1. 3D Polygon Rendering Pipeline 원본 – (http://www.cs.princeton.edu/courses/archive/fall00/cs426/lectures/pipeline/index.htm) Thomas Funkhouser (Princeton University) C0S 426 고려대학교 그래픽스 연구실 민성환

2. Basis 3D Plolygon rendering –3 차원으로 모델링 된 물체의 형상에 대해 색 감, 질감, 그림자, 빛의 반사 및 굴절 효과등 을 부여하는 과정 Pipeline – 하나의 process( 작업 ) 을 서로 다른 기능을 가진 여러 개의 subprocess 로 나누어 각 프 로세서가 동시에 서로 다른 데이터 처리

3. 3D polygon rendering Many applicatons use rendering of 3d polygons with direct illumination

4. 3d polygon rendering (cont) What steps are necessary to utilize spatial coherence while drawing these polygons into a 2D image?

5. 3d Rendering Pipeline This is a pipelined sequence of operations to draw a 3D primitive into a 2D image For direct illumination

6. Example OpenGL executes steps of 3D rendering pipeline for each polygon. glBegin(GL_POLYGON) glVertex3f(0.0,0.0,0.0); … glEnd();

7. In Pipeline Transform into3d world coordinate system

8. In Pipeline Illuminate according to lighting and reflectance

9. In Pipeline Transform into 3D camera coordinate system

10. In Pipeline Transform into 2D camera coordinate system

11. In Pipeline Clip primitives outside camera ’ s view

12. In Pipeline Draw pixels

13. In Pipeline Transform

14. Transformations

15. Transformations review Transformations map points from one coordinate system to another

16. Viewing Transformations Viewing transformations

17. Viewing Transformation 1.Translate the view reference point to the origin of the world-coordinate system 2.Apply rotations to align the axes with the world axes,respectively

18. Projection General definition –Transform points in n-space to m-space(m<n) In computer graphics –Map 3D camera coordinates to 2D screen coordinates

19. Taxonomy of Projections

21. Parallel Projection Center of projection is at infinity –Direction of projection (DOP) same for all points

22. Orthographic Projections DOP perpendicular to view plane

23. Oblique Projections DOP not perpendicular to view plane

24. Parallel Projection Matrix General parallel projection transformation z Where L1 is the inverse of tanα,which is also the value of L when z=1

25. Parallel Projection Matrix General parallel projection transformation z

26. Taxonomy of Projections

27. Perspective Projection Map points onto “ view plane ” along “ projectors ” emanating from “ center of projection ” (cop)

28. Perspective Projetion How many vanishing point?

29. Perspective Projection View Volume

30. Perspective Projection Compute 2D coordinates from 3D coordinates with similar triangles

31. Perspective Projection (Cont)

32. Perspective Projection Matrix 4x4 matrix representation?

33. Perspective Projection Matrix 4x4 matrix representation?

34. Perspective Vs. Parallel Perspective projection – Size varies inversely with distance – looks realistic –Distance and angles are not(in general) preserved –Parallel line do not (in general) remain parallel Parallel projection –Good for exact measurements –Parallel lines remain parallel –Angles are not (in general) preserved –Less realistic looking