1 / 13

Projections and Perspectives

Learn about the transformation from 3D model coordinates to 2D pixel coordinates, different types of projections, parallel and perspective projections, and the importance of projections in achieving realism in 3D rendering.

isnapp
Download Presentation

Projections and Perspectives

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. Projections and Perspectives Dr Nicolas Holzschuch University of Cape Town e-mail: holzschu@cs.uct.ac.za Modified by Longin Jan Latecki latecki@temple.edu

  2. 3D Model Coordinates 2D Pixel Coordinates Projections and Perspectives • We have to display our 3D model • Screen is 2D • Transformation from 3D model coordinates to 2D pixels coordinates.

  3. Projections • Representation of a 3D scene, for a virtual observer • One viewpoint: • position of the observer • One direction of view: • direction where the observer is looking • One “up vector”: • vertical for the observer

  4. Different projections • Parallel projections: • no shortening due to distance • several kinds, depending on orientation: • isometric, cavalier,… • Perspective projections: • shortening of objects in the distance • several kind, depending on orientation: • one, two, three vanishing points

  5. Parallel Projection Matrix • Parallel projection onto z=0 plane: x’=x, y’=y, w’=w • Matrix for this projection:

  6. Perspective Projection Matrix • Projection onto plane z=0, with center of projection at z=-d:

  7. Distance to projection plane d Center of Projection Projection Plane

  8. Field of view • Distance to projection plane not intuitive • Easier notion: field of view • FOV= angle, in degrees • Expresses how wide is my vision

  9. Field of view d Center of Projection 1 a -1 Projection Plane

  10. Homogeneous coordinates • Essential for perspective projection • Note the shortening of distances uses w • Impossible todo without homogeneous

  11. Other viewpoints • If we are viewing from another point? • Translations: • until viewpoint is at origin • Rotations: • until direction of viewing is on z-axis • Back to the previous case

  12. Translate Projection Rotate 3D Model Coordinates 2D Pixel Coordinates Canonical 3D coord. Canonical Coordinates • After translation, before projection: canonical 3D coordinates.

  13. Projections: discussion • Projections have several goals: • exactitude (e.g. plans for architects) • realism (view of a scene, VR) • visualization • artistic view: non-linear perspectives (e.g. Rubber Soul) • An important part of realism in 3D rendering

More Related