Lecture 5 Cameras, Projection, and Image Formation

In 3D, we map points from 3-space to the projection plane (PP) along projectors emanating from the center of projection (COP) There are two basic types of projections: w Perspective - distance from COP to PP finite w Parallel - distance from COP to PP infinite Perspective vs parallel projections Perspective projections pros and cons:

Perspective Projection through Parallelly Projected Slabs for

as the distance in the image plane between the correct perspectively projected point and the point produced by the projected-slabs algo-rithm In the rendering pipeline, the difference between parallel and perspective projection appears after the world coordinates have been transformed to view coordinates To transform from view

Orthographic and Perspective Projection

Figure 10 1: Parallel view volume far plane near plane d n d f u c x c w h Figure 10 2: Perspective view volume We construct the projection transform by considering how it will a ect the 8 corners of the original view volume, under whichever projection system is being employed 10 3 1 Constructing the canonical orthographic view vol-ume

The Geometry of Perspective Projection

-Itisthe projection of a 3D object onto a plane by a set of parallel rays orthogonal to the image plane -Itisthe limit of perspective projection as f −> ∞(i e , f /Z −>1) orthographic proj eqs: x =X, y =Y (drop Z)-Using matrix notation: xh yh zh w = 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 X Y Z 1

7 PICTORIAL Drawing

Fig 7 1 Principle of central projection In perspective projection, the perspective view formed on the picture plane is of a different size and shape as compared to the actual object II Parallel projection: is a type of projection made on a picture plane in such a way that an observer is located at an infinite distance from the object being

Parallel Projections for Stereo Reconstruction

Parallel projection has more measures kept invariant than perspective projection For 1D parallel projection, it can keep the ratio of length invariant, in addition to type, incidence and cross ratio in perspective projection As shown in Fig 5, let Mi=(xi,yi,zi), i=1,2,3 be three points on the same spatial line, the length ratio defined as 1 3 1 2

Lecture 5 Cameras, Projection, and Image Formation

Modeling Projection Projection is a matrix multiply using homogeneous coordinates: divide by third coordinate and throw it out to get image coords This is known as perspective projection • The matrix is the projection matrix • Can also formulate as a 4x4 (today’s handout does this) divide by fourth coordinate and throw last two

CS 4204 Computer Graphics 3D views and projection

•Projection of a circle in a plane not parallel to the projection plane is an ellipse Can see three principal faces of a box-like object Some optical illusions possible •Parallel lines appear to diverge Does not look real because far objects are scaled the same as near objects Used in CAD applications

CLASSICAL VIEWING how images have been formed by architects

Perspective vs Parallel •Classical viewing developed different techniques for drawing each type of projection •For graphics all projections done same way using a single pipeline perspective •Fundamental distinction between parallel and perspective viewing • even though mathematically parallel viewing is the limit of perspective

[PDF] Lecture 5 Cameras, Projection, and Image Formation

Projections - coursescswashingtonedu

Perspective Projection through Parallelly Projected Slabs for

Orthographic and Perspective Projection

The Geometry of Perspective Projection

7 PICTORIAL Drawing

Parallel Projections for Stereo Reconstruction

Lecture 5 Cameras, Projection, and Image Formation

CS 4204 Computer Graphics 3D views and projection

CLASSICAL VIEWING how images have been formed by architects