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Geometric Objects and Basic Transformations

Geometric Objects and Basic Transformations. Paul Taylor 2010. 3D Coordinate systems. DirectX OpenGL. http://alt.pluralsight.com/wiki/default.aspx/Craig.DirectX/CoordinateSystemsTutorial.html. xMax , 0. 2D Coordinates in Windows. 0,0. 0, yMax. xMax , yMax.

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Geometric Objects and Basic Transformations

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  1. Geometric Objects and Basic Transformations Paul Taylor 2010

  2. 3D Coordinate systems DirectX OpenGL http://alt.pluralsight.com/wiki/default.aspx/Craig.DirectX/CoordinateSystemsTutorial.html

  3. xMax, 0 2D Coordinates in Windows 0,0 0, yMax xMax, yMax

  4. In both OpenGL and Direct3D Z is the depth of the viewport!!!! hence the Z-buffer (Depth Buffer)

  5. Z Buffer Depth • Due to the scalar nature of the Pyramid Viewport • Depth precision drops as the distance between the Near and Far planes are moved apart • This will result in more artefacts and visual errors

  6. Using the Z Buffer glEnable(GL_DEPTH_TEST); This enables the Z buffer, but is entirely useless without: glDepthFunc(GL_LEQUAL); You’ll find that the default for the Depth buffer usually doesn’t work.

  7. Viewport types • Orthogonal • No depth perception (scaling) • Projected • This is the typical 3D viewport • Objects \ Vertices are scaled and rotated based on the ‘virtual’ distance from the screen

  8. Viewport Creation • glOrtho(left, right, bottom, top, near, far) • gluOrtho2D • Sets the Near and Far values to 1.0 • (Only renders objects with z=1.0) • Same as glOrtho with near & far = 1.0 • GluPerspective(…) • Creates the Viewport Frame based on a FOV • GlFrustrum(…) • Create the Viewport in a more numerical way • Create your viewport matrix manually if you like!

  9. Matriceis • GL_PROJECTION • GL_MODEL_VIEW • GL_TEXTURE_MATRIX

  10. Matrix Math (Joy!) • Matrix Addition • Matrix Multiplication • Translation and Rotation Matrices

  11. Matrix Addition = + = +

  12. Matrix Multiplication Row,Colum = x = x

  13. That’s great, what do I need them for? Translation Matrices • Coordinates from Object Coordinates to world Coordinates Object Translation World Typically we use a Matrix Multiplication = +

  14. Scalar Matrices Object Scalar (1/10) World This can be done by glScalef(x,y,z); = x

  15. Translation by Multiplication • This is a computationally longer way to do a simple translation • glTranslatef(x,y,z); = x

  16. Rotational Matrices glRotatef(Theta,x,y,z); http://en.wikipedia.org/wiki/Rotation_matrix#Dimension_three A Rotation around the unit vector u = (ux,uy,uz)

  17. Putting it all together Typically you will want to: Translate Rotate Scale Matrix Multiplication is the inverse to the logical order! So: Scale then Rotate, then Translate

  18. Retrieving Matrices • This is slow! • The Video Matricies are 4x4 hence: GLfloat matrix[16]; glGetFloatv(GL_PROJECTION_MATRIX, &matrix[0]); matrix = Simillarly you can do this for GL_MODEL_VIEW and GL_TEXTURE_MATRIX Setting your own Matrix void glLoadMatrixf( &matrix[0]);

  19. BG115 has XNA

  20. Silent Hill 5 (Homecoming) From Jason Allen (Lead Designer) …” We made a decision during development to support invert aim and not invert camera.  Unfortunately none of the team nor any of our test group actually had a preference for playing with an inverted camera, so the issue of its omission never came up.”… http://72.14.235.132/search?q=cache:ylhQ9HOmPg4J:gamesblog.ugo.com/index.php/gamesblog/more/silent_hill_homecomings_jason_allen_on_inverted_aim/+silent+hill+5+no+camera+invert&cd=3&hl=en&ct=clnk&gl=au&client=firefox-a

  21. Matrix Mathematics Continued • Matrix Cross Product • We use this to create Normals

  22. Matrix Dot Product

  23. Normalising Matrcies

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  25. LIST OF EXHIBITORS AT 2010 ENGINEERING EXPO Monash University Engineering

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