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Shape defined Panoramas

John Brosz & Faramarz Samavati University of Calgary Shape Modeling International – June 2010. Shape defined Panoramas. Outline. Scenario/Motivation Goals Related Work Observations Projection Surface Formulation Rendering Applications.

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Shape defined Panoramas

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  1. John Brosz & Faramarz Samavati University of Calgary Shape Modeling International – June 2010 Shape defined Panoramas

  2. Outline Scenario/Motivation Goals Related Work Observations Projection Surface Formulation Rendering Applications

  3. Figure from Transformations & Projection in Computer Graphics, Salomon, Springer, 2006

  4. i = R Figure from Transformations & Projection in Computer Graphics, Salomon, Springer, 2006

  5. z j = + ( i, j ) = ( R , , + ) Figure from Transformations & Projection in Computer Graphics, Salomon, Springer, 2006

  6. Spherical Projection Equation ( i, j ) =

  7. Goals Create panoramas that: Allow for exploration & customization Are defined by modeling Build on existing intuition Allow for visual understanding Single Viewpoint: no “slit cameras”.

  8. Related WorkPanoramas from Perspective Images Image from http://www.cirq.de/mosaicing.html Image from Szeliski & Shum, Creating full view panoramic image mosaics and environment maps, Siggraph 1997

  9. Related WorkCorrecting Distortion Images from Carrol, Agrawala & Agarwala, Optimizing Content-Preserving Projections for Wide-Angled Images, Siggraph 2009

  10. Related WorkSingle-Center Projections Normal Map Panorama Images from Trapp & Döllner, Generalization of Single-Center Projections Using Projection Tile Screens, VISIGRAPP, 2008

  11. Common Panoramas

  12. Observations Shapes are associated with panoramas

  13. Observations Shapes are associated with panoramas Angular change

  14. Observations ( i, j ) = ( R , , + ) ( i, j ) = Shapes are associated with panoramas Angular Change Parameterization is important

  15. Shape Defined Panoramas • Defined by two curves • Outline: closed, controls horizontal sampling

  16. Shape Defined Panoramas • Defined by two curves • Outline: closed, controls horizontal sampling

  17. Shape Defined Panoramas • Defined by two curves • Outline: closed, controls horizontal sampling • Profile: open, controls vertical sampling

  18. Shape Defined Panoramas • Defined by two curves • Outline: closed, controls horizontal sampling • Profile: Open, controls vertical sampling • Curves parameterized by arc-length

  19. Shape Defined Panoramas Outline Profile Extrusion Surface Mix between surface of revolution and surface extrusion

  20. Shape Defined Panoramas Outline Profile Panorama Surface Mix between surface of revolution and surface extrusion

  21. Example 1 Outline Profile

  22. Example 2 Outline

  23. Before Example 2 After

  24. Shape Defined Panoramas Multiple Profiles

  25. Shape Defined Panoramas Multiple Profiles

  26. Rendering Ray-tracing Image Re-sampling Nonlinear Projection on GPU

  27. Rendering x x Ray-tracing

  28. Rendering Image Re-sampling

  29. Rendering • Nonlinear Projection on GPU • Find projection equation • Project vertices with equation on GPU • Be careful with seams

  30. Find Projection Equation World Coordinates Normalized Device Coordinates

  31. Find Projection Equation • Only surfaces that map onto spherical coordinates. • Projection Surface: Q(u,v) = (x,y,z) • Projection Volume: t (0,0,0) + (1-t) Q(u,v) • Find spherical coordinates of p = (x,y,z) • Search for u,vs.t. Q(u,v) with same spherical coords. • t = || p || || Q(u,v) ||

  32. Find Projection Equation • Search for u,vs.t. Q(u,v) with same spherical coords.

  33. Project Vertices with GPU Triangle w/ Linear Fill Algorithm Nonlinearly ProjectedTriangle • Override projection matrix with nonlinear projection equation. • This only moves vertices! Triangles are filled as if linearly projected.

  34. Seams

  35. Seams

  36. Rendering Performance Single pass algorithm 60 fps with 100K polygons on NVIDIA 8800 GTS

  37. Application:Custom Panorama

  38. Application:Re-projecting Panoramas

  39. Application:Animated Projection

  40. Application:Interactive Local Editing

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