Matrix3d Structure

SystemObject
  SystemValueType
    Teigha.GeometryMatrix3d

	Name	Description
	Matrix3d	Constructor for the Matrix3d class. Creates a matrix with elements taken from the passed array.

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	Name	Description
	CoordinateSystem3d	Property that represents coordinate system information for this matrix (origin and positive directions for x, y and z axes).
	ElementAt	Property that represents an element of this matrix at the specified row and column indices.
	Identity	Property that represents an identity matrix.
	Normal	Property that represents value formed as a result of taking the absolute value of each element of the upper 3x3 of the matrix and returning the absolute value of the largest such element.
	Translation	Property that represents translation part of the matrix as a vector.

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	Name	Description
	AlignCoordinateSystem	Returns the matrix that maps the coordinate system defined by the fromOrigin origin and the fromXAxis, fromYAxis and fromZAxis axes, to the coordinate system defined by the toOrigin origin and the toXAxis, toYAxis and toZAxis axes.
	Displacement	Returns the displacement (translation) matrix by the specified vector.
	Equals	Checks objects for equality. (Overrides ValueTypeEquals(Object))
	GetDeterminant	Returns the determinant of this matrix.
	GetHashCode	Retrieves the object hash code. (Overrides ValueTypeGetHashCode)
	GetScale	Returns the scale factor of this matrix. The scale factor is the square root of the longest column vector of the linear part of this matrix.
	GetType	(Inherited from Object)
	Inverse	Returns the inverse of this matrix.
	IsEqualTo(Matrix3d)	Checks whether this matrix is equal to the passed matrix.
	IsEqualTo(Matrix3d, Tolerance)	Checks whether this matrix is equal to the passed matrix according to the specified tolerance.
	IsInverse(Matrix3d)	Checks whether the passed matrix is inverse.
	IsInverse(Matrix3d, Tolerance)	Checks whether the passed matrix is inverse according to the specified tolerance.
	IsScaledOrtho	Checks whether the column vectors of the linear part of this matrix are perpendicular to each other.
	IsScaledOrtho(Tolerance)	Checks whether the column vectors of the linear part of this matrix are perpendicular to each other according to the specified tolerance.
	IsSingular	Checks whether this matrix is singular.
	IsSingular(Tolerance)	Checks whether this matrix is singular according to the specified tolerance.
	IsUniscaledOrtho	Checks whether the column vectors of the linear part of this matrix are of equal length and perpendicular to each other.
	IsUniscaledOrtho(Tolerance)	Checks whether the column vectors of the linear part of this matrix are of equal length and perpendicular to each other according to the specified tolerance.
	Mirroring(Line3d)	Returns the matrix that mirrors about the specified line.
	Mirroring(Plane)	Returns the matrix that mirrors about the specified plane.
	Mirroring(Point3d)	Returns the matrix that mirrors about the specified point.
	PlaneToWorld(Plane)	Returns the matrix that maps the plane coordinate system to the world coordinate system (WCS).
	PlaneToWorld(Vector3d)	Returns the matrix that maps the plane coordinate system to the world coordinate system (WCS).
	PostMultiplyBy	Sets this matrix to the product of (this matrix) * rightSide and returns the resulting matrix.
	PreMultiplyBy	Sets this matrix to the product of leftSide * (this matrix) and returns the resulting matrix.
	Projection	Returns the matrix that parallel projects onto the specified plane in the specified direction.
	Rotation	Returns the matrix that rotates by angle about the axis passing through the center.
	Scaling	Returns the matrix that scales by a scale factor about the center.
	ToArray	Returns an array that contains matrix elements. Matrix elements are assigned by rows (data11, data12 ... data44). The resulting array contains 16 elements.
	ToString	Returns a string representation of this matrix. (Overrides ValueTypeToString)
	ToString(IFormatProvider)	Returns an equivalent string representation of this object.
	ToString(String, IFormatProvider)	Returns an equivalent string representation of this object.
	Transpose	Returns the transpose of this matrix.
	WorldToPlane(Plane)	Returns the matrix that maps the world coordinate system (WCS) to the plane coordinate system.
	WorldToPlane(Vector3d)	Returns the matrix that maps the world coordinate system (WCS) to the plane coordinate system.

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	Name	Description
	Equality(Matrix3d, Matrix3d)	Equality operator for the Matrix3d structure. Checks whether matrix elements are equal.
	Inequality(Matrix3d, Matrix3d)	Inequality operator for the Matrix3d structure. Checks whether matrix elements are not equal.
	Multiply(Matrix3d, Matrix3d)	Multiplication operator for the Matrix3d structure. Multiplies left matrix by right matrix (a*b).

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Matrix3d may be viewed as an array[4][4] of doubles. A Matrix3d, M, can be expressed as a 4 by 4 matrix, in the form

   a00   a01   a02   t0
   a10   a11   a12   t1
   a20   a21   a22   t2
     0     0     0    1

The linear part of M is the matrix

   a00   a01   a02
   a10   a11   a12
   a20   a21   a22

The translational part of M is the column

   t0
   t1
   t2

The origin of the coordinate system of M is (t0, t1, t2).

Reference