2 DIMENSIONAL VIEWING

1. Computer Engineering Kocaeli University 2 DIMENSIONAL VIEWING

2. 3D View Scene Model 3D World Scene Model Model Viewing Pipeline Revisited Modeling Transformations Viewing Transformations M1 V M2 M3 WCS VCS MCS Rasterization 2D/3D Device Scene P Clip Normalize NDCS Projection DCS SCS 2D Image

3. Model - World • Model coordinates to World coordinates:Modelling transformations Model coordinates: 1 circle (head), 2 circles (eyes), 1 line group (nose), 1 arc (mouth), 2 arcs (ears). With their relative coordinates and sizes World coordinates: All shapes with their absolute coordinates and sizes. circle(0,0,2) circle(-.6,.8,.3) circle(.6,.8,.3) lines[(-.4,0),(-.5,-.3),(.5,.3),(.4,0)] arc(-.6,0,.6,0,1.8,180,360) arc(-2.2,.2,-2.2,-.2,.8,45,315) arc(2.2,.2,2.2,-.2,.8,225,135)

4. World - Viewing • World coordinates to Viewing coordinates:Viewing transformations World coordinates Viewing coordinates:Viewers position and view angle. i.e. rotated/translated

5. View - Device • Projection: 3D to 2D. Clipping depends on viewing frame/volume. Normalization: device independent coordinates Viewing coordinates: Device Independent Coordinates: Invisible shapes deleted, others reduced to visible parts. 3 arcs, 1 circle, 1 line group

6. Unit measures Pixels Device Independen Coordinates – Screen or Device Coordinates • Device Independent Coordinates to Device Coordinates. Rasterization Screen Coordinates or Device Coordinates Device Independent Coordinates

7. 2D Viewing • World coordinates to Viewing coordinates • Window to Viewport. Window: A region of the scene selected for viewing (also called clipping window)Viewport: A region on display device for mapping to window Viewport Window World Coordinates Viewing Coordinates

8. Clipping Window vs. Viewport • The clipping window selects what we want to see in our virtual 2D world. • The viewport indicates where it is to be viewed on the output device (or within the display window) • By default the viewport have the same location and dimensions of the GLUT display window you create • But it can be modified so that only a part of the display window is used for OpenGL display

9. The clipping window Rectangular Window Rotated Window

10. Transformations Between Coordinates Systems • Rule: Transform one coordinate frames towards the other in the opposite direction of the representation change.

11. Transformations Between Coordinates Systems • Two Steps: • Translate so that the origin (x0,y0) of the x´y´ system is moved to the origin of the xy system. • Rotate the x´ axis onto the x axis.

12. Transformations Between Coordinates Systems

13. World-coordinates to Viewing Coordinates • Mwc,vc= R·T

14. Coordinate Representation • Normalized Coordinates: A graphic system first converts world coordinate positions to normalized device coordinates, in the range 0 to 1.This makes the system independent of the output-devices. • An initial modeling coordinate position is transferred to a device coordinate position with the sequence • The modeling and world coordinate positions in this transformation can be any floating values; normalized coordinates satisfy the inequalities

15. Normalization

16. Calculating Device Coordinates • Coordinate transformation:Different sizes and/or height width ratios? • For any point: • should hold. And;

17. The transformation matrix for the viewing transformation EKRAN

18. The transformation matrix for the viewing transformation

19. What happens if Sx=Sy=1 • ???

20. Say we want to map this to a 640x480 viewport Where is the black point mapped in screen coordinates? Example 0.4 0.3 -0.4 -0.2 480 640

21. OpenGL Related

22. OpenGL 2D Viewing Functions • OpenGL, GLU, and GLUT provide functions to specify clipping windows, viewports, and display windows within a video screen.

23. OpenGL 2D Viewing Example • 2 Viewports • One triangle is displayed in two colors and orientations in 2 viewports glutInitWindowSize (600, 300); glClear (GL_COLOR_BUFFER_BIT); glColor3f(0.0, 0.0, 1.0); glViewport(0, 0, 300, 300); drawCenteredTriangle(); glColor3f(1.0, 0.0, 0.0); glViewport(300, 0, 300, 300); glRotatef(90.0, 0.0, 0.0, 1.0); drawCenteredTriangle();

24. Setting up a 2D Clipping-Window • glMatrixMode (GL_PROJECTION) • glLoadIdentity (); //reset, so that new viewing parameters are not combined with old ones (if any) • gluOrtho2D (xwmin, xwmax, ywmin, ywmax); or • glOrtho (xwmin, xwmax, ywmin, ywmax, zwmin, zwmax); • Objects within the clipping window are transformed to normalized coordinates (-1,1)

25. Setting up a Viewport • glViewport (xvmin, yvmin, vpWidth, vpHeight); • All the parameters are given in integer screen coordinates relative to the lower-left corner of the display window. • If we do not invoke this function, by default, a viewport with the same size and position of the display window is used (i.e., all of the GLUT window is used for OpenGL display)

26. Creating a GLUT Display Window • glutInitWindowPosition (xTopLeft, yTopLeft); • the integer parameters are relative to the top-left corner of the screen • glutInitWindowSize (dwWidth, dwHeight); • glutCreateWindow (“Title of Display Window”); • glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB) • Specification of the buffer that will be used • glClearColor (red, green, blue, alpha) • Specify the background color

27. Multiple GLUT windows • Multiple windows may be created within an OpenGL program • Need window ids to manage multiple windows • windowID = glutCreateWindow(“Window1”); • glutDestroyWindow (windowID) // to distroy the window • General functions (like glutInitDisplayMode) are applied to the current display window. We can set the current window to a specific window with: • glutSetWindow (windowID);

28. Other functions • GLUT provide functions to relocate, resize, minimize, resize to fullscreen, change window title, hide, show, bring to front, or send to back, select a specific cursor for the current display window. (pages 309-311 in the textbook)

29. Display callback function • Each separate GLUT window can have its own function to specify what will be drawn inside. E.g., • glutSetWindow (w1); • glutDisplayFunction (wireframeDisplay); • glutSetWindow (w2); • glutDisplayFunction (solidDisplay); • Display callback functions are called only when GLUT determines that the display content should be renewed. To update the display manually call: glutPostRedisplay(); • glutIdleFunc (functionName) could be used in animations