A presentation on the basics of 3D render systems and their application to 2D sprite rendering.

1. Sprite Rendering Games, Interaction and Robotics 2011

2. The Game Loop

3. Synthesis vs Analysis Computer Graphics Computer Vision

4. Rendering Steps A virtual scene is described, usually in terms of 3D surfaces in mathematical form. A virtual camera is positioned and oriented to produce the desired view of the scene. Various light sources are defined. The visual properties of the surfaces in the scene are described. The render equationis solved. Chapter 10. Game Engine Architecture, 2009, A K Peters, Ltd.

5. Triangle Meshes An example of a polygon mesh. Chrschn, 2007.

6. Texture Mapping A depiction of how UV-Mapping works, showing the classic example of mapping a globe. Drawing by TSchmits, 2008.

7. 3D Projection Principle of the geometrical perspective projection. Drawing by Joachim Baecker, 2005.

8. Coordinate Systems Left-Handed Right-Handed Handedness cartesian coordinate system in 3D. Gustavb, 2006.

9. What’s in a Sprite?

10. What’s in a Sprite?

11. Transformation Matrix 𝑇𝑥=𝑨𝑥

12. Transformation Matrix 𝑇𝑥=𝑨𝑥 Translation 𝑨=10𝑡𝑥01𝑡𝑦001

13. Transformation Matrix 𝑇𝑥=𝑨𝑥 Rotation 𝑨=cos𝜃−sin𝜃0sin𝜃cos𝜃0001

14. Transformation Matrix 𝑇𝑥=𝑨𝑥 Scale 𝑨=𝑠𝑥000𝑠𝑦0001

15. Composite Transformation 𝑩𝑨𝑥=𝑩𝑨𝑥 𝑨𝑨−1𝑥=𝑥

16. Orthographic Projection Projection lines orthogonal to projection plane. Distance to viewpoint does not decrease apparent size of object.

17. Rendering Sprites 𝑻=𝑻𝑺𝑹

18. Bibliography Game Engine Architecture, Jason Gregory, 2009, A K Peters, Ltd. OpenGL® Programming Guide: The Official Guide to Learning OpenGL®, Version 2.1, 6th Edition, 2007, Addison-Wesley Professional