How do we control what we see?

1. How do we control what we see? • World • Window and viewport • Camera

2. Window placement • Window size • Mapping viewport

3. Window

4. Window

5. Zoom: • Set_window( -60, +60, -30, +30 )

6. Zoom • Set_window( -21, +21, -11, +11 )

7. Window • Pan A. Set_window(-40, +20,-15,+15) B.Set_window(-20,+40,-15,+15)

8. Window in OpenGL glutInitWindowSize(W,H); glutInitWindowPosition(100,100);

9. Viewport • define a viewport in Normalized Device Coordinates (NDC) • Map from NDC or Physical device using notes from previous class on mappings Set_viewport2(Xvmin,Xvmax,Yvmin,Yvmax)

10. Now Map [a,b] [c,d] • First map [a,b] to [0,1] • (We already did this) • Then map [0,1] to [c,d]

11. Now Map [a,b] [c,d] • Scale [0,1] by (d-c) • Then translate by c • That is, in 1D homogeneous form:

12. All Together: [a,b] [c,d]

13. Now Map Rectangles

14. Transformation in x and y

15. This is the Viewport Transformation • Good for mapping objects from one coordinate system to another • This is what we do with windows and viewports 15

16. Viewport Set_window( -30, +30, -15, +15); Set_viewport(0.0, 0.5, 0.0, 0.5); -- lower left Draw_house; Set_viewport(0.5, 1.0, 0.0, 0.5); -- lower right Draw_house; Set_viewport(0.0, 0.5, 0.5, 1.0); -- upper left Draw_house; Set_viewport( 0.5, 1.0, 0.5, 1.0); -- upper right Draw_house;

17. Viewport in OpenGL void glViewport( GLint x, GLint y, GLsizei width, GLsizei height ) x, y Specify the lower left corner of the viewport rectangle, in pixels. The initial value is (0,0). width, height Specify the width and height of the viewport. When a GL context is first attached to a window, width and height are set to the dimensions of that window.

18. ViewTransformations • Viewport

19. Specifying Camera

20. Synthetic camera model

21. 3D Viewing Projections

22. Perspective Projection Eye = e Gaze = LookAt = g Up = y Distance to viewplane = d Z = distance to object on z axis viewplane y yp g e d z

25. Vanishing Points: One Point Perspective

26. Vanishing Points: Two Point Perspective

27. Three-Point Perspective

28. http://www.khulsey.com/3_point_perspective.html

29. Perspective

30. y x From side User’s point of view viewplane y z z Out of screen x Out of screen

33. From the Side viewplane y yL z zL x xL Out of screen Out of screen

35. Frustum Perspective Specifying perspective view in OpenGL

36. glFrustum void glFrustum(GLdouble left, GLdouble right, GLdouble bottom, GLdouble top, GLdouble near, GLdouble far);

37. gluPerspective aspect = w/h void gluPerspective(GLdouble fovy, GLdouble aspect, GLdouble near, GLdouble far);

39. Positioning the Camera • Use gluLookAt to specify • Eye location • “Look-at” point • “up” vector • gluLookAt(10,10,10,1,2,3,0,0,1); • Eye is (10,10,10) • Look at point is (1,2,3) • Up is (0,0,1) • Usually done in GL_PROJECTION matrix and combined with perspective matrix

40. Assignment #3

41. Credits • Slides and text • Rich Riesenfeld’s Introduction to CG slides • SIGGRAPH Educators Hypercard slides • http:///www.siggraph.org/education/materials/HyperGraph/viewing/view3d/3dprojec.htm • Some Image from Ed Angel’s book