1 / 48

3D Viewing

3D Viewing. 3D Viewing Transformation Pipeline. MC. Modeling Transformation. WC. Viewing Transformation. VC. Projection Transformation. PC. Normalization Transformation and Clipping. NC. Viewport Transformation. DC. 3D Viewing Transformation Pipeline. MC. Modeling Transformation.

sol
Download Presentation

3D Viewing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 3D Viewing

  2. 3D Viewing Transformation Pipeline MC Modeling Transformation WC Viewing Transformation VC Projection Transformation PC Normalization Transformation and Clipping NC Viewport Transformation DC

  3. 3D Viewing Transformation Pipeline MC Modeling Transformation WC Viewing Transformation VC Projection Transformation PC Normalization Transformation and Clipping NC Viewport Transformation DC

  4. yw yv xv V zv P0 xw zw 3D Viewing V view up vector P0 = (x0, y0, z0) view point N viewplane normal Viewplane is at point zvp in negative zv direction V is perpendicular to N N

  5. yv xv zv 3D Viewing xv yv zv is a right-handed viewing coordinate system v u n

  6. yw yw xw xw zw zw 3D Viewing Transformation from World to Viewing Coordinates: 1. Translate viewing coordinate origin to the origin of world coordinate system 2. Apply rotations to align xv yv zv axes with xw yw zw axes respectively MWC,VC = R . T yv xv zv P0 yv xv zv

  7. 3D Viewing Transformation Pipeline MC Modeling Transformation WC Viewing Transformation VC Projection Transformation PC Normalization Transformation and Clipping NC Viewport Transformation DC

  8. Projections isometric axonometric orthogonal Parallel cavalier oblique cabinet Perspective

  9. Projections view plane view plane Perspective projection Parallel projection

  10. Orthogonal Projection

  11. Orthogonal Projection Axonometric: displays more than one face of an object Isometric: projection plane intersects each coordinate axis at the sane distance from the origin Isometric

  12. 3D Viewing Transformation Pipeline MC Modeling Transformation WC Viewing Transformation VC Projection Transformation PC Normalization Transformation and Clipping NC Viewport Transformation DC

  13. yv xv zv Orthogonal Projection Clipping view volume clipping window far plane near plane

  14. Orthogonal Projection Normalization Mortho,norm . R . T ynorm znorm (1,1,1) xnorm yv (-1,-1,-1) xv zv

  15. Oblique Projection Oblique projection: projection path is not perpendicular to the view plane view plane

  16. Oblique Projection yv (xp,yp,zvp) xv zv a f (x,y,zvp) (x,y,z)

  17. Oblique Projection xp = x + L1 (zvp – z) cos f yp = y + L1 (zvp – z) sin f shearing transformation L1 f view plane

  18. Oblique Projection Cavalier Projection Cabinet Projection f = 450 f = 300 f = 450 f = 300

  19. yv xv zv Oblique Projection (xp,yp,zvp) window a f Vp view volume (x,y,zvp) Vp (x,y,z)

  20. Oblique Projection MWC,VC . Morth,norm . Mobl Mobl,norm window window shear Vp Vp orthogonal coordinates

  21. Parallel Projection View plane Viewer’s position

  22. Perspective Projection View plane Viewer’s position

  23. Perspective Projection yv projection reference point (prp) xv zv view plane

  24. Perspective Projection yv (xp,yp,zvp) (xprp,yprp,zprp) zv xv (x,y,z)

  25. Perspective Projection At any point (xp, yp, zp) along the projection line: zp = zvp xp = x (zprp-zvp) / (zprp-z) + xprp (zvp-z) / (zprp-z) yp = y (zprp-zvp) / (zprp-z) + yprp (zvp-z) / (zprp-z)

  26. Perspective Projection Vanishing point y x z One-point perspective projection x-axis vanishing point z-axis vanishing point Two-point perspective projection

  27. Perspective Projection Far plane Near plane Viewer’s position

  28. Perspective Projection Far plane Near plane Viewer’s position

  29. Perspective Projection Clipping window Rectangular Frustum view volume projection reference point (prp) q Far clipping plane Near clipping plane

  30. Perspective Projection P=(x, y, z, 1) Ph=(xh, yh, zh, h) xp = x (zprp-zvp) / (zprp-z) + xprp (zvp-z) / (zprp-z) yp = y (zprp-zvp) / (zprp-z) + yprp (zvp-z) / (zprp-z) h = zprp-z xh = x (zprp-zvp) + xprp (zvp-z) yp = y (zprp-zvp) + yprp (zvp-z) xp = xh /h yp = yh /h

  31. Perspective Projection Ph= Mpers . P Mpers = zprp-zvp 0 -xprp xprpzprp 0 zprp-zvp -yprp yprpzprp 0 0 sz tz 0 0 -1 zprp

  32. Perspective Projection Symmetric Frustum Frustum center line Far plane view volume Clipping window Near plane q view plane (xprp, yprp, zvp) (xprp, yprp, zprp)

  33. Perspective Projection 200 600

  34. Perspective Projection Then apply normalization transformation Parallelepiped view volume Symmetric Frustum Perspective Mapping

  35. Perspective Projection 1. Transform to asymmetric frustum (z-axis shear) 2. Normalize viewvolume Parallelepiped view volume Oblique Frustum Perspective Mapping (xprp, yprp, zprp)=(0,0,0)

  36. Perspective Projection shzx= -(xwmin+xwmax)/2.znear Mshear = shzy= -(ywmin+ywmax)/2.znear assuming that viewplane is at the position of the near plane Mpers = Moblpers= Mpers . Mshear 1 0 shzx 0 0 1 shzy 0 0 0 1 0 0 0 0 1 znear 0 0 0 0 -znear 0 0 0 0 sz tz 0 0 -1 0

  37. xv PRP zv Perspective Projection Normalization ynorm (xwmax, ywmaz, zfar) transformed frustum znorm (1,1,1) xnorm yv (-1,-1,-1) (xwmin, ywmin, znear)

  38. Perspective Projection Mnormpers = Mxyscale . Moblpers = = -znearsx 0 sx(xwmin+xwmax)/2 0 0 -znearsy sy(ywmin+ywmax)/20 0 0 sz tz 0 0 -1 0 -2znearsx/(xwmax-xwmin) 0 (xwmin+xwmax)/(xwmax-xwmin) 0 0 -2znearsy/(ywmax-ywmin) (ywmin+ywmax)/(ywmax-ywmin)0 0 0 (znear+zfar)/(znear-zfar) -2.znear.zfar/(znear-zfar) 0 0 -1 0

  39. Perspective Projection For symmetric frustum with field-of-view angle q: Mnormsymmpers = Mnormsymmpers . R . T cot(q/2)/aspect 0 0 0 0 cot(q/2) 00 0 0 (znear+zfar)/(znear-zfar) -2.znear.zfar/(znear-zfar) 0 0 -1 0

  40. 3D Viewing Transformation Pipeline MC Modeling Transformation WC Viewing Transformation VC Projection Transformation PC Normalization Transformation and Clipping NC Viewport Transformation DC

  41. Viewport Transformation Mnormviewvol,3Dscreen = ynorm (xvmax, yvmax, 0) znorm viewport screen (1,1,1) xnorm (-1,-1,-1) (xvmin, yvmin, 0) (xvmax-xvmin)/2 0 0 (xvmin+xvmax)/2 0 (yvmax-yvmin)/2 0 (yvmin+yvmax)/2 0 0 1/2 1/2 0 0 0 1

  42. 3D Clipping Inside if: -h≤xh≤h, -h≤yh≤h, -h≤zh≤h Use sign bits of h±xh, h±yh, h±zh to set bit1-bit6 6 5 4 3 2 1 far near top bottom right left ynorm znorm (1,1,1) xnorm (-1,-1,-1)

  43. Point Clipping Test sign bits of h±xh, h±yh, h±zh If region code is 000000 then inside otherwise eliminate

  44. Line Clipping 1. Test region codes • if 000000 for both endpoints => inside • if RC1 V RC2 = 000000 => trivially accept • if RC1Λ RC2 ≠ 000000 => trivially reject 2. If a line fails the above tests, use line equation to determine whether there is an intersection

  45. Polygon Clipping 1. Check coordinate limits of the object • if all limits are inside all boundaries => save the entire object • if all limits are outside any one of the boundaries => eliminate the entire object 2. Otherwise process the vertices of the polygons • Apply 2D polygon clipping Clip edges to obtain new vertex list. • Update polygon tables to add new surfaces If the object consists of triangle polygons, use Sutherland-Hodgman algorithm.

  46. OpenGL • glMatrixMode (GL_MODELVIEW) • gluLookAt (x0, y0, z0, xref, yref, zref, Vx, Vy, Vz) Designates the origin of the viewing reference frame as, • the world coordinate position P0=(x0, y0, z0) • the reference position Pref=(xref, yref, zref) and • the viewup vector V=(Vx, Vy, Vz) • glMatrixMode (GL_PROJECTION) • gluOrtho (xwmin, xwmax, ywmin, ywmax, dnear, dfar) Orthogonal projection

  47. OpenGL • glMatrixMode (GL_PROJECTION) • gluPerspective (theta, aspect, dnear, dfar) • theta: field-of-view angle (00 – 1800) • aspect: aspect ratio of the clipping window (width/height) • dnear, dfar: positions of the near and far planes (must have positive values) • glFrustum (xwmin, xwmax, ywmin, ywmax, dnear, dfar) • if xwmin = -xwmax and ywmin = -ywmax then symmetric view volume • glViewport (xvmin, yvmin, vpWidth, vpHeight) • xvmin, yvmin: screen position of the lower-left corner of the viewport relative to the lower-left corner of the display window • vpWidth, vpHeight: width and height of the viewport

  48. OpenGL float eye_x, eye_y, eye_z; void init (void) { glClearColor (1.0, 1.0, 1.0, 0.0); // Set display-window color to white. glMatrixMode (GL_PROJECTION); // Set projection parameters. glLoadIdentity(); gluPerspective(80.0, 1.0, 50.0, 500.0); // degree, aspect, near, far glMatrixMode (GL_MODELVIEW); eye_x = eye_y = eye_z = 60; gluLookAt(eye_x, eye_y, eye_z, 0,0,0, 0,1,0); // eye, look-at, view-up } void main (int argc, char** argv) { glutInit (&argc, argv); // Initialize GLUT. glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB); // Set display mode. glutInitWindowPosition (50, 500); // Set top-left display-window position. glutInitWindowSize (400, 300); // Set display-window width and height. glutCreateWindow ("An Example OpenGL Program"); // Create display window. glViewport (0, 0, 400, 300); init ( ); // Execute initialization procedure. glutDisplayFunc (my_objects); // Send graphics to display window. glutReshapeFunc(reshape); glutKeyboardFunc(keybrd); glutMainLoop ( ); // Display everything and wait. }

More Related