3D viewing -a.pdf

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3D Viewing

Chapter 7

3D pipeline

3D Viewing coordinates and viewing transformations

Projections

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3D Viewing Overview

More complicated than 2D because there are more possibilities.

Coordinate reference for viewing needs more parameters than in 2D.

What kind of projection?

How to give the illusion of depth?

Identifying visible lines and surfaces

Surface rendering

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Camera Position and Orientation

To know how to display a 3D scene, we need to know

Where we are looking from

What direction we are looking

Which direction is up

One way to model this is to think of how you take a picture with a camera

The film plane is where the image will be.

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If you look at a wire frame diagram, it can be difficult to tell what is in front.

This can also be true for solid figures if the color is flat.

Possible solutions

Make brightness inversely proportional to distance from viewer.

Make distant objects fuzzier like the effect of haze in real life.

Give visible lines different brightness (or color) than invisible ones.

Render surfaces with lighting effects which gives cues about orientation.

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3D Viewing Pipeline

Use a similar sequence to what we did in 2D.

You need more information to specify the viewing transformation.

You need to specify how to project from 3D to 2D.

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Specifying Viewing Coordinates

Specify a viewing reference frame by

giving

P0 = (x0, y0, z0) which is the view-

ing origin (eye or camera position).

V which is the view-up vector

zview axis eye is usually looking

toward zview = inf.

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uvn Coordinate Reference Frame

Usually consider a viewing plane that is perpendicular to zview .

View-up vector establishes where up is in the viewing plane.

It need to be perpendicular to zview.

Third coordinate direction is determined by requirement that the directionsbe orthogonal.

uvn coordinate system defined by

n = N|N| = (nx, ny, nz)

u = VN|V| = (ux, uy, uz)

v = n u = (vx, vy, vz)

yview

xview

zview

nu

v

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World to Viewing Coordinate Transformations

Translate viewing origin to world origin

T =

1 0 0 x0

0 1 0 y0

0 0 1 z0

0 0 0 1

Rotate to align viewing and world coordinate axes

B =

ux uy uz 0

vx vy vz 0

nx ny nz 0

0 0 0 1

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Composite transform is

MW CV C = R T =

ux uy uz u P0

vx vy vz v P0

nx ny nz n P0

0 0 0 1

where P0 is the vector from the world coordinate origin to the viewing coor-

dinate origin.

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Projections

Parallel

Coordinates are transformed

along parallel lines

Relative sizes are preserved

Parallel lines remain parallel

Perspective

Projection lines converge at a

point

More distant objects are rela-

tively smaller

Closer to the way we actually see

things

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3D viewing -a.pdf