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Viewing1

Often it is helpful to envision viewing incomputer graphics using a synthetic camera We can move, orient, rotate, and snap theshutter of the camera to capture a 2D imageIntroduction to Computer Graphics - Foley, Van Dam, Feiner, Hughes & Phillips2

The camera is code which produces an image(either on screen or to file)– Object is a 3D model consisting of points, lines,surfaces, etc.– Our coordinate system for camera is different thanthat of the object u, v, n for camera x, y, z for object3

Of course it's a bit more than just “pushing thebutton” to capture the image Image acquisition requires of a number ofsteps, usually consisting of.– Specification of projection type– Specification of viewing parameters– Clipping in 3D– Projection and DisplayIntroduction to Computer Graphics - Foley, Van Dam, Feiner, Hughes & Phillips4

In general, projects consist of transforming ann-dimensional system into a system with adimension less than n We'll focus on the common 3D to 2Dprojection5

Perspective Drawing Handbook - Joseph D'Amelio6

Projection of 3D defined by straight projectionrays called projectors Rays emulate from a center of projection Rays pass through each point of an object andintersect a projection plane to form theprojection7

Usually the center of projection is a finitedistance away from the projection plane For some projections, it is convenient to think ofcenter of projection as infinitely awayIntroduction to Computer Graphics - Foley, Van Dam, Feiner, Hughes & Phillips8

Size varies inversely with respect to thedistance from the center of projection Tends to look more realistic– Cannot generally measure Shape Object distances Angles (except front faces)– Parallel lines appear no longer parallel9

Less realistic because perspectiveforeshortening is lacking Can however, use for exact measurements– Parallel lines remain parallel– Angles still only preserved for front faces10

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Any set of parallel lines not parallel to theprojection plane– Converge to a vanishing point In 3D, parallel lines meet only at infinity12

Lines parallel to x, y do not convergeIntroduction to Computer Graphics - Foley, Van Dam, Feiner, Hughes & Phillips13

Introduction to Computer Graphics - Foley, Van Dam, Feiner, Hughes & Phillips14

June Ruivivar15

Lines parallel to y do not convergeIntroduction to Computer Graphics - Foley, Van Dam, Feiner, Hughes & Phillips16

Hillcrest Building - springgrove.com17

All lines converge18

travelnow.com - Hilton New York19

Li Shen - UMass Dartmouth20

Orthographic parallel projections– Direction of projection and normal to projection planeare the same (or reverse) Oblique parallel projections– If the direction of projection is not normal toprojection plane21

Most common are top/plan, front & sideelevations– Frequently found in engineering and architecturaldrawingsIntroduction to Computer Graphics - Foley, Van Dam, Feiner, Hughes & Phillips22

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Object (3D)Shader (3D)World (3D) At RiSphere,RiPatch, . At RiShader At RiWorldBeginRaster (2D)Screen (2D)Camera (3D) 0,0 to width,height Axes: , 0,0 at center ofprojection Axes: , At RiProjection Camera at origin Axes: , , ForwardNDC (2D) 0,0 to 1,1 Axes: ,

MODELVIEWPROJECTIONObject (3D)Eye (3D)Clip (3D) When rendering Eye at origin Axes: , , Back Eye: 0,0,- Axes: , , ForwardWindow (2D)NDC (3D) 0,0 to width,height -1,-1,-1 to 1,1,1glViewport/glDepthRange

Perspective Drawing Handbook - Joseph D'Amelio 6 . 7 Projection of 3D defined by straight projection rays called projectors Rays emulate from a center of projection Rays pass through each point of an object and intersect a projection plane to form the projection .

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