class M33d

3x3 double precision floating point transformation matrix.

M33d()

Default constructor: initialize to identity

1 0 0

0 1 0

0 0 1

M33d(a: double)

Initialize to scalar constant

a a a

a a a

a a a

M33d(a: double, b: double, c: double, d: double, e: double, f: double, g: double, h: double, i: double)

Construct from given scalar values:

a b c

d e f

g h i

__getitem__(i: int) → V3d

Return the i-th row.

__eq__(o: M33d) → bool

Return True if both matrix are equal.

__neq__(o: M33d) → bool

Return True if both matrix are not equal.

__mul__(o: M33d) → M33d

Matrix-matrix multiplication

__mul__(a: double) → M33d

Component-wise multiplication

__truediv__(a: double) → M33d

Component-wise division

__add__(o: M33d) → M33d

Component-wise addition

__sub__(o: M33d) → M33d

Component-wise subtraction

__neg__() → M33d

Component-wise multiplication by -1

determinant() → double

Determinant

equalWithAbsError(m: M33d, e: double) → bool

Compare two matrices and test if they are “approximately equal”: @return True if the coefficients of this and m are the same with an absolute error of no more than e, i.e., for all i, j:

abs (this[i][j] - m[i][j]) <= e

equalWithRelError(m: M33d, e: double) → bool

Compare two matrices and test if they are “approximately equal”: @return True if the coefficients of this and m are the same with a relative error of no more than e, i.e., for all i, j:

abs (this[i] - v[i][j]) <= e * abs (this[i][j])

fastMinor(r0: int, r1: int, c0: int, c1: int) → double

Build a minor using the specified rows and columns

gjInverse() → M33d

Return the inverse using the Gauss-Jordan method. Significantly slower, leaving this unmodified. Slower but more accurate than inverse().

gjInvert()

Invert in place using the Gauss-Jordan method. Significantly slower but more accurate than invert().

inverse() → M33d

Return the inverse using the determinant, leaving this unmodified.

invert()

Invert in place using the determinant

negate()

Component-wise multiplication by -1

makeIdentity()

Set to the identity matrix

minorOf(r: int, c: int) → double

Calculate the matrix minor of the (r,c) element

multVecMatrix(v: V2d) → V2d

Transform the point v by the matrix

multDirMatrix(v: V2d) → V2d

Transform the vector v by the matrix

rotate(r: double)

Rotate the given matrix by r (in radians)

scale(s: V2d)

Scale the matrix by s

shear(h: V2d)

Shear the matrix in x for each y coord. by given factor xy and shear y for each x coord. by given factor yx

shear(xy: double)

Shear the matrix in x for each y coord. by given factor xy

setScale(s: double)

Set matrix to scale by given uniform factor

setScale(r: V2d)

Set matrix to scale by given vector

setShear(h: V2d)

Set matrix to shear x for each y coord. by given factor h.x and to shear y for each x coord. by given factor h.y

setTranslation(t: V2d)

Set matrix to translation by given vector

transpose()

Transpose

translate(t: V2d)

Translate the matrix by t

translation() → V2d

Return translation component

transposed() → M33d

Return the transpose