# Matrix An affine transformation matrix performs a linear mapping from 2D coordinates to other 2D coordinates that preserves the “straightness” and “parallelness” of lines. Such a coordinate transformation can be represented by a 3 row by 3 column matrix with an implied last row of `[ 0 0 1 ]`. This matrix transforms source coordinates `(x, y)` into destination coordinates `(x',y')` by considering them to be a column vector and multiplying the coordinate vector by the matrix according to the following process: ``` [ x ] [ a c tx ] [ x ] [ a * x + c * y + tx ] [ y ] = [ b d ty ] [ y ] = [ b * x + d * y + ty ] [ 1 ] [ 0 0 1 ] [ 1 ] [ 1 ] ``` Note the locations of b and c. This class is optimized for speed and minimizes calculations based on its knowledge of the underlying matrix (as opposed to say simply performing matrix multiplication). ## Constructors * `Matrix()` Creates a 2D affine transformation matrix that describes the identity transformation. * Returns: * `Matrix` * `Matrix(a, b, c, d, tx, ty)` Creates a 2D affine transformation matrix. * Parameters: * `a:` `Number` — the a property of the transform * `b:` `Number` — the b property of the transform * `c:` `Number` — the c property of the transform * `d:` `Number` — the d property of the transform * `tx:` `Number` — the tx property of the transform * `ty:` `Number` — the ty property of the transform * Returns: * `Matrix` * `Matrix(values)` Creates a 2D affine transformation matrix. * Parameters: * `values:` Array of `Numbers` — the matrix values to initialize this matrix with * Returns: * `Matrix` * `Matrix(matrix)` Creates a 2D affine transformation matrix. * Parameters: * `matrix:` `Matrix` — the matrix to copy the values from * Returns: * `Matrix` ## Properties * `a` The value that affects the transformation along the x axis when scaling or rotating, positioned at (0, 0) in the transformation matrix. * Type: * `Number` * `b` The value that affects the transformation along the y axis when rotating or skewing, positioned at (1, 0) in the transformation matrix. * Type: * `Number` * `c` The value that affects the transformation along the x axis when rotating or skewing, positioned at (0, 1) in the transformation matrix. * Type: * `Number` * `d` The value that affects the transformation along the y axis when scaling or rotating, positioned at (1, 1) in the transformation matrix. * Type: * `Number` * `tx` The distance by which to translate along the x axis, positioned at (2, 0) in the transformation matrix. * Type: * `Number` * `ty` The distance by which to translate along the y axis, positioned at (2, 1) in the transformation matrix. * Type: * `Number` * `values` The matrix values as an array, in the same sequence as they are passed to `initialize(a, b, c, d, tx, ty)`. Read only. * Type: * Array of `Numbers` * `translation` The translation of the matrix as a vector. Read only. * Type: * `Point` * `scaling` The scaling values of the matrix, if it can be decomposed. Read only. * Type: * `Point` * See also: * `decompose`() * `rotation` The rotation angle of the matrix, if it can be decomposed. Read only. * Type: * `Number` * See also: * `decompose`() ## Methods * `set(...values)` Sets the matrix to the passed values. Note that any sequence of parameters that is supported by the various `Matrix`() constructors also work for calls of `set()`. * Parameters: * `values:` `any value` * Returns: * `Point` * `clone()` * Returns: * `Matrix` — a copy of this transform * `equals(matrix)` Checks whether the two matrices describe the same transformation. * Parameters: * `matrix:` `Matrix` — the matrix to compare this matrix to * Returns: * `Boolean` — `true` if the matrices are equal, `false` otherwise * `toString()` * Returns: * `String` — a string representation of this transform * `reset()` Resets the matrix by setting its values to the ones of the identity matrix that results in no transformation. * `apply([recursively])` Attempts to apply the matrix to the content of item that it belongs to, meaning its transformation is baked into the item’s content or children. * Parameters: * `recursively:` `Boolean` — controls whether to apply transformations recursively on children — optional, default: `true` * Returns: * `Boolean` — `true` if the matrix was applied, `false` otherwise * `translate(point)` Concatenates this matrix with a translate transformation. * Parameters: * `point:` `Point` — the vector to translate by * Returns: * `Matrix` — this affine transform * `translate(dx, dy)` Concatenates this matrix with a translate transformation. * Parameters: * `dx:` `Number` — the distance to translate in the x direction * `dy:` `Number` — the distance to translate in the y direction * Returns: * `Matrix` — this affine transform * `scale(scale[, center])` Concatenates this matrix with a scaling transformation. * Parameters: * `scale:` `Number` — the scaling factor * `center:` `Point` — the center for the scaling transformation — optional * Returns: * `Matrix` — this affine transform * `scale(hor, ver[, center])` Concatenates this matrix with a scaling transformation. * Parameters: * `hor:` `Number` — the horizontal scaling factor * `ver:` `Number` — the vertical scaling factor * `center:` `Point` — the center for the scaling transformation — optional * Returns: * `Matrix` — this affine transform * `rotate(angle, center)` Concatenates this matrix with a rotation transformation around an anchor point. * Parameters: * `angle:` `Number` — the angle of rotation measured in degrees * `center:` `Point` — the anchor point to rotate around * Returns: * `Matrix` — this affine transform * `rotate(angle, x, y)` Concatenates this matrix with a rotation transformation around an anchor point. * Parameters: * `angle:` `Number` — the angle of rotation measured in degrees * `x:` `Number` — the x coordinate of the anchor point * `y:` `Number` — the y coordinate of the anchor point * Returns: * `Matrix` — this affine transform * `shear(shear[, center])` Concatenates this matrix with a shear transformation. * Parameters: * `shear:` `Point` — the shear factor in x and y direction * `center:` `Point` — the center for the shear transformation — optional * Returns: * `Matrix` — this affine transform * `shear(hor, ver[, center])` Concatenates this matrix with a shear transformation. * Parameters: * `hor:` `Number` — the horizontal shear factor * `ver:` `Number` — the vertical shear factor * `center:` `Point` — the center for the shear transformation — optional * Returns: * `Matrix` — this affine transform * `skew(skew[, center])` Concatenates this matrix with a skew transformation. * Parameters: * `skew:` `Point` — the skew angles in x and y direction in degrees * `center:` `Point` — the center for the skew transformation — optional * Returns: * `Matrix` — this affine transform * `skew(hor, ver[, center])` Concatenates this matrix with a skew transformation. * Parameters: * `hor:` `Number` — the horizontal skew angle in degrees * `ver:` `Number` — the vertical skew angle in degrees * `center:` `Point` — the center for the skew transformation — optional * Returns: * `Matrix` — this affine transform * `append(matrix)` Appends the specified matrix to this matrix. This is the equivalent of multiplying `(this matrix) * (specified matrix)`. * Parameters: * `matrix:` `Matrix` — the matrix to append * Returns: * `Matrix` — this matrix, modified * `prepend(matrix)` Prepends the specified matrix to this matrix. This is the equivalent of multiplying `(specified matrix) * (this matrix)`. * Parameters: * `matrix:` `Matrix` — the matrix to prepend * Returns: * `Matrix` — this matrix, modified * `appended(matrix)` Returns a new matrix as the result of appending the specified matrix to this matrix. This is the equivalent of multiplying `(this matrix) * (specified matrix)`. * Parameters: * `matrix:` `Matrix` — the matrix to append * Returns: * `Matrix` — the newly created matrix * `prepended(matrix)` Returns a new matrix as the result of prepending the specified matrix to this matrix. This is the equivalent of multiplying `(specified matrix) * (this matrix)`. * Parameters: * `matrix:` `Matrix` — the matrix to prepend * Returns: * `Matrix` — the newly created matrix * `invert()` Inverts the matrix, causing it to perform the opposite transformation. If the matrix is not invertible (in which case `isSingular`() returns true), `null` is returned. * Returns: * `Matrix` — this matrix, or `null`, if the matrix is singular. * `inverted()` Creates a new matrix that is the inversion of this matrix, causing it to perform the opposite transformation. If the matrix is not invertible (in which case `isSingular`() returns true), `null` is returned. * Returns: * `Matrix` — this matrix, or `null`, if the matrix is singular. * `isIdentity()` * Returns: * `Boolean` — whether this matrix is the identity matrix * `isInvertible()` Checks whether the matrix is invertible. A matrix is not invertible if the determinant is 0 or any value is infinite or NaN. * Returns: * `Boolean` — whether the matrix is invertible * `isSingular()` Checks whether the matrix is singular or not. Singular matrices cannot be inverted. * Returns: * `Boolean` — whether the matrix is singular * `transform(point)` Transforms a point and returns the result. * Parameters: * `point:` `Point` — the point to be transformed * Returns: * `Point` — the transformed point * `transform(src, dst, count)` Transforms an array of coordinates by this matrix and stores the results into the destination array, which is also returned. * Parameters: * `src:` Array of `Numbers` — the array containing the source points as x, y value pairs * `dst:` Array of `Numbers` — the array into which to store the transformed point pairs * `count:` `Number` — the number of points to transform * Returns: * `Array of Numbers` — the dst array, containing the transformed coordinates * `inverseTransform(point)` Inverse transforms a point and returns the result. * Parameters: * `point:` `Point` — the point to be transformed * Returns: * `Point` * `decompose()` Decomposes the affine transformation described by this matrix into `scaling`, `rotation` and `skewing`, and returns an object with these properties. * Returns: * `Object` — the decomposed matrix * `applyToContext(ctx)` Applies this matrix to the specified Canvas Context. * Parameters: * `ctx:` `CanvasRenderingContext2D` --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. 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