transformation-matrix

Javascript isomorphic 2D affine transformations written in ES6 syntax. Manipulate transformation matrices with this totally tested library!

Transformations, i.e. linear invertible automorphisms, are used to map a picture into another one with different size, position and orientation. Given a basis, transformations are represented by means of squared invertible matrices, called transformation matrices. A geometric transformation is defined as a one-to-one mapping of a point space to itself, which preservers some geometric relations of figures. - Geometric Programming for Computer Aided Design

This library allows us to:

generate transformation matrices for the following operations: translation, rotation, scale, shear, skew
merge multiple transformation matrices in a single matrix that is the composition of multiple matrices
work with strings in both directions: parse, render
apply a transformation matrix to point(s)

Usage example (ES6)

import {scale, rotate, translate, compose, applyToPoint} from 'transformation-matrix';
let {scale, rotate, translate, compose, applyToPoint} = window.TransformationMatrix;
let {scale, rotate, translate, compose, applyToPoint} = require('transformation-matrix')

let matrix = compose(
  translate(40,40),
  rotate(Math.PI/2),
  scale(2, 4)
);

applyToPoint(matrix, {x: 42, y: 42});
// { x: -128, y: 124.00000000000001 }

applyToPoint(matrix, [16, 24]);
//  [ -56, 72 ]

Setup

npm install transformation-matrix
# or
yarn add transformation-matrix

<script src="https://unpkg.com/transformation-matrix@1"></script>

Data Model

A Transformation Matrix is defined as an Object with 6 keys: a, b, c, d, e and f.

const matrix = { a: 1, c: 0, e: 0,
                 b: 0, d: 1, f: 0 }

A Point can be defined in two different ways:

as Object, with inside two keys: x and y

const point = { x: 24, y: 42 }

as Array, with two items in the form [x, y]

const point = [ 24, 42 ]

Live Demo

available at http://chrvadala.github.io/transformation-matrix/

Reference

Functions

applyToPoint(matrix, point) ⇒ Object | Array: Calculate a point transformed with an affine matrix
applyToPoints(matrix, points) ⇒ array: Calculate an array of points transformed with an affine matrix
fromObject(object) ⇒ Object: Extract an affine matrix from an object that contains a,b,c,d,e,f keys Each value could be a float or a string that contains a float
fromString(string) ⇒ Object: Parse a string matrix formatted as matrix(a,b,c,d,e,f)
fromTransformAttribute(transformString) ⇒ Object: Parser for SVG Trasform Attribute http://www.w3.org/TR/SVG/coords.html#TransformAttribute
Warning: This should be considered BETA until it is released a stable version of pegjs.
fromTriangles(t1, t2) ⇒ Object: Returns a matrix that transforms a triangle t1 into another triangle t2, or throws an exception if it is impossible.
identity() ⇒ Object: Identity matrix
inverse(matrix) ⇒ Object: Calculate a matrix that is the inverse of the provided matrix
isAffineMatrix(object) ⇒ boolean: Check if the object contain an affine matrix
rotate(angle, [cx], [cy]) ⇒ Object: Calculate a rotation matrix
rotateDEG(angle, [cx], [cy]) ⇒ Object: Calculate a rotation matrix with a DEG angle
scale(sx, [sy]) ⇒ Object: Calculate a scaling matrix
shear(shx, shy) ⇒ Object: Calculate a shear matrix
skew(ax, ay) ⇒ Object: Calculate a skew matrix
skewDEG(ax, ay) ⇒ Object: Calculate a skew matrix using DEG angles
smoothMatrix(m, [precision]) ⇒ Object: Rounds all elements of the given matrix using the given precision
toCSS(matrix) ⇒ string: Serialize the matrix to a string that can be used with CSS or SVG
toSVG(matrix) ⇒ string: Serialize the matrix to a string that can be used with CSS or SVG
toString(matrix) ⇒ string: Serialize the matrix to a string that can be used with CSS or SVG
transform(...matrices) ⇒ Object: Merge multiple matrices into one
compose(...matrices) ⇒ Object: Merge multiple matrices into one (alias of transform)
translate(tx, [ty]) ⇒ Object: Calculate a translate matrix

Changelog

0.0 - Preview version
1.0 - First public version
1.1 - Splits lib into different files
1.2 - Adds shear operation
1.3 - Adds umd support
1.4 - Adds typescript definitions
1.5 - Upgrades deps
1.6 - Adds optional parameter support on translate(tx), scale(sx), rotate(angle, cx, cy)
1.7 - Upgrades deps
1.8 - Fixes #12, Adds fromTransformAttribute, Discontinues node 4 support
1.9 - Adds skew(ax, ay), Upgrades deps, Improves fromTransformAttribute
1.10- Updates typescript definitions #15
1.11- Upgrades deps
1.12- Migrates tests on Jest, Integrates standard.js, Upgrades deps
1.13- Adds compose function, Upgrades deps, Exposes skew operation #37
1.14- Adds support for points defined as Array in the form [x, y] #38
1.15- Adds fromTriangle and smoothMatrix functions #41

Some projects using transformation-matrix

Contributors

chrvadala (author)
forabi
nidu (PEG.js descriptor)
aubergene
SophiaLi1

API

applyToPoint(matrix, point) ⇒ `Object` | `Array`

Calculate a point transformed with an affine matrix

Kind: global function
Returns: Object | Array - Point

Param	Description
matrix	Affine matrix
point	Point

applyToPoints(matrix, points) ⇒ `array`

Calculate an array of points transformed with an affine matrix

Kind: global function
Returns: array - Array of points

Param	Description
matrix	Affine matrix
points	Array of points

fromObject(object) ⇒ `Object`

Extract an affine matrix from an object that contains a,b,c,d,e,f keys Each value could be a float or a string that contains a float

Kind: global function
Returns: Object - }

Param
object

fromString(string) ⇒ `Object`

Parse a string matrix formatted as matrix(a,b,c,d,e,f)

Kind: global function
Returns: Object - Affine matrix

Param	Description
string	String with a matrix

fromTransformAttribute(transformString) ⇒ `Object`

Parser for SVG Trasform Attribute http://www.w3.org/TR/SVG/coords.html#TransformAttribute
Warning: This should be considered BETA until it is released a stable version of pegjs.

Kind: global function
Returns: Object - Parsed matrices

Param	Description
transformString	string

fromTriangles(t1, t2) ⇒ `Object`

Returns a matrix that transforms a triangle t1 into another triangle t2, or throws an exception if it is impossible.

Kind: global function
Returns: Object - Affine matrix which transforms t1 to t2
Throws:

Exception if the matrix becomes not invertible

Param	Type	Description
t1	`Array.<{x: number, y: number}>` \| `Array.<Array.<number>>`	an array of points containing the three points for the first triangle
t2	`Array.<{x: number, y: number}>` \| `Array.<Array.<number>>`	an array of points containing the three points for the second triangle

identity() ⇒ `Object`

Identity matrix

Kind: global function
Returns: Object - Affine matrix

inverse(matrix) ⇒ `Object`

Calculate a matrix that is the inverse of the provided matrix

Kind: global function
Returns: Object - Affine matrix

Param	Description
matrix	Affine matrix

isAffineMatrix(object) ⇒ `boolean`

Check if the object contain an affine matrix

Kind: global function

Param
object

rotate(angle, [cx], [cy]) ⇒ `Object`

Calculate a rotation matrix

Kind: global function
Returns: Object - Affine matrix *

Param	Description
angle	Angle in radians
[cx]	If (cx,cy) are supplied the rotate is about this point
[cy]	If (cx,cy) are supplied the rotate is about this point

rotateDEG(angle, [cx], [cy]) ⇒ `Object`

Calculate a rotation matrix with a DEG angle

Kind: global function
Returns: Object - Affine matrix

Param	Description
angle	Angle in degree
[cx]	If (cx,cy) are supplied the rotate is about this point
[cy]	If (cx,cy) are supplied the rotate is about this point

scale(sx, [sy]) ⇒ `Object`

Calculate a scaling matrix

Kind: global function
Returns: Object - Affine matrix

Param	Default	Description
sx		Scaling on axis x
[sy]	`sx`	Scaling on axis y (default sx)

shear(shx, shy) ⇒ `Object`

Calculate a shear matrix

Kind: global function
Returns: Object - Affine matrix

Param	Description
shx	Shear on axis x
shy	Shear on axis y

skew(ax, ay) ⇒ `Object`

Calculate a skew matrix

Kind: global function
Returns: Object - Affine matrix

Param	Description
ax	Skew on axis x
ay	Skew on axis y

skewDEG(ax, ay) ⇒ `Object`

Calculate a skew matrix using DEG angles

Kind: global function
Returns: Object - Affine matrix

Param	Description
ax	Skew on axis x
ay	Skew on axis y

smoothMatrix(m, [precision]) ⇒ `Object`

Rounds all elements of the given matrix using the given precision

Kind: global function
Returns: Object - the rounded matrix

Param	Type	Description
m	`Object`	a matrix to round
[precision]		a precision to use for Math.round. Defaults to 10000000000 (meaning which rounds to the 10th digit after the comma).

toCSS(matrix) ⇒ `string`

Serialize the matrix to a string that can be used with CSS or SVG

Kind: global function
Returns: string - String that contains a matrix formatted as matrix(a,b,c,d,e,f)

Param	Description
matrix	Affine matrix

toSVG(matrix) ⇒ `string`

Serialize the matrix to a string that can be used with CSS or SVG

Kind: global function
Returns: string - String that contains a matrix formatted as matrix(a,b,c,d,e,f)

Param	Description
matrix	Affine matrix

toString(matrix) ⇒ `string`

Serialize the matrix to a string that can be used with CSS or SVG

Kind: global function
Returns: string - String that contains a matrix formatted as matrix(a,b,c,d,e,f)

Param	Description
matrix	Affine matrix

transform(...matrices) ⇒ `Object`

Merge multiple matrices into one

Kind: global function
Returns: Object - Affine matrix

Param	Type	Description
...matrices	`object`	list of matrices

compose(...matrices) ⇒ `Object`

Merge multiple matrices into one (alias of transform)

Kind: global function
Returns: Object - Affine matrix

Param	Type	Description
...matrices	`object`	list of matrices

translate(tx, [ty]) ⇒ `Object`

Calculate a translate matrix

Kind: global function
Returns: Object - Affine matrix

Param	Default	Description
tx		Translation on axis x
[ty]	`0`	Translation on axis y

Name		Name	Last commit message	Last commit date
Latest commit History 168 Commits
src		src
test		test
.babelrc		.babelrc
.editorconfig		.editorconfig
.gitignore		.gitignore
.travis.yml		.travis.yml
LICENSE		LICENSE
README.md		README.md
README.template.hbs		README.template.hbs
disclaimer.hbs		disclaimer.hbs
example.js		example.js
index.html		index.html
package.json		package.json
transformation-matrix.d.ts		transformation-matrix.d.ts
webpack-umd.config.js		webpack-umd.config.js
yarn.lock		yarn.lock

License

Shuhei-Tsunoda/transformation-matrix

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transformation-matrix

Usage example (ES6)

Setup

Data Model

Live Demo

Reference

Functions

Changelog

Some projects using transformation-matrix

Contributors

API

applyToPoint(matrix, point) ⇒ Object | Array

applyToPoints(matrix, points) ⇒ array

fromObject(object) ⇒ Object

fromString(string) ⇒ Object

fromTransformAttribute(transformString) ⇒ Object

fromTriangles(t1, t2) ⇒ Object

identity() ⇒ Object

inverse(matrix) ⇒ Object

isAffineMatrix(object) ⇒ boolean

rotate(angle, [cx], [cy]) ⇒ Object

rotateDEG(angle, [cx], [cy]) ⇒ Object

scale(sx, [sy]) ⇒ Object

shear(shx, shy) ⇒ Object

skew(ax, ay) ⇒ Object

skewDEG(ax, ay) ⇒ Object

smoothMatrix(m, [precision]) ⇒ Object

toCSS(matrix) ⇒ string

toSVG(matrix) ⇒ string

toString(matrix) ⇒ string

transform(...matrices) ⇒ Object

compose(...matrices) ⇒ Object

translate(tx, [ty]) ⇒ Object

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applyToPoint(matrix, point) ⇒ `Object` | `Array`

applyToPoints(matrix, points) ⇒ `array`

fromObject(object) ⇒ `Object`

fromString(string) ⇒ `Object`

fromTransformAttribute(transformString) ⇒ `Object`

fromTriangles(t1, t2) ⇒ `Object`

identity() ⇒ `Object`

inverse(matrix) ⇒ `Object`

isAffineMatrix(object) ⇒ `boolean`

rotate(angle, [cx], [cy]) ⇒ `Object`

rotateDEG(angle, [cx], [cy]) ⇒ `Object`

scale(sx, [sy]) ⇒ `Object`

shear(shx, shy) ⇒ `Object`

skew(ax, ay) ⇒ `Object`

skewDEG(ax, ay) ⇒ `Object`

smoothMatrix(m, [precision]) ⇒ `Object`

toCSS(matrix) ⇒ `string`

toSVG(matrix) ⇒ `string`

toString(matrix) ⇒ `string`

transform(...matrices) ⇒ `Object`

compose(...matrices) ⇒ `Object`

translate(tx, [ty]) ⇒ `Object`

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