Mat4D

Description

struct Tinman.Core.Math.Vectors.Mat4D

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

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

Public / Constants

Identity

public static readonly attribute Identity → (Mat4D)

The identity matrix.

Zero

public static readonly attribute Zero → (Mat4D)

The zero matrix.

Public / Constructors

FromColumns

[Pure]
public static method FromColumns → (4)

col1 ⁱⁿ : Vec4D: The first column vector.
col2 ⁱⁿ : Vec4D: The second column vector.
col3 ⁱⁿ : Vec4D: The third column vector.
col4 ⁱⁿ : Vec4D: The fourth column vector.
returns → Mat4D: The matrix.

Creates a new instance of Mat4D.

FromRows

[Pure]
public static method FromRows → (4)

row1 ⁱⁿ : Vec4D: The first row vector.
row2 ⁱⁿ : Vec4D: The second row vector.
row3 ⁱⁿ : Vec4D: The third row vector.
row4 ⁱⁿ : Vec4D: The fourth row vector.
returns → Mat4D: The matrix.

Creates a new instance of Mat4D.

LookAt

[Pure]
public static method LookAt → (4)

origin ⁱⁿ : Vec3D: The origin position.
target ⁱⁿ : Vec3D: The look-at position.
up ⁱⁿ : Vec3D: The up-direction vector.
rightHanded ⁱⁿ : bool: true to create a right-handed coordinate system,
false to create a left-handed one.
returns → Mat4D: The transformation matrix.

Creates a look-at transformation matrix.

Mat4D

public constructor Mat4D → (16)

m11 ⁱⁿ : float64: Matrix component in first row, first column.
m12 ⁱⁿ : float64: Matrix component in first row, second column.
m13 ⁱⁿ : float64: Matrix component in first row, third column.
m14 ⁱⁿ : float64: Matrix component in first row, fourth column.
m21 ⁱⁿ : float64: Matrix component in second row, first column.
m22 ⁱⁿ : float64: Matrix component in second row, second column.
m23 ⁱⁿ : float64: Matrix component in second row, third column.
m24 ⁱⁿ : float64: Matrix component in second row, fourth column.
m31 ⁱⁿ : float64: Matrix component in third row, first column.
m32 ⁱⁿ : float64: Matrix component in third row, second column.
m33 ⁱⁿ : float64: Matrix component in third row, third column.
m34 ⁱⁿ : float64: Matrix component in third row, fourth column.
m41 ^opt : float64 = 0: Matrix component in fourth row, first column.
m42 ^opt : float64 = 0: Matrix component in fourth row, second column.
m43 ^opt : float64 = 0: Matrix component in fourth row, third column.
m44 ^opt : float64 = 1: Matrix component in fourth row, fourth column.

Creates a new instance of Mat4D.

Orthographic

[Pure]
public static method Orthographic → (7)

left ⁱⁿ : float64: The X-coordinate to map to -1.
right ⁱⁿ : float64: The X-coordinate to map to +1.
top ⁱⁿ : float64: The Y-coordinate to map to -1.
bottom ⁱⁿ : float64: The Y-coordinate to map to +1.
zNear ⁱⁿ : float64: The Z-coordinate to map to 0 resp. -1.
zFar ⁱⁿ : float64: The Z-coordinate to map to +1.
nearAtZero ⁱⁿ : bool: true to map zNear ⁱⁿ to 0,
false to map zNear ⁱⁿ to -1.
returns → Mat4D: The projection matrix.

Creates an orthographic projection matrix.

PerspectiveFov

[Pure]
public static method PerspectiveFov → (6)

fov ⁱⁿ : float64: The field-of-view along the viewport Y-axis, in radians.
aspect ⁱⁿ : float64: The viewport aspect ratio (width divided by height).
n ⁱⁿ : float64: Near clipping plane Z-value (will be mapped to 0 resp. -1 in clip-space; see nearAtZero ⁱⁿ for details).
f ⁱⁿ : float64: Far clipping plane Z-value (will be mapped to 1 in clip-space).
nearAtZero ⁱⁿ : bool: 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 ⁱⁿ : bool: Create projection matrix for a right-handed (true) or left-handed (false) coordinate system?
returns → Mat4D: The projection matrix.

Creates a perspective projection matrix.

Rotate

_2 overloads

[Pure]
public static method Rotate¹ → (2)

axis ⁱⁿ : Vec3D: Unit-length rotation axis vector.
angle ⁱⁿ : float64: The rotation angle, in radians.
returns → Mat4D: The resulting matrix.

Returns a rotation matrix (counter-clockwise around the given axis for right-handed coordinate system).

[Pure]
public static method Rotate² → (4)

x ⁱⁿ : float64: X-component of unit-length rotation axis vector.
y ⁱⁿ : float64: Y-component of unit-length rotation axis vector.
z ⁱⁿ : float64: Z-component of unit-length rotation axis vector.
angle ⁱⁿ : float64: The rotation angle, in radians.
returns → Mat4D: The resulting matrix.

Returns a rotation matrix (counter-clockwise around the given axis for right-handed coordinate system).

RotateX

[Pure]
public static method RotateX → (1)

angle ⁱⁿ : float64: The rotation angle, in radians.
returns → Mat4D: The resulting matrix.

Returns a rotation matrix (counter-clockwise around X-axis for right-handed coordinate system).

RotateY

[Pure]
public static method RotateY → (1)

angle ⁱⁿ : float64: The rotation angle, in radians.
returns → Mat4D: The resulting matrix.

Returns a rotation matrix (counter-clockwise around Y-axis for right-handed coordinate system).

RotateZ

[Pure]
public static method RotateZ → (1)

angle ⁱⁿ : float64: The rotation angle, in radians.
returns → Mat4D: The resulting matrix.

Returns a rotation matrix (counter-clockwise around Z-axis for right-handed coordinate system).

Scale

_3 overloads

[Pure]
public static method Scale¹ → (1)

f ⁱⁿ : float64: The scale factor.
returns → Mat4D: The resulting matrix.

Returns a scaling matrix.

[Pure]
public static method Scale² → (1)

f ⁱⁿ : Vec4D: The scale factors.
returns → Mat4D: The resulting matrix.

Returns a scaling matrix.

[Pure]
public static method Scale³ → (4)

fx ⁱⁿ : float64: The scale factor along the X-axis.
fy ⁱⁿ : float64: The scale factor along the Y-axis.
fz ⁱⁿ : float64: The scale factor along the Z-axis.
fw ⁱⁿ : float64: The scale factor along the W-axis.
returns → Mat4D: The resulting matrix.

Returns a scaling matrix.

Translate

_2 overloads

[Pure]
public static method Translate¹ → (1)

v ⁱⁿ : Vec3D: The translation vector.
returns → Mat4D: The translation matrix.

Returns a translation matrix.

[Pure]
public static method Translate² → (3)

x ⁱⁿ : float64: X-component of translation vector.
y ⁱⁿ : float64: Y-component of translation vector.
z ⁱⁿ : float64: Z-component of translation vector.
returns → Mat4D: The translation matrix.

Returns a translation matrix.

Warp

[Pure]
public static method Warp → (6)

a0 ⁱⁿ : Vec3D: First vertex of source triangle.
b0 ⁱⁿ : Vec3D: Second vertex of source triangle.
c0 ⁱⁿ : Vec3D: Third vertex of source triangle.
a1 ⁱⁿ : Vec3D: First vertex of target triangle.
b1 ⁱⁿ : Vec3D: Second vertex of target triangle.
c1 ⁱⁿ : Vec3D: Third vertex of target triangle.
returns → Mat4D: The homogeneous 3D warp matrix.

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

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.

Public / Methods

EqualsAlmost

[Pure]
public method EqualsAlmost → (1)

other ⁱⁿ : Mat4D: The other matrix.
returns → bool: true if both matrices are similar, false if they are not.

Checks if this matrix and the given one are similar but necessarily equal.

See also: Maths.Similar²

GetColumn

[Pure]
public method GetColumn → (1)

index ⁱⁿ : int32: The zero-based column index.
returns → Vec4D: The column vector.

Returns a column vector.

GetRow

[Pure]
public method GetRow → (1)

index ⁱⁿ : int32: The zero-based row index.
returns → Vec4D: The row vector.

Returns a row vector.

Lerp

[Pure]
public method Lerp → (2)

other ⁱⁿ : Mat4D: The other matrix.
factor ⁱⁿ : float64: The interpolation factor (0: this, 1: other ⁱⁿ).
returns → Mat4D: The resulting matrix.

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

Mul

[Pure]
public method Mul → (1)

m ⁱⁿ : Mat4D: The matrix.
returns → Mat4D: The resulting matrix.

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

Mul3

_2 overloads

[Pure]
public method Mul3¹ → (2)

v ⁱⁿ : Vec3D: The vector.
w ⁱⁿ : float64: The W-component to assume.
returns → Vec3D: 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 Mul3² → (4)

x ⁱⁿ : float64: X-component of vector.
y ⁱⁿ : float64: Y-component of vector.
z ⁱⁿ : float64: Z-component of vector.
w ⁱⁿ : float64: The W-component to assume.
returns → Vec3D: The resulting vector, scaled by 1/result.W.

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

Mul4

_2 overloads

[Pure]
public method Mul4¹ → (1)

v ⁱⁿ : Vec4D: The vector.
returns → Vec4D: The resulting vector.

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

[Pure]
public method Mul4² → (4)

x ⁱⁿ : float64: X-component of vector.
y ⁱⁿ : float64: Y-component of vector.
z ⁱⁿ : float64: Z-component of vector.
w ⁱⁿ : float64: W-component of vector.
returns → Vec4D: The resulting vector.

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

PerspectiveRay

[Pure]
public method PerspectiveRay → (6)

translation ⁱⁿ : Vec3D: The translation components, if they have been omitted in the view projection, otherwise Vec3D.Zero.
pixelX ⁱⁿ : float64: Pixel X-coordinate (see remarks).
pixelY ⁱⁿ : float64: Pixel Y-coordinate (see remarks).
screenWidth ⁱⁿ : int32: Screen width, in pixels.
screenHeight ⁱⁿ : int32: Screen height, in pixels.
nearAtZero ⁱⁿ : bool: 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).
returns → Ray: The ray

Computes a ray for a screen-pixel.

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.

ToArray

public method ToArray → (4)

values ⁱⁿ : float64 [ ]: [not-null]
The output array.
offset ^opt : int32 = 0: Offset into values ⁱⁿ to top-left matrix element.
strideRow ^opt : int32 = 4: Array index distance between matrix rows.
strideCol ^opt : int32 = 1: Array index distance between matrix columns.

Copies matrix elements to the given array.

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

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).

ToString

_2 overloads

[Pure]
public method ToString² → (1)

flags ⁱⁿ : FormatFlags: The format flags to use.
returns → string: The string representation.

Returns the string representation of this matrix.

The Mat4D.ToString¹ method uses FormatFlags.Precision15.

See also: Vec4D.ToString²

Public / Attributes

Determinant

public attribute Determinant → (get)

value : float64: The determinant value.

Returns the determinant of this matrix.

Inverse

public attribute Inverse → (get)

value : Mat4D: The inverse matrix.

Returns the inverse of this matrix.

M11

public readonly attribute M11 → (float64)

Matrix component in first row, first column.

M12

public readonly attribute M12 → (float64)

Matrix component in first row, second column.

M13

public readonly attribute M13 → (float64)

Matrix component in first row, third column.

M14

public readonly attribute M14 → (float64)

Matrix component in first row, fourth column.

M21

public readonly attribute M21 → (float64)

Matrix component in second row, first column.

M22

public readonly attribute M22 → (float64)

Matrix component in second row, second column.

M23

public readonly attribute M23 → (float64)

Matrix component in second row, third column.

M24

public readonly attribute M24 → (float64)

Matrix component in second row, fourth column.

M31

public readonly attribute M31 → (float64)

Matrix component in third row, first column.

M32

public readonly attribute M32 → (float64)

Matrix component in third row, second column.

M33

public readonly attribute M33 → (float64)

Matrix component in third row, third column.

M34

public readonly attribute M34 → (float64)

Matrix component in third row, fourth column.

M41

public readonly attribute M41 → (float64)

Matrix component in fourth row, first column.

M42

public readonly attribute M42 → (float64)

Matrix component in fourth row, second column.

M43

public readonly attribute M43 → (float64)

Matrix component in fourth row, third column.

M44

public readonly attribute M44 → (float64)

Matrix component in fourth row, fourth column.

Transpose

public attribute Transpose → (get)

value : Mat4D: The transposed matrix.

Returns the transpose of this matrix.

Serialization

Serializer

public static readonly attribute Serializer → (ITypeSerializer<Mat4D>)

The serialization helper object for values of Mat4D.

Mat4D

Description

Public / Constants

Identity

Zero

Public / Constructors

From​Columns

From​Rows

Look​At

Mat4​D

Orthographic

Perspective​Fov

Rotate

Rotate​X

Rotate​Y

Rotate​Z

Scale

Translate

Warp

Public / Methods

Equals​Almost

Get​Column

Get​Row

Lerp

Mul

Mul3

Mul4

Perspective​Ray

To​Array

To​String

Public / Attributes

Determinant

Inverse

M11

M12

M13

M14

M21

M22

M23

M24

M31

M32

M33

M34

M41

M42

M43

M44

Transpose

Serialization

Serializer

FromColumns

FromRows

LookAt

Mat4D

PerspectiveFov

RotateX

RotateY

RotateZ

EqualsAlmost

GetColumn

GetRow

PerspectiveRay

ToArray

ToString