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Viewing 1

http:// www.ugrad.cs.ubc.ca /~cs314/Vjan2016. University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2016. Viewing 1. Viewing. Using Transformations. three ways modelling transforms place objects within scene (shared world) affine transformations viewing transforms

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Viewing 1

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  1. http://www.ugrad.cs.ubc.ca/~cs314/Vjan2016 University of British Columbia CPSC 314 Computer Graphics Jan-Apr 2016 Viewing 1

  2. Viewing

  3. Using Transformations • three ways • modelling transforms • place objects within scene (shared world) • affine transformations • viewing transforms • place camera • rigid body transformations: rotate, translate • projection transforms • change type of camera • projective transformation

  4. Rendering Pipeline Scene graphObject geometry ModellingTransforms ViewingTransform ProjectionTransform

  5. Rendering Pipeline • result • all vertices of scene in shared 3D world coordinate system Scene graphObject geometry ModellingTransforms ViewingTransform ProjectionTransform

  6. Rendering Pipeline • result • scene vertices in 3D view (camera) coordinate system Scene graphObject geometry ModellingTransforms ViewingTransform ProjectionTransform

  7. Rendering Pipeline • result • 2D screen coordinates of clipped vertices Scene graphObject geometry ModellingTransforms ViewingTransform ProjectionTransform

  8. Viewing and Projection • need to get from 3D world to 2D image • projection: geometric abstraction • what eyes or cameras do • two pieces • viewing transform: • where is the camera, what is it pointing at? • perspective transform: 3D to 2D • flatten to image

  9. Coordinate Systems • result of a transformation • names • convenience • animal: leg, head, tail • standard conventions in graphics pipeline • object/modelling • world • camera/viewing/eye • screen/window • raster/device

  10. viewing transformation projection transformation modeling transformation viewport transformation Projective Rendering Pipeline OCS - object/model coordinate system WCS - world coordinate system VCS - viewing/camera/eye coordinate system CCS - clipping coordinate system NDCS - normalized device coordinate system DCS - device/display/screen coordinate system object world viewing O2W W2V V2C VCS WCS OCS clipping C2N CCS perspectivedivide normalized device N2D NDCS device DCS

  11. viewing transformation modeling transformation Viewing Transformation y image plane VCS z OCS z y Peye y x x WCS object world viewing VCS OCS WCS Mmod Mcam modelviewmatrix

  12. Basic Viewing • starting spot - GL • camera at world origin • probably inside an object • y axis is up • looking down negative z axis • why? RHS with x horizontal, y vertical, z out of screen • translate backward so scene is visible • move distance d = focal length

  13. Convenient Camera Motion • rotate/translate/scale versus • eye point, gaze/lookatdirection, up vector • lookAt(ex,ey,ez,lx,ly,lz,ux,uy,uz)

  14. Convenient Camera Motion • rotate/translate/scale versus • eye point, gaze/lookat direction, up vector y lookat x Pref WCS view up z eye Peye

  15. y lookat x Pref WCS view v VCS up z eye Peye u w Placing Camera in World Coords: V2W • treat camera as if it’s just an object • translate from origin to eye • rotate view vector (lookat – eye) to w axis • rotate around w to bring up into vw-plane

  16. y lookat x Pref WCS view v VCS up z eye Peye u w Deriving V2W Transformation • translate origin to eye

  17. y lookat x Pref WCS view v VCS up z eye Peye u w Deriving V2W Transformation • rotate view vector (lookat – eye) to w axis • w: normalized opposite of view/gaze vector g

  18. y lookat x Pref WCS view v VCS up z eye Peye u w Deriving V2W Transformation • rotate around w to bring up into vw-plane • u should be perpendicular to vw-plane, thus perpendicular to w and up vector t • v should be perpendicular to u and w

  19. Deriving V2W Transformation • rotate from WCS xyz into uvw coordinate system with matrix that has columns u, v, w • reminder: rotate fromuvwto xyz coord sys with matrix M that has columnsu,v,w MV2W=TR

  20. V2W vs. W2V • MV2W=TR • we derived position of camera as object in world • invert for lookAt: go from world to camera! • MW2V=(MV2W)-1=R-1T-1 • inverse is transpose for orthonormal matrices • inverse is negative for translations

  21. V2W vs. W2V • MW2V=(MV2W)-1=R-1T-1

  22. Moving the Camera or the World? • two equivalent operations • move camera one way vs. move world other way • example • initial GL camera: at origin, looking along -zaxis • create a unit square parallel to camera at z = -10 • translate in z by 3 possible in two ways • camera moves to z = -3 • Note GL models viewing in left-hand coordinates • camera stays put, but world moves to -7 • resulting image same either way • possible difference: are lights specified in world or view coordinates?

  23. World vs. Camera Coordinates Example a = (1,1)W C2 b = (1,1)C1 = (5,3)W c c = (1,1)C2= (1,3)C1= (5,5)W b a C1 W

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