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Eisele","email":"robert@raw.org","url":"https://raw.org/"},"license":"MIT","homepage":"https://raw.org/book/algebra/quaternions/","keywords":["math","quaternion","number","vector","spherical interpolation","parser","slerp","quat","euler","geometry","3d","vector","matrix"],"repository":{"type":"git","url":"git+ssh://git@github.com/rawify/Quaternion.js.git"},"description":"The RAW rotation library using quaternions","maintainers":[{"name":"infusion","email":"robert@raw.org"}],"readme":"# Quaternion.js - ℍ in JavaScript\n\n[![NPM Package](https://img.shields.io/npm/v/quaternion.svg?style=flat)](https://npmjs.org/package/quaternion \"View this project on npm\")\n[![MIT license](http://img.shields.io/badge/license-MIT-brightgreen.svg)](http://opensource.org/licenses/MIT)\n\nQuaternion.js is a well tested JavaScript library for 3D rotations. Quaternions can be used everywhere, from the rotation calculation of your mobile phone over computer games to the rotation of satellites and all by avoiding the [Gimbal lock](https://en.wikipedia.org/wiki/Gimbal_lock). The library comes with examples to make you get started much quicker without worrying about the math behind. But if you care, have a look at the [Quaternion Introduction](https://raw.org/book/algebra/quaternions/).\n\n\n## Examples\n\n```js\nconst Quaternion = require('quaternion');\n\nconst q = new Quaternion(\"99.3+8i\");\nc.mul(1,2,3,4).div([3,4,1]).sub(7, [1, 2, 3]);\n```\n\n\n### HTML5 Device Orientation\n\nIn order to create a HTML element, which always rotates in 3D with your mobile device, all you need is the following snippet. Look at the examples folder for a complete version.\n\n```javascript\nconst deg = Math.PI / 180;\nwindow.addEventListener(\"deviceorientation\", function(ev) {\n\n // Update the rotation object\n const q = Quaternion.fromEulerLogical(ev.alpha * deg, ev.beta * deg, -ev.gamma * deg, 'ZXY');\n\n // Set the CSS style to the element you want to rotate\n elm.style.transform = q.toCSSTransform();\n\n}, true);\n```\n\n\n## Parser\n\n\nAny function (see below) as well as the constructor of the *Quaternion* class parses its input like this.\n\nYou can pass either Objects, Doubles or Strings.\n\n\n### Arguments\n\n\nCalling the constructor with no parameters will create a unit quaternion.\n\n```javascript\nnew Quaternion() // 1 + 0i + 0j + 0k\n```\n\nThe typical use case contains all quaternion parameters\n\n```javascript\nnew Quaternion(w, x, y, z)\n```\n\n### Objects\n\nQuaternion as angle and vector. **Note:** This is not equivalent to *Quaternion.fromAxisAngle()*!\n\n```javascript\nnew Quaternion(w, [x, y, z])\n```\n\nQuaternion as an object (it's ok to leave components out)\n```javascript\nnew Quaternion({w: w, x: x, y: y, z: z})\n```\n\nQuaternion out of a complex number, e.g. [Complex.js](https://github.com/rawify/Complex.js), with `y=z=0`.\n```javascript\nnew Quaternion({re: real, im: imaginary})\n```\n\nQuaternion out of a 4 elements vector\n```javascript\nnew Quaternion([w, x, y, z])\n```\nAugmented Quaternion out of a 3 elements vector\n```javascript\nnew Quaternion([x, y, z])\n```\n\n### Doubles\n\n```javascript\nnew Quaternion(55.4);\n```\n\n### Strings\n\n```javascript\nnew Quaternion('1 - 2i - 3j - 4k')\nnew Quaternion(\"123.45\");\nnew Quaternion(\"15+3i\");\nnew Quaternion(\"i\");\n```\n\n\n## Functions\n\n\nEvery stated parameter *n* in the following list of functions behaves in the same way as the constructor examples above\n\n**Note:** Calling a method like *add()* without parameters passes a quaternion with all elements zero, not one!\n\n### Quaternion add(n)\n\nAdds two quaternions Q1 and Q2\n\n### Quaternion sub(n)\n\nSubtracts a quaternions Q2 from Q1\n\n### Quaternion neg()\n\nCalculates the additive inverse, or simply it negates the quaternion\n\n### Quaternion norm()\n\nCalculates the length/modulus/magnitude or the norm of a quaternion\n\n### Quaternion normSq()\n\nCalculates the squared length/modulus/magnitude or the norm of a quaternion\n\n### Quaternion normalize()\n\nNormalizes the quaternion to have |Q| = 1 as long as the norm is not zero. Alternative names are the signum, unit or versor\n\n### Quaternion mul(n)\n\nCalculates the Hamilton product of two quaternions. Leaving out the imaginary part results in just scaling the quat.\n\n**Note:** This function is not commutative, i.e. order matters!\n\n### Quaternion scale(s)\n\nScales a quaternion by a scalar, faster than using multiplication\n\n### Quaternion dot()\n\nCalculates the dot product of two quaternions\n\n### Quaternion inverse()\n\nCalculates the inverse of a quat for non-normalized quats such that *Q-1 * Q = 1* and *Q * Q-1 = 1*\n\n### Quaternion div(n)\n\nMultiplies a quaternion with the inverse of a second quaternion\n\n### Quaternion conjugate()\n\nCalculates the conjugate of a quaternion. If the quaternion is normalized, the conjugate is the inverse of the quaternion - but faster.\n\n### Quaternion pow(n)\n\nCalculates the power of a quaternion raised to the quaternion n\n\n### Quaternion exp()\n\nCalculates the natural exponentiation of the quaternion\n\n### Quaternion log()\n\nCalculates the natural logarithm of the quaternion\n\n### double real()\n\nReturns the real `w` part of the quaternion\n\n### Quaternion imag()\n\nReturns the imaginary part `[x, y, z]` of the quaternion as a 3D vector / array\n\n### boolean equals(n)\n\nChecks if two quats are the same\n\n### boolean isFinite()\n\nChecks if all parts of a quaternion are finite\n\n### boolean isNaN()\n\nChecks if any of the parts of the quaternion is not a number\n\n### boolean isUnit()\n\nChecks if the quaternion is a unit quaternion of length 1.\n\n### String toString()\n\nGets the Quaternion as a well formatted string\n\n### Array toVector()\n\nGets the actual quaternion as a 4D vector / array\n\n### Array toMatrix(2D=false)\n\nCalculates the 3x3 rotation matrix for the current quat as a 9 element array or alternatively as a 2D array\n\n### Array toMatrix4(2D=false)\n\nCalculates the homogeneous 4x4 rotation matrix for the current quat as a 16 element array or alternatively as a 2D array\n\n### String toCSSTransform()\n\nDetermines the homogeneous rotation matrix string used for CSS 3D transforms\n\n### Array toAxisAngle()\n\nCalculates the axis and angle representation of the current quaternion\n\n### Array toEuler(order=\"ZXY\")\n\nCalculates the Euler angles represented by the current quat in the given Tait-Bryan order. The returned triplet order matches the `order` string.\n\n### Quaternion clone()\n\nClones the current object\n\n### Array rotateVector(v)\n\nRotates a 3 component vector, represented as an `[x,y,z]` array or an `{x,y,z}` object using the current quaternion in an [efficient manner](https://raw.org/proof/vector-rotation-using-quaternions/).\n\n### Quaternion slerp(q)(pct)\n\nReturns a function to spherically interpolate between two quaternions. Called with a percentage `[0, 1]`, the function returns the interpolated Quaternion.\n\n### Quaternion.fromAxisAngle(axis, angle)\n\nGets a quaternion by a rotation given as an axis and angle\n\n\n### Quaternion.fromMatrix(matrix)\n\nGets a quaternion given a rotation matrix, either as a 1x9 array or a 3x3 array.\n\n\n### Quaternion.fromEuler(ϕ, θ, ψ[, order=\"ZXY\"]) / Quaternion.fromEulerLogical(ψ, θ, ϕ[, order=\"YXZ\"])\n\nEuler angles are probably the reason to use quaternions. The definition is mostly sloppy and you can only decide how it was defined based on the matrix representation. A `ZXY` in one definition is the multiplication order read from right to left and in another the execution order from left to right. Quaternion.js provides two functions, `fromEulerLogical()`, where the angles and order are applied from left to right (logical application order) and `fromEuler()` which reverses the order of the argument list (technical multiplication order).\n\nSo for `fromEulerLogical(ϕ, θ, ψ, \"ZXY\")`, for example means first rotate around Z axis by ϕ then around X axis by θ and then around axis Y by ψ (`RotY(ψ)RotX(θ)RotZ(ϕ)`).\n\nThe order of `fromEuler()` can take the string value `ZXY (default), XYZ / RPY, YXZ, ZYX / YPR, YZX, XZY, ZYZ, ZXZ, YXY, YZY, XYX, XZX`.\n\n#### Relations\n\n- `fromEulerLogical(ϕ, θ, ψ, 'ZYX') = axisAngle([1, 0, 0], ψ) axisAngle([0, 1, 0], θ) axisAngle([0, 0, 1], ϕ)`\n- `fromEulerLogical(ϕ, θ, ψ, 'ZYX') = fromEuler(ψ, θ, ϕ, 'YXZ')`\n- Mathematica `RollPitchYawMatrix[{α, β, γ}] = fromEulerLogical(α, β, γ, 'ZYX')`\n- W3C devicemotion `fromEulerLogical(ev.alpha * DEG, ev.beta * DEG, -ev.gamma * DEG, 'ZXY')`\n- Three.js chose a different argument format:\n - `fromEuler(x, y, z, 'XYZ') = ThreeJSfromEuler(x, y, z, 'XYZ')`\n - `fromEuler(x, y, z, 'YXZ') = ThreeJSfromEuler(y, x, z, 'YXZ')`\n - `fromEuler(x, y, z, 'ZXY') = ThreeJSfromEuler(y, z, x, 'ZXY')`\n - `fromEuler(x, y, z, 'ZYX') = ThreeJSfromEuler(z, y, x, 'ZYX')`\n - `fromEuler(x, y, z, 'YZX') = ThreeJSfromEuler(z, x, y, 'YZX')`\n - `fromEuler(x, y, z, 'XZY') = ThreeJSfromEuler(x, z, y, 'XZY')`\n\n\n### Quaternion.fromVectors(u, v)\n\nCalculates the quaternion to rotate vector `u` onto vector `v`, represented as 3 element arrays, which can be done [elegantly using quaternions](https://raw.org/proof/quaternion-from-two-vectors/).\n\n### Quaternion.random()\n\nGets a spherical random number\n\n## Constants\n\n\n### Quaternion.ZERO\n\nA quaternion zero instance (additive identity)\n\n### Quaternion.ONE\n\nA quaternion one instance (multiplicative identity)\n\n### Quaternion.I\n\nAn imaginary number i instance\n\n### Quaternion.J\n\nAn imaginary number j instance\n\n### Quaternion.K\n\nAn imaginary number k instance\n\n\n\n\n## Installation\n\nYou can install `Quaternion.js` via npm:\n\n```bash\nnpm install quaternion\n```\n\nOr with yarn:\n\n```bash\nyarn add quaternion\n```\n\nAlternatively, download or clone the repository:\n\n```bash\ngit clone https://github.com/rawify/Quaternion.js\n```\n\n## Usage\n\nInclude the `quaternion.min.js` file in your project:\n\n```html\n\n\n```\n\nOr in a Node.js project:\n\n```javascript\nconst Quaternion = require('quaternion');\n```\n\nor\n\n```javascript\nimport Quaternion from 'quaternion';\n```\n\n\n## Coding Style\n\nLike all my libraries, Quaternion.js is written to minimize size after compression with Google Closure Compiler in advanced mode. The code style is optimized to maximize compressibility. If you extend the library, please preserve this style.\n\n## Building the library\n\nAfter cloning the Git repository run:\n\n```\nnpm install\nnpm run build\n```\n\n## Run a test\n\nTesting the source against the shipped test suite is as easy as\n\n```\nnpm run test\n```\n\n## Copyright and Licensing\n\nCopyright (c) 2025, [Robert Eisele](https://raw.org/)\nLicensed under the MIT license.\n","readmeFilename":"README.md","users":{"jpepe":true,"omnicode":true}}