18 Matrix
Chuck Walbourn редактировал(а) эту страницу 2022-04-26 16:45:12 -07:00
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

Vector2, Vector3, Vector4, Quaternion