struct Mat4D in Tinman.Core.Math.Vectors

A 4x4 matrix with 64-bit floating-point precision.

struct

Mat4D

implements

IEquatable<Mat4D>

Remarks

/                      \
|  M11  M12  M13  M14  |
|  M21  M22  M23  M24  |
|  M31  M32  M33  M34  |
|  M41  M42  M43  M44  |
\                      /

Serialization

Serializer

The serialization helper object for values of Mat4D.

public static readonly field	Serializer
type	ITypeSerializer<Mat4D>

Public / Constants

Identity

The identity matrix.

public static readonly field	Identity
type	Mat4D

Zero

The zero matrix.

public static readonly field	Zero
type	Mat4D

Public / Attributes

Determinant

Returns the determinant of this matrix.

public property	Determinant { get }
type	float64
value		The determinant value.

Inverse

Returns the inverse of this matrix.

public property	Inverse { get }
type	Mat4D
value		The inverse matrix.

M11

Matrix component in first row, first column.

public readonly field	M11
type	float64

M12

Matrix component in first row, second column.

public readonly field	M12
type	float64

M13

Matrix component in first row, third column.

public readonly field	M13
type	float64

M14

Matrix component in first row, fourth column.

public readonly field	M14
type	float64

M21

Matrix component in second row, first column.

public readonly field	M21
type	float64

M22

Matrix component in second row, second column.

public readonly field	M22
type	float64

M23

Matrix component in second row, third column.

public readonly field	M23
type	float64

M24

Matrix component in second row, fourth column.

public readonly field	M24
type	float64

M31

Matrix component in third row, first column.

public readonly field	M31
type	float64

M32

Matrix component in third row, second column.

public readonly field	M32
type	float64

M33

Matrix component in third row, third column.

public readonly field	M33
type	float64

M34

Matrix component in third row, fourth column.

public readonly field	M34
type	float64

M41

Matrix component in fourth row, first column.

public readonly field	M41
type	float64

M42

Matrix component in fourth row, second column.

public readonly field	M42
type	float64

M43

Matrix component in fourth row, third column.

public readonly field	M43
type	float64

M44

Matrix component in fourth row, fourth column.

public readonly field	M44
type	float64

Transpose

Returns the transpose of this matrix.

public property	Transpose { get }
type	Mat4D
value		The transposed matrix.

Public / Constructors

Mat4D

Creates a new instance of Mat4D.

public constructor	Mat4D (float64 m11, float64 m12, float64 m13, float64 m14, float64 m21, float64 m22, float64 m23, float64 m24, float64 m31, float64 m32, float64 m33, float64 m34, float64 m41, float64 m42, float64 m43, float64 m44)
params	m11		Matrix component in first row, first column.
	m12		Matrix component in first row, second column.
	m13		Matrix component in first row, third column.
	m14		Matrix component in first row, fourth column.
	m21		Matrix component in second row, first column.
	m22		Matrix component in second row, second column.
	m23		Matrix component in second row, third column.
	m24		Matrix component in second row, fourth column.
	m31		Matrix component in third row, first column.
	m32		Matrix component in third row, second column.
	m33		Matrix component in third row, third column.
	m34		Matrix component in third row, fourth column.
	m41		Matrix component in fourth row, first column.
	m42		Matrix component in fourth row, second column.
	m43		Matrix component in fourth row, third column.
	m44		Matrix component in fourth row, fourth column.

Public / Methods

DecomposeTranslation

Decomposes this matrix into a reduced matrix without translational components and an offset vector.

[Pure]
public method	DecomposeTranslation (out Mat4D reduced, out Vec3D offset)
params	reduced		Output of reduced matrix (see MV' above).
	offset		Output of transformed offset vector (see O above).

Remarks:

The typical vertex coordinate 3D transformation pipeline can be describes as follows:

v* := P * MV * v

where v is a vertex point in model-space, MV is the combined model-view matrix, P is the projection matrix and v* is the transformed vertex point in clip-space. Most often, the combined model-view-projection matrix P * MV is computed by the CPU and sent to a GPU shader for further processing. Significant precision issues will arise if the following conditions hold true:

• The model-view-projection matrix is transmitted using 32-bit floating point precision only.
• The model-view matrix MV contains translational components of great magnitude.

In order to circumvent these problems, the 3D transformation pipeline can be rewritten as follows:

v* := P * MV' * (v - O)

where O is an offset vector that represents the removed translational components of MV transformed back into model-space and MV' is the reduced model-view matrix (i.e. without translational components).

Equals

public method	Equals (Mat4D other)
type	bool
params	other

EqualsAlmost

public method	EqualsAlmost (Mat4D other)
type	bool
params	other

Lerp

Performs a component-wise linear interpolation between this matrix and the given one.

[Pure]
public method	Lerp (Mat4D other, float64 factor)
type	Mat4D
params	other		The other matrix.
	factor		The interpolation factor (0: this, 1: other).
returns			The resulting matrix.

LookAt

[Pure]
public static method	LookAt (Vec3D origin, Vec3D target, Vec3D up, bool rightHanded)
type	Mat4D
params	origin
	target
	up
	rightHanded

Mul

Multiplies this matrix (left-side) with the given one (right-side): result = this * m.

[Pure]
public method	Mul (Mat4D m)
type	Mat4D
params	m		The matrix.
returns			The resulting matrix.

Mul3

Multiplies this matrix (left-side) with the given homogeneous 3D vector (right-side): result = this * v.

[Pure]
public method	Mul3 (Vec3D v, float64 w)
type	Vec3D
params	v		The vector.
	w		The W-component to assume.
returns			The resulting vector, scaled by 1/result.W.

---

Multiplies this matrix (left-side) with the given homogeneous 3D vector (right-side): result = this * v.

[Pure]
public method	Mul3 (float64 x, float64 y, float64 z, float64 w)
type	Vec3D
params	x		X-component of vector.
	y		Y-component of vector.
	z		Z-component of vector.
	w		The W-component to assume.
returns			The resulting vector, scaled by 1/result.W.

Mul4

Multiplies this matrix (left-side) with the given 4D vector (right-side): result = this * v.

[Pure]
public method	Mul4 (Vec4D v)
type	Vec4D
params	v		The vector.
returns			The resulting vector.

---

Multiplies this matrix (left-side) with the given 4D vector (right-side): result = this * v.

[Pure]
public method	Mul4 (float64 x, float64 y, float64 z, float64 w)
type	Vec4D
params	x		X-component of vector.
	y		Y-component of vector.
	z		Z-component of vector.
	w		W-component of vector.
returns			The resulting vector.

Orthographic

public static method	Orthographic (float64 left, float64 right, float64 top, float64 bottom, float64 zNear, float64 zFar, bool nearAtZero, bool rightHanded)
type	Mat4D
params	left
	right
	top
	bottom
	zNear
	zFar
	nearAtZero
	rightHanded

PerspectiveFov

Creates a perspective projection matrix.

[Pure]
public static method	PerspectiveFov (float64 fov, float64 aspect, float64 n, float64 f, bool nearAtZero, bool rightHanded)
type	Mat4D
params	fov		The field-of-view along the viewport Y-axis, in radians.
	aspect		The viewport aspect ratio (width divided by height).
	n		Near clipping plane Z-value (will be mapped to 0 resp. -1 in clip-space; see nearAtZero for details).
	f		Far clipping plane Z-value (will be mapped to 1 in clip-space).
	nearAtZero		When true, the near clipping plane will be mapped to 0 in clip-space (e.g. Direct3D); when false it will be mapped to -1 (e.g. OpenGL).
	rightHanded		Create projection matrix for a right-handed (true) or left-handed (false) coordinate system?
returns			The projection matrix.

PerspectiveRay

Computes a ray for a screen-pixel.

[Pure]
public method	PerspectiveRay (Vec3D translation, float64 pixelX, float64 pixelY, int32 screenWidth, int32 screenHeight, bool nearAtZero, out Vec3D origin, out Vec3D direction)
params	translation		The translation components, if they have been omitted in the view projection, otherwise Zero.
	pixelX		Pixel X-coordinate (see remarks).
	pixelY		Pixel Y-coordinate (see remarks).
	screenWidth		Screen width, in pixels.
	screenHeight		Screen height, in pixels.
	nearAtZero		When true, the near clipping plane will be mapped to 0 in clip-space (e.g. Direct3D); when false it will be mapped to -1 (e.g. OpenGL).
	origin		Output for origin of ray.
	direction		Output for unit-length ray direction vector.

Remarks:

This matrix must be the inverse of a combined world-view-projection matrix (for example, PerspectiveFov). The pixel coordinates (0,0) refer to the top-left corner of the top-left screen pixel. The pixel coordinates (w,h) refer to the bottom-right corner of the bottom-right screen pixel (where w and h are the screen width resp. height). If you want to cast rays for pixel centers, you have to add an offset of 0.5 to the pixel coordinates.

Rotate

[Pure]
public static method	Rotate (Vec3D axis, float64 angle)
type	Mat4D
params	axis
	angle

---

[Pure]
public static method	Rotate (float64 x, float64 y, float64 z, float64 angle)
type	Mat4D
params	x
	y
	z
	angle

RotateX

Returns a rotation matrix (counter-clockwise around X-axis).

[Pure]
public static method	RotateX (float64 angle)
type	Mat4D
params	angle		The rotation angle, in radians.
returns			The resulting matrix.

RotateY

Returns a rotation matrix (counter-clockwise around Y-axis).

[Pure]
public static method	RotateY (float64 angle)
type	Mat4D
params	angle		The rotation angle, in radians.
returns			The resulting matrix.

RotateZ

Returns a rotation matrix (counter-clockwise around Z-axis).

[Pure]
public static method	RotateZ (float64 angle)
type	Mat4D
params	angle		The rotation angle, in radians.
returns			The resulting matrix.

Scale

Returns a scaling matrix.

[Pure]
public static method	Scale (float64 f)
type	Mat4D
params	f		The scale factor.
returns			The resulting matrix.

---

Returns a scaling matrix.

[Pure]
public static method	Scale (Vec4D f)
type	Mat4D
params	f		The scale factors.
returns			The resulting matrix.

---

Returns a scaling matrix.

[Pure]
public static method	Scale (float64 fx, float64 fy, float64 fz, float64 fw)
type	Mat4D
params	fx		The scale factor along the X-axis.
	fy		The scale factor along the Y-axis.
	fz		The scale factor along the Z-axis.
	fw		The scale factor along the W-axis.
returns			The resulting matrix.

ToArray

Copies matrix elements to the given array.

[Pure]
public method	ToArray ([] float64[] values, int32 offset = 0, int32 strideRow = 4, int32 strideCol = 1)
params	values	[not-null]	The output array.
	offset		Offset into values to top-left matrix element. Defaults to 0.
	strideRow		Array index distance between matrix rows. Defaults to 4.
	strideCol		Array index distance between matrix columns. Defaults to 1.

Remarks:

The method uses the following indexing scheme to write values to values:

values[offset + (row - 1) * strideRow + (col - 1) * strideCol := matrix[row, col];

where row and col depict the matrix row and column number (starting at 1).

Translate

Returns a translation matrix.

[Pure]
public static method	Translate (Vec3D v)
type	Mat4D
params	v		The translation vector.
returns			The translation matrix.

---

Returns a translation matrix.

[Pure]
public static method	Translate (float64 x, float64 y, float64 z)
type	Mat4D
params	x		X-component of translation vector.
	y		Y-component of translation vector.
	z		Z-component of translation vector.
returns			The translation matrix.

Warp

Computes an invertible 3D homogeneous warp matrix that transforms the given source triangle onto the specified target triangle.

[Pure]
public static method	Warp (Vec3D a0, Vec3D b0, Vec3D c0, Vec3D a1, Vec3D b1, Vec3D c1)
type	Mat4D
params	a0		First vertex of source triangle.
	b0		Second vertex of source triangle.
	c0		Third vertex of source triangle.
	a1		First vertex of target triangle.
	b1		Second vertex of target triangle.
	c1		Third vertex of target triangle.
returns			The homogeneous 3D warp matrix.

Remarks:

The fourth row of the returned matrix will always be (0,0,0,1), so it is not necessary to perform the homogeneous divide. Also all elements along the main diagonal will be 1.