History of projection - PDF Free Download

History of projection Ancient times: Greeks wrote about laws of perspective Renaissance: perspective is adopted by artists Duccio c. 1308

History of projection Later Renaissance: perspective formalized precisely da Vinci c. 1498

Plane projection in drawing [Carlbom & Paciorek 78]

Pinhole imaging Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Plane projection in drawing [CS 417 Spring 2002]

Plane projection in photography This is another model for what we are doing applies more directly in realistic rendering [CS 417 Spring 2002]

Plane projection in photography [Richard Zakia]

Jovan Popovic at MIT

modeling WorldCoords viewing glortho gluperspective glfrustrum Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Viewing transformation [Cornell] the view matrix rewrites all coordinates in eye space

void glulookat( GLdouble eyex, GLdouble eyey, GLdouble eyez, GLdouble centerx, GLdouble centery, GLdouble centerz, GLdouble upx, GLdouble upy, GLdouble upz ); glmatrixmode(gl_modelview); glloadidentity(); glulookat( 0.0, 0.0, 5.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0); glmatrixmode(gl_projection); glloadidentity(); gluperspective(50.0, 1.0, 3.0, 7.0);

glulookat() ModelView Matrix

Q about glulookat glulookat(eye, at, up) (A) glulookat(7,0,3, 2,0,3, 0,1,0); (B) glulookat(2,0,3, 7,0,3, 0,1,0); (C) gltranslate(-2,0,-3); glrotatey(-90); (D) glulookat(2,0,3, 7,0,3, 0,-1,0);

modeling WorldCoords viewing glortho gluperspective glfrustrum Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Classical projections Emphasis on cube-like objects traditional in mechanical and architectural drawing Planar Geometric Projections Parallel Perspective Multiview Orthographic Orthographic Axonometric Oblique One-point Two-point Three-point [after Carlbom & Paciorek 78]

Parallel projection Viewing rays are parallel rather than diverging like a perspective camera that s far away

Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Multiview orthographic [Carlbom & Paciorek 78] projection plane parallel to a coordinate plane projection direction perpendicular to projection plane

Multiview orthographic [Carlbom & Paciorek 78]

Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

[Marschner] [Levoy] Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Q about gluperspective gluperspective(fovydegrees, aspect, znear, zfar); (A)gluPerspective(50, 1, 1, 1000); (B) gluperspective(50, 1.3, 0, 1000); (C) gluperspective(30, 1.3, 2, 15); (D)gluPerspective(180, 1, 3, 7); (E) Don t know

http://www.cs.princeton.edu/~min/cs426/jar/threed.html Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Focal length: pinhole optics Verify focal length equivalence of pinhole and lens What is the view angle for a given focal length & 24x36mm film f d pinhole s Film/ sensor pinhole scene Film/ sensor Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Lenses 24mm 50mm 135mm Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Focal length: pinhole optics What happens when the focal length is doubled? Projected object size Amount of light gathered f d 2f s Film/ sensor pinhole scene Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Focal length: pinhole optics What happens when the focal length is doubled? What happens when the scene is twice as far? How do we get the same relative object size when the focal length is doubled? What is the difference then? Is it equivalent to get closer and to zoom in? f d 2f 2d s Film/ sensor pinhole scene Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Perspective vs. viewpoint Focal lens does NOT ONLY change subject size Same size by moving the viewpoint Different perspective (e.g. background) Snapshot-Perspective-Speed, aperture-filter-lighting-processing & Print-Make up-retouching Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Perspective vs. viewpoint Telephoto makes it easier to select background (a small change in viewpoint is a big change in background. Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Perspective vs. viewpoint Portrait: distortion with wide angle Why? Wide angle Standard Telephoto Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Focal length: pinhole optics What happens when the film is half the size? Application: Real film is 36x24mm On the 20D, the sensor is 22.5 x 15.0 mm Conversion factor on the 20D? On the SD500, it is 1/1.8 " (7.18 x 5.32 mm) What is the 7.7-23.1mm zoom on the SD500? f d 2f ½s Film/ sensor pinhole scene Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Exposure Two main parameters: Aperture (in f stop) Shutter speed (in fraction of a second) Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Pinhole limit Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Do we ever want the frustum to be non symetric for left/right? Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu

Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu Oblique Perspective Projection

Frédo Durand MIT Computer Science and Artificial Intelligence Laboratory - fredo@mit.edu