蔡侑庭 (Yu-Ting Tsai) National Chiao Tung University, Taiwan. Prof. Wen-Chieh Lin s CG Slides OpenGL 2.1 Specification

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1 蔡侑庭 (Yu-Ting Tsai) Department of Computer Science National Chiao Tung University, Taiwan Prof. Wen-Chieh Lin s CG Slides OpenGL 2.1 Specification OpenGL Programming Guide, Chap. 3 & Appendix F

2 2 OpenGL Buffers Five Basic Steps for GLUT Initialize GLUT Initialize Buffers Create Display Window Set Event Routines Start Event Parsing Loop GLUT Event Routines

3 3 Sample Code week_ 3.zip void MyDisplay() {... } void MyReshape( int nwidth, int nheight ) {... }

4 4 Eye Coordinates Normalized Device Coordinates Clip C di t Coordinates

5 5 y y z x x Left-Handed Coordinates z Right-Handed Coordinates OpenGL

6 6 Unified Way to Treat OpenGL Coordinates In most cases, w o is 1 (default value) Camera is always at the origin [0, 0, 0, 1] T Viewing direction always points toward negative z-axis Transformations are applied only to object coordinates Vice versa

7 7 Transformation matrices remain in effect until you change them OpenGL is a state t machine Call glloadidentity to reset transformation matrices if needed Each transformation at o function call Multiplies its result with current matrix Changes current matrix

8 8 g glmatrixmode( ( GL_MODELVIEW ); glloadidentity(); gltranslate( tx, tx ty, ty tz ); glrotate( θ, rx, ry, rz ); glscale( sx, sy, sz ); Eye Coordinates

9 9 Transformations are applied to object coordinates in reverse order glmatrixmode( GL_MODELVIEW ); gltranslate( tx, ty, tz ); glrotate( θ, rx, ry, rz ); glscale( sx, sy, sz ); glbegin( GL_POLYGON ); glend();

10 10 Rotations are applied to object coordinates with respect to the origin gltranslate( tx, ty, tz ); glrotate( θ, rx, ry, rz ); glrotate( θ, rx, ry, rz ); gltranslate( tx, ty, tz ); glbegin( GL_POLYGON ); glbegin( GL_POLYGON ); y y x x z z

11 11 g glmatrixmode( ( GL_PROJECTION ); glloadidentity(); glortho( l, l rr, b b, tt, n n, f ); [ glfrustum( l, r, b, t, n, f ); ] [ gluperspective( θ, aspect, n, f ); ] Eye Coordinates Clip Coordinates

12 12 glortho( l, r, b, t, n, f ) y l t z Camera x b n r f

13 13 glfrustum( l, r, b, t, n, f ) y l t z Camera x b n r f

14 14 gluperspective( θ, aspect = w / h, n, f ) y w z Camera x θ n h f

15 15 Automatically Performed by OpenGL (Graphics Hardware) Clip Coordinates Normalized Device Coordinates

16 16... gldepthrange( l, l u ); glviewport( x, y, w, h ); Normalized Device Coordinates

17 17 glviewport( x, y, w, h )& gldepthrange( l, u ) h [x, y] w

18 18 glviewport( x, y, w, h )& gldepthrange( l, u ) The y-axis of window coordinates points upward Normalized device coordinates [-1, 1] [-1, 1] [-1, 1] Mapped to [x, x + w] [y, y + h] [l, u]

19 19 Uniform Spacing (Orthographic) v e [-n, -f] v c [-1, 1] v d [-1, 1] v w [l, u] Camera

20 20 Non-Uniform Spacing (Perspective) v e [-n, -f] v c [-n, f] v d [-1, 1] v w [l, u] Camera

21 21 OpenGL Coordinate System Right-Handed Coordinates Basic OpenGL Transformations Modelview Transformations Translation, rotation, & scale Projection Transformations Orthographic & perspective projection Viewport Transformation

22 22 More on OpenGL Transformations Discussion on Assignment I Recitation of Selected Topics?

23 23 How to achieve non-uniform depth spacing for orthographic projection?

24 24 How to achieve uniform depth spacing for perspective projection?

25 25 Prof. Wen-Chieh Lin s CG Slides OpenGL Specifications OpenGL Programming Guide, Chap. 3 & Appendix F Sudhansu K. Semwal s OpenGL Tutorial html

26 26 Thank You! Any Questions?