Download as PDF, PPTX
Uploaded byMohammad Shaker
XNA L02–Basic Matrices and Transformations
The document discusses 3D matrix transformations in XNA game development. It explains that to render a 3D scene, a camera matrix, projection matrix, and separate world matrix for each object must be set up. It provides details on creating view matrices with CreateLookAt, projection matrices with CreatePerspectiveFieldOfView or CreateOrthographic, and transforming objects using world matrices created from scaling, rotation, translation and other transformations. Multiple transformations can be combined by multiplying the matrices together in order.
More Related Content
![Ultra Fast, Cross Genre, Procedural Content Generation in Games [Master Thesis]](https://cdn.slidesharecdn.com/ss_thumbnails/mshaker-present-160529192144-thumbnail.jpg?width=600ounds&width=560&fit=bounds)
Similar to XNA L02–Basic Matrices and Transformations
XNA L02–Basic Matrices and Transformations
- 1. Mohammad Shaker mohammadshaker.com @ZGTRShaker 2011, 2012, 2013, 2014 XNA Game Development L02 –Transformations and Basic Matrices
- 2.
- 3.
- 4.
- 5.
- 6. XNA Matrices •Matrix.CreateRotationX, Matrix.CreateRotationY, and Matrix.CreateRotationZ: Each of these creates a rotation matrix for each of the axes. • Matrix.Translation: Creates a translation matrix (one or more axes). • Matrix.Scale: Creates a scale matrix (one or more axes). • Matrix.CreateLookAt: Creates a view matrix used to position the camera, by setting the 3D position of the camera, the 3D position it is facing, and which direction is “up” for the camera. • Matrix.CreatePerspectiveFieldOfView: Creates a projection matrix that uses a perspective view.
- 7. Basic Matrices View,Projection and World Matrices
- 8. Basic Matrices •View,Projection and World Matrices
- 9.
- 10. RULE TO SEEA 3D SCENE YOU SHOULD SET UP:
- 11. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA
- 12. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA PROJECTION
- 13. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA PROJECTION WORLD MATRIX
- 14. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 15. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 16. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 17. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 18. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 19.
- 20. XNA Matrices •Matrix.CreateRotationX, Matrix.CreateRotationY, and Matrix.CreateRotationZ: Each of these creates a rotation matrix for each of the axes. • Matrix.Translation: Creates a translation matrix (one or more axes). • Matrix.Scale: Creates a scale matrix (one or more axes). • Matrix.CreateLookAt: Creates a view matrix used to position the camera, by setting the 3D position of the camera, the 3D position it is facing, and which direction is “up” for the camera. • Matrix.CreatePerspectiveFieldOfView: Creates a projection matrix that uses a perspective view.
- 21. View Matrices Matrix.CreateLookAt(Vector3cameraPosition, Vector3 cameraTarget, Vector3 cameraUpVector);
- 22. View Matrices Matrix.CreateLookAt(Vector3cameraPosition, Vector3 cameraTarget, Vector3 cameraUpVector);
- 23. View Matrices Matrix.CreateLookAt(Vector3cameraPosition, Vector3 cameraTarget, Vector3 cameraUpVector);
- 24. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 25. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 26.
- 27. XNA Matrices •Matrix.CreateRotationX, Matrix.CreateRotationY, and Matrix.CreateRotationZ: Each of these creates a rotation matrix for each of the axes. • Matrix.Translation: Creates a translation matrix (one or more axes). • Matrix.Scale: Creates a scale matrix (one or more axes). • Matrix.CreateLookAt: Creates a view matrix used to position the camera, by setting the 3D position of the camera, the 3D position it is facing, and which direction is “up” for the camera. • Matrix.CreatePerspectiveFieldOfView: Creates a projection matrix that uses a perspective view.
- 28.
- 29. Projection Matrices TheDifference?!
- 30. Projection Matrices TheDifference?! perspective
- 31. Projection Matrices TheDifference?! perspective orthographic
- 32.
- 33.
- 34.
- 35. Projection Matrices Realistic? perspective orthographic
- 36. Projection Matrices •ProjectionMatries Realistic? perspective orthographic
- 37. Projection Matrices Architecture? perspective orthographic
- 38. Projection Matrices Architecture? perspective orthographic
- 39. Projection Matrices Usability? perspective orthographic
- 40. Projection Matrices Usability? perspective orthographic
- 41. XNA Matrices •Matrix.CreateRotationX, Matrix.CreateRotationY, and Matrix.CreateRotationZ: Each of these creates a rotation matrix for each of the axes. • Matrix.Translation: Creates a translation matrix (one or more axes). • Matrix.Scale: Creates a scale matrix (one or more axes). • Matrix.CreateLookAt: Creates a view matrix used to position the camera, by setting the 3D position of the camera, the 3D position it is facing, and which direction is “up” for the camera. • Matrix.CreatePerspectiveFieldOfView: Creates a projection matrix that uses a perspective view.
- 42. Orthographic Projections •Anorthographic projection can be created with the following code: Matrix.CreateOrthographic(float width, float height, float zNearPlane, float zFarPlane);
- 43. Orthographic Projections •Anorthographic projection can be created with the following code: •Off-center orthogonal projection: Matrix.CreateOrthographic(float width, float height, float zNearPlane, float zFarPlane); Matrix.CreateOrthographicOffCenter(float left, float right, float bottom, float top, float zNearPlane, float zFarPlane);
- 44. Orthographic Projections •Ummm…. Matrix.CreateOrthographicOffCenter(-1, 1, -1, 1, 0.1f, 100f); Matrix.CreateOrthographic(2, 2, 0.1f, 100f);
- 45. Orthographic Projections •Ummm…. Matrix.CreateOrthographicOffCenter(-1, 1, -1, 1, 0.1f, 100f); Matrix.CreateOrthographic(2, 2, 0.1f, 100f);
- 46. Perspective Projections •PerspectiveFieldOfView Matrix.CreatePerspectiveFieldOfView(float fieldOfView, float aspectRatio, float nearPlaneDistance, float farPlaneDistance);
- 47. Perspective Projections Matrix.CreatePerspectiveFieldOfView(floatfieldOfView, float aspectRatio, float nearPlaneDistance, float farPlaneDistance);
- 48. Perspective Projections Matrix.CreatePerspectiveFieldOfView(floatfieldOfView, float aspectRatio, float nearPlaneDistance, float farPlaneDistance);
- 49. Perspective Projections Matrix.CreatePerspectiveFieldOfView(floatfieldOfView, float aspectRatio, float nearPlaneDistance, float farPlaneDistance);
- 50. Perspective Projections •Perspectiveprojections Matrix.CreatePerspectiveFieldOfView(float fieldOfView, float aspectRatio, float nearPlaneDistance, float farPlaneDistance);
- 51. Perspective Projections Matrix.CreatePerspectiveFieldOfView(floatfieldOfView, float aspectRatio, float nearPlaneDistance, float farPlaneDistance);
- 52. Perspective Projections Matrix.CreatePerspectiveFieldOfView(floatfieldOfView, float aspectRatio, float nearPlaneDistance, float farPlaneDistance);
- 53. Perspective Projections Matrix.CreatePerspective( float width, float height, float nearPlaneDistance, float farPlaneDistance);
- 54. Perspective Projections Matrix.CreatePerspective( float width, float height, float nearPlaneDistance, float farPlaneDistance);
- 55. Perspective Projections Matrix.CreatePerspective( float width, float height, float nearPlaneDistance, float farPlaneDistance);
- 56. Perspective Projections Matrix.CreatePerspectiveOffCenter( float left, float right, float bottom, float top, float nearPlaneDistance, float farPlaneDistance);
- 57. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 58. RULE TO SEEA 3D SCENE YOU SHOULD SET UP: CAMERA (Singleton, for all objects) PROJECTION (Singleton, for all objects) WORLD MATRIX (For each object separately)
- 59. World MatrixEach Objectin 3D Has Its own World Matrix
- 60.
- 61. World Matrix •Example •Let’s assume that the coordinates of the triangle vertices are as follows:
- 62. World Matrix •Example •To translate 40 units over the y axis’s positive direction,allyou need to do is to add 40 toeachy position, and you have the new coordinates for the vertices:
- 63.
- 64.
- 65. Identity Scale Rotate Orbit Translate
- 66. Transformations •Load IdentityMatrix Matrix.Identity(); Identity Scale Rotate Orbit Translate
- 67. Transformations •Create scalematrix Matrix.CreateScale(float scaleAmount); Identity Scale Rotate Orbit Translate
- 68. Transformations •Create amatrix that rotates around the x-axis: Matrix.CreateRotateX(float angleInRadians); •Create a matrix that rotatesaround the y-axis: Matrix.CreateRotateY(float angleInRadians); •Create a matrix that rotatesaround the z-axis: Matrix.CreateRotateZ(float angleInRadians); Identity Scale Rotate Orbit Translate
- 69. Transformations •Create amatrix that rotates points around an arbitrary axis: Matrix.CreateFromAxisAngle(Vector3 axis, float angleInRadians); Identity Scale Rotate Orbit Translate
- 70. Transformations •Create anOrbit matrix?! Identity Scale Rotate Orbit Translate
- 71. Transformations •Create anOrbit matrix?! It’s just “Translate then Rotate” Identity Scale Rotate Orbit Translate
- 72. Transformations •Create atranslation matrix: Matrix.CreateTranslation(Vector3 position); Identity Scale Rotate Orbit Translate
- 73. Transformations •Multiple WorldTransformations
- 74. Transformations •Multiple WorldTransformations
- 75. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Identity Scale Rotate Orbit Translate
- 76. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Identity Scale Rotate Orbit Translate
- 77. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Identity Scale Rotate Orbit Translate
- 78. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Identity Scale Rotate Orbit Translate
- 79. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Matrixresult = Matrix.CreateTranslation(newVector3(10, 0, 0)) * Matrix.CreateRotationX(MathHelper.ToRadians(45)); Identity Scale Rotate Orbit Translate
- 80. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Matrixresult = Matrix.CreateTranslation(newVector3(10, 0, 0)) * Matrix.CreateRotationX(MathHelper.ToRadians(45)); Identity Scale Rotate Orbit Translate
- 81. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Matrixresult = Matrix.CreateTranslation(newVector3(10, 0, 0)) * Matrix.CreateRotationX(MathHelper.ToRadians(45)); Not the same! Identity Scale Rotate Orbit Translate
- 82. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Matrixresult = Matrix.CreateTranslation(newVector3(10, 0, 0)) * Matrix.CreateRotationX(MathHelper.ToRadians(45)); Not the same! Identity Scale Rotate Orbit Translate
- 83. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateRotationX(MathHelper.ToRadians(45)) * Matrix.CreateTranslation(newVector3(10, 0, 0)); Matrixresult = Matrix.CreateTranslation(newVector3(10, 0, 0)) * Matrix.CreateRotationX(MathHelper.ToRadians(45)); Not the same! Identity Scale Rotate Orbit Translate
- 84. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateTranslation(newVector3(10, 0, 0)) * Matrix.CreateRotationX(MathHelper.ToRadians(45)); Identity Scale Rotate Orbit Translate
- 85. Transformations •Multiple WorldTransformations Matrixresult = Matrix.CreateTranslation(newVector3(10, 0, 0)) * Matrix.CreateRotationX(MathHelper.ToRadians(45)); Identity Scale Rotate Orbit Translate
- 86. Test’emlive! Souvenir, 9:03AM, Tuesday, Aug.16th-2011 still awake :S
- 87.
- 88. Custom Matrices MatrixcustomMatrix= new Matrix( floatm11, floatm12, floatm13, floatm14, floatm21, floatm22, floatm23, floatm24, floatm31, floatm32, floatm33, floatm34, floatm41, floatm42, floatm43, floatm44);
- 89. Custom Matrices •CustomMatrices Matrix customMatrix= new Matrix( floatm11, floatm12, floatm13, floatm14, floatm21, floatm22, floatm23, floatm24, floatm31, floatm32, floatm33, floatm34, floatm41, floatm42, floatm43, floatm44); customMatrix.M31 = 4;
- 90. Basic Matrices -AFinal Example Vector3cameraPosition= newVector3(30.0f, 30.0f, 30.0f); Vector3cameraTarget= newVector3(0.0f, 0.0f, 0.0f); // Look back at the origin floatfovAngle= MathHelper.ToRadians(45); // convert 45 degrees to radians floataspectRatio= graphics.PreferredBackBufferWidth/ graphics.PreferredBackBufferHeight; floatnear = 0.01f; // the near clipping plane distance floatfar = 100f; // the far clipping plane distance Matrixworld = Matrix.CreateTranslation(10.0f, 0.0f, 10.0f); Matrixview = Matrix.CreateLookAt(cameraPosition, cameraTarget, Vector3.Up); Matrixprojection = Matrix.CreatePerspectiveFieldOfView(fovAngle, aspectRatio, near, far);
- 91. Basic Matrices -AFinal Example Vector3cameraPosition= newVector3(30.0f, 30.0f, 30.0f); Vector3cameraTarget= newVector3(0.0f, 0.0f, 0.0f); // Look back at the origin float fovAngle= MathHelper.ToRadians(45); // convert 45 degrees to radians float aspectRatio= graphics.PreferredBackBufferWidth/ graphics.PreferredBackBufferHeight; float near = 0.01f; // the near clipping plane distance float far = 100f; // the far clipping plane distance Matrix world = Matrix.CreateTranslation(10.0f, 0.0f, 10.0f); Matrixview = Matrix.CreateLookAt(cameraPosition, cameraTarget, Vector3.Up); Matrix projection = Matrix.CreatePerspectiveFieldOfView(fovAngle, aspectRatio, near, far);
- 92. Basic Matrices -AFinal Example Vector3 cameraPosition= new Vector3(30.0f, 30.0f, 30.0f); Vector3 cameraTarget= new Vector3(0.0f, 0.0f, 0.0f); // Look back at the origin floatfovAngle= MathHelper.ToRadians(45); // convert 45 degrees to radians floataspectRatio= graphics.PreferredBackBufferWidth/ graphics.PreferredBackBufferHeight; floatnear = 0.01f; // the near clipping plane distance floatfar = 100f; // the far clipping plane distance Matrix world = Matrix.CreateTranslation(10.0f, 0.0f, 10.0f); Matrix view = Matrix.CreateLookAt(cameraPosition, cameraTarget, Vector3.Up); Matrixprojection = Matrix.CreatePerspectiveFieldOfView(fovAngle, aspectRatio, near, far);
- 93. Basic Matrices -AFinal Example Vector3 cameraPosition= new Vector3(30.0f, 30.0f, 30.0f); Vector3 cameraTarget= new Vector3(0.0f, 0.0f, 0.0f); // Look back at the origin float fovAngle= MathHelper.ToRadians(45); // convert 45 degrees to radians float aspectRatio= graphics.PreferredBackBufferWidth/ graphics.PreferredBackBufferHeight; float near = 0.01f; // the near clipping plane distance float far = 100f; // the far clipping plane distance Matrix world = Matrix.CreateTranslation(10.0f, 0.0f, 10.0f); Matrix view = Matrix.CreateLookAt(cameraPosition, cameraTarget, Vector3.Up); Matrix projection = Matrix.CreatePerspectiveFieldOfView(fovAngle, aspectRatio, near, far);
- 94. Basic Matrices -AFinal Example Vector3 cameraPosition= new Vector3(30.0f, 30.0f, 30.0f); Vector3 cameraTarget= new Vector3(0.0f, 0.0f, 0.0f); // Look back at the origin float fovAngle= MathHelper.ToRadians(45); // convert 45 degrees to radians float aspectRatio= graphics.PreferredBackBufferWidth/ graphics.PreferredBackBufferHeight; float near = 0.01f; // the near clipping plane distance float far = 100f; // the far clipping plane distance Matrix world = Matrix.CreateTranslation(10.0f, 0.0f, 10.0f); Matrix view = Matrix.CreateLookAt(cameraPosition, cameraTarget, Vector3.Up); Matrix projection = Matrix.CreatePerspectiveFieldOfView(fovAngle, aspectRatio, near, far);
- 95. Basic Matrices -AFinal Example Vector3 cameraPosition= new Vector3(30.0f, 30.0f, 30.0f); Vector3 cameraTarget= new Vector3(0.0f, 0.0f, 0.0f); // Look back at the origin float fovAngle= MathHelper.ToRadians(45); // convert 45 degrees to radians float aspectRatio= graphics.PreferredBackBufferWidth/ graphics.PreferredBackBufferHeight; float near = 0.01f; // the near clipping plane distance float far = 100f; // the far clipping plane distance Matrix world = Matrix.CreateTranslation(10.0f, 0.0f, 10.0f); Matrix view = Matrix.CreateLookAt(cameraPosition, cameraTarget, Vector3.Up); Matrix projection = Matrix.CreatePerspectiveFieldOfView(fovAngle, aspectRatio, near, far);