1 / 17

Viewing Transformations

Viewing Transformations. Viewing parameters Viewing projections - Parallel - Parallel orthographic projection - Parallel oblique projection. Viewing transformations. Viewing transformations are concerned with projecting 3D objects onto 2D surfaces. View up-direction. U. Viewing

morse
Download Presentation

Viewing Transformations

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. Viewing Transformations Viewing parameters Viewing projections - Parallel - Parallel orthographic projection - Parallel oblique projection

  2. Viewing transformations • Viewing transformations are concerned with projecting 3D objects onto 2D surfaces

  3. View up-direction U Viewing distance View plane N V Handedness axis Direction of gaze View Reference Point (eye position) Virtual camera Yw Zw Xw

  4. Projection plane Projection lines Y X Z Viewing projections • Parallel • centre of projection in the infinity • the projection lines are parallel

  5. Parallel orthographic projection • Projection lines perpendicular to the projection plane • Transformation matrix xp = x yp = y

  6. Parallel oblique projection • Projection lines parallel, but not perpendicular to the projection plane Projection lines Projection plane Y X Z

  7. Y a L sin P' L P( 0,0 1) a Z a L cos X Parallel oblique projection Matrix

  8. Parallel projections • preserve relative dimensions of the objects • do not give realistic appearance

  9. Perspective projections • The projection lines meet in one or more projection centre(s) Y X COP (Centre of Projection) Z

  10. P' COP at the centre of the viewing coordinate system • projection plane is at distance D from the COP • on the positive part of the z axis (ZCOP = 0) y P COP z D

  11. P = (x, y, z) P' = (xp, yp, D )

  12. Transformation matrix Example point transformation

  13. P' Projection plane at the centre of the viewing coordinate system • projection plane is at distance D from the COP • on the negative part of the z axis (ZCOP = -D) y P COP z D

  14. y P COP P' z D P = (x, y, z) P' = (xp, yp, 0 )

  15. Transformation matrix Example point transformation

  16. Perspective projections • do not preserve relative dimensions • give realistic appearance

  17. Clipping • Used to restrict the depth of the projected scene Back clipping plane Front clipping plane View plane

More Related