Содержание
DirectXTK | SimpleMath |
---|
A four by four row-major matrix modeled after the XNA Game Studio 4 (Microsoft.Xna.Framework.Matrix
) math library.
A 4x4 matrix is commonly used in computer graphics for 2D and 3D transformations.
Header
#include <SimpleMath.h>
Initialization
using namespace DirectX::SimpleMath;
Matrix m; // Creates an identity matrix
Matrix m(1, 2, 3, 4,
5, 6, 7, 8,
9, 10, 11, 12,
13, 14, 15, 16); // Creates a matrix [1 2 3 4
// | 5 6 7 8
// | 9 10 11 12
// | 13 14 15 16 ]
Matrix m( Vector3(1,2,3),
Vector3(4,5,6),
Vector(7,8,9) ); // Creates a matrix [1 2 3 0
// | 4 5 6 0
// | 7 8 9 0
// | 0 0 0 1 ]
Matrix m( Vector4(1, 2, 3, 4),
Vector4(5, 6, 7, 8),
Vector4(9, 10, 11, 12),
Vector4(13, 14, 15, 16) ); // Creates a matrix [1 2 3 4
// | 5 6 7 8
// | 9 10 11 12
// | 13 14 15 16 ]
float arr[16] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 };
Matrix m( arr ); // Creates a matrix [1 2 3 0
// | 4 5 6 0
// | 7 8 9 0
// | 0 0 0 1 ]
Fields
- _11, _12, _13, _14: First row of matrix
- _21, _22, _23, _24: Second row of matrix
- _31, _32, _33, _34: Third row of matrix
- _41, _42, _43, _44: Fourth row of matrix
Properties
- Up: The up direction vector from the matrix
- Down: The down direction vector from the matrix
- Right: The right direction vector from the matrix
- Left: The left direction vector from the matrix
- Forward: The forward direction vector in right-handed (RH) coordinates from the matrix
- Backward: The backward direction vector in right-handed (RH) coordinates from the matrix
- Translation: Returns the translation in the matrix
Methods
-
Comparison operators:
==
and!=
-
Assignment operators:
=
,+=
,-=
,*=
,/=
-
Unary operators:
+
,-
-
Binary operators:
+
,-
,*
,/
-
Decompose: Decomposes the matrix into rotation (a Quaternion), scaling, and translation components. Returns
false
if the matrix can't be decomposed. -
Transpose: Computes the transpose of the matrix. Note that for a pure rotation matrix, this is the same as the inverse.
-
Invert: Computes the inverse of the matrix using Cramer's rule. It returns
false
if the matrix is not invertible. -
Determinant: Computes the determinant of the matrix.
-
ToEuler: Computes rotation about y-axis (y), then x-axis (x), then z-axis (z) as angles in radians. The return value is compatible with one of the overloads of
CreateFromYawPitchRoll
. This result is only valid if the input matrix's upper 3x3 contains only rotation (i.e. no scaling).
Statics
-
CreateBillboard: Creates a spherical billboard that rotates around a specified object position
-
CreateConstrainedBillboard: Creates a cylindrical billboard that rotates around a specified axis
-
CreateTranslation: Creates a matrix for translating by the given X, Y, Z offset. Note you can create the inverse of this matrix by passing -X, -Y, -Z.
-
CreateScale: Creates a matrix for scaling by the given X, Y, and Z scale factors. Note you can create the inverse of this matrix by passing 1/X, 1/Y, 1/Z.
-
CreateRotationX, CreateRotationY, CreateRotationZ: Creates a matrix for rotation about the x-axis / y-axis / z-axis by angle given in radians.
-
CreateFromAxisAngle: Creates a matrix a rotation about a given 3-vector axis and an angle given in radians.
-
CreatePerspective, CreatePerspectiveFieldOfView, CreatePerspectiveOffCenter: Creates perspective projection in right-handed (RH) coordinates
-
CreateOrthographic, CreateOrthographicOffCenter: Creates orthographic projection in right-handed (RH) coordinates
-
CreateLookAt: Creates a look-at matrix in right-handed (RH) coordinates
For Left-Handed (LH) viewing coordinates, you can use the DirectXMath functions directly which interop freely with
Matrix
.
-
CreateWorld
-
CreateFromQuaternion: Converts a quaternion to a matrix.
-
CreateFromYawPitchRoll: Rotates about y-axis (yaw), then x-axis (pitch), then z-axis (roll) by given angles in radians. There is an overload which takes Vector3 which provides x, y, and z angles in radians.
The original D3DXmath library took the rotations in the the Yaw, Pitch, Roll order and that order was replicated in XNA Game Studio. In DirectXMath, the order was normalized to Roll (X), Pitch (Y), Yaw (Z) for the parameters, but the application of the rotations is in the same order.
-
CreateShadow: Creates transform that flattens geometry into a specified Plane as if casting a shadow from a specified light source
-
CreateReflection: Creates transform that reflects the coordinate system about a specified Plane.
-
Lerp: Linearly interpolates two matrices element-wise (useful for blending transformations).
-
Transform
Constants
- Identity: An identity matrix
Remark
Matrix can freely convert to and from a XMFLOAT4X4
and XMMATRIX
.
You can copy or assign a Matrix from a XMFLOAT3X3
or XMFLOAT4X3
.
See also
For Use
- Universal Windows Platform apps
- Windows desktop apps
- Windows 11
- Windows 10
- Windows 8.1
- Windows 7 Service Pack 1
- Xbox One
Architecture
- x86
- x64
- ARM64
For Development
- Visual Studio 2022
- Visual Studio 2019 (16.11)
- clang/LLVM v12 - v18
- MinGW 12.2, 13.2
- CMake 3.20
Related Projects
DirectX Tool Kit for DirectX 12
Tools
All content and source code for this package are subject to the terms of the MIT License.
This project has adopted the Microsoft Open Source Code of Conduct. For more information see the Code of Conduct FAQ or contact opencode@microsoft.com with any additional questions or comments.