3x3) by a given angle (expressed in radians) around a given axis (1x3). 24 * 25 * Syntax: 26 * 27 * math.rotationMatrix(theta) 28 * math.rotationMatrix(theta, format) 29 * math.rotationMatrix(theta, [v]) 30 * math.rotationMatrix(theta, [v], format) 31 * 32 * Examples: 33 * 34 * math.rotationMatrix(math.pi / 2) // returns [[0, -1], [1, 0]] 35 * math.rotationMatrix(math.bignumber(1)) // returns [[bignumber(cos(1)), bignumber(-sin(1))], [bignumber(sin(1)), bignumber(cos(1))]] 36 * math.rotationMatrix(math.complex(1 + i)) // returns [[cos(1 + i), -sin(1 + i)], [sin(1 + i), cos(1 + i)]] 37 * math.rotationMatrix(math.unit('1rad')) // returns [[cos(1), -sin(1)], [sin(1), cos(1)]] 38 * 39 * math.rotationMatrix(math.pi / 2, [0, 1, 0]) // returns [[0, 0, 1], [0, 1, 0], [-1, 0, 0]] 40 * math.rotationMatrix(math.pi / 2, matrix([0, 1, 0])) // returns matrix([[0, 0, 1], [0, 1, 0], [-1, 0, 0]]) 41 * 42 * 43 * See also: 44 * 45 * matrix, cos, sin 46 * 47 * 48 * @param {number | BigNumber | Complex | Unit} theta Rotation angle 49 * @param {Array | Matrix} [v] Rotation axis 50 * @param {string} [format] Result Matrix storage format 51 * @return {Array | Matrix} Rotation matrix 52 */ 53 return typed(name, { 54 '': function _() { 55 return config.matrix === 'Matrix' ? matrix([]) : []; 56 }, 57 string: function string(format) { 58 return matrix(format); 59 }, 60 'number | BigNumber | Complex | Unit': function numberBigNumberComplexUnit(theta) { 61 return _rotationMatrix2x2(theta, config.matrix === 'Matrix' ? 'dense' : undefined); 62 }, 63 'number | BigNumber | Complex | Unit, string': function numberBigNumberComplexUnitString(theta, format) { 64 return _rotationMatrix2x2(theta, format); 65 }, 66 'number | BigNumber | Complex | Unit, Array': function numberBigNumberComplexUnitArray(theta, v) { 67 var matrixV = matrix(v); 68 69 _validateVector(matrixV); 70 71 return _rotationMatrix3x3(theta, matrixV, undefined); 72 }, 73 'number | BigNumber | Complex | Unit, Matrix': function numberBigNumberComplexUnitMatrix(theta, v) { 74 _validateVector(v); 75 76 var storageType = v.storage() || (config.matrix === 'Matrix' ? 'dense' : undefined); 77 return _rotationMatrix3x3(theta, v, storageType); 78 }, 79 'number | BigNumber | Complex | Unit, Array, string': function numberBigNumberComplexUnitArrayString(theta, v, format) { 80 var matrixV = matrix(v); 81 82 _validateVector(matrixV); 83 84 return _rotationMatrix3x3(theta, matrixV, format); 85 }, 86 'number | BigNumber | Complex | Unit, Matrix, string': function numberBigNumberComplexUnitMatrixString(theta, v, format) { 87 _validateVector(v); 88 89 return _rotationMatrix3x3(theta, v, format); 90 } 91 }); 92 /** 93 * Returns 2x2 matrix of 2D rotation of angle theta 94 * 95 * @param {number | BigNumber | Complex | Unit} theta The rotation angle 96 * @param {string} format The result Matrix storage format 97 * @returns {Matrix} 98 * @private 99 */ 100 101 function _rotationMatrix2x2(theta, format) { 102 var Big = isBigNumber(theta); 103 var minusOne = Big ? new BigNumber(-1) : -1; 104 var cosTheta = cos(theta); 105 var sinTheta = sin(theta); 106 var data = [[cosTheta, multiplyScalar(minusOne, sinTheta)], [sinTheta, cosTheta]]; 107 return _convertToFormat(data, format); 108 } 109 110 function _validateVector(v) { 111 var size = v.size(); 112 113 if (size.length < 1 || size[0] !== 3) { 114 throw new RangeError('Vector must be of dimensions 1x3'); 115 } 116 } 117 118 function _mul(array) { 119 return array.reduce((p, curr) => multiplyScalar(p, curr)); 120 } 121 122 function _convertToFormat(data, format) { 123 if (format) { 124 if (format === 'sparse') { 125 return new SparseMatrix(data); 126 } 127 128 if (format === 'dense') { 129 return new DenseMatrix(data); 130 } 131 132 throw new TypeError("Unknown matrix type \"".concat(format, "\"")); 133 } 134 135 return data; 136 } 137 /** 138 * Returns a 3x3 matrix of rotation of angle theta around vector v 139 * 140 * @param {number | BigNumber | Complex | Unit} theta The rotation angle 141 * @param {Matrix} v The rotation axis vector 142 * @param {string} format The storage format of the resulting matrix 143 * @returns {Matrix} 144 * @private 145 */ 146 147 148 function _rotationMatrix3x3(theta, v, format) { 149 var normV = norm(v); 150 151 if (normV === 0) { 152 throw new RangeError('Rotation around zero vector'); 153 } 154 155 var Big = isBigNumber(theta) ? BigNumber : null; 156 var one = Big ? new Big(1) : 1; 157 var minusOne = Big ? new Big(-1) : -1; 158 var vx = Big ? new Big(v.get([0]) / normV) : v.get([0]) / normV; 159 var vy = Big ? new Big(v.get([1]) / normV) : v.get([1]) / normV; 160 var vz = Big ? new Big(v.get([2]) / normV) : v.get([2]) / normV; 161 var c = cos(theta); 162 var oneMinusC = addScalar(one, unaryMinus(c)); 163 var s = sin(theta); 164 var r11 = addScalar(c, _mul([vx, vx, oneMinusC])); 165 var r12 = addScalar(_mul([vx, vy, oneMinusC]), _mul([minusOne, vz, s])); 166 var r13 = addScalar(_mul([vx, vz, oneMinusC]), _mul([vy, s])); 167 var r21 = addScalar(_mul([vx, vy, oneMinusC]), _mul([vz, s])); 168 var r22 = addScalar(c, _mul([vy, vy, oneMinusC])); 169 var r23 = addScalar(_mul([vy, vz, oneMinusC]), _mul([minusOne, vx, s])); 170 var r31 = addScalar(_mul([vx, vz, oneMinusC]), _mul([minusOne, vy, s])); 171 var r32 = addScalar(_mul([vy, vz, oneMinusC]), _mul([vx, s])); 172 var r33 = addScalar(c, _mul([vz, vz, oneMinusC])); 173 var data = [[r11, r12, r13], [r21, r22, r23], [r31, r32, r33]]; 174 return _convertToFormat(data, format); 175 } 176 });