CAP4730: Computational Structures in Computer Graphics

3D Concepts

Outline

• Basic Idea of 3D

• Projections

• What are some things we didn’t have to worry about before?

• What are some new things we can do?

Right Handed Coordinate System

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+Y

+Z

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+Y

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Viewing a 3D world

We have a model in this world and would like to view it from a new position.

We’ll call this new position the camera or eyepoint. Our job is to figure out what the model looks like on the display plane.

+X

+Y

+Z

Parallel Projection

+X

+Y

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Perspective Projection

+X

+Y

+Z

What are some new things to think about?

Hidden Surface Removal

Visibility

Depth Cueing

How to make a 2D image appear as 3D!

• Output is typically 2D Images

• Yet we want to show a 3D world!

• How can we do this?– We can include ‘cues’ in the image that give

our brain 3D information about the scene– These cues are visual depth cues

Visual Depth Cues

• Monoscopic Depth Cues (single 2D image)

• Stereoscopic Depth Cues (two 2D images)

• Motion Depth Cues (series of 2D images)

• Physiological Depth Cues (body cues)

Monoscopic Depth Cues• Interposition

– An object that occludes another is closer• Shading

– Shape info. Shadows are included here• Size

– Usually, the larger object is closer• Linear Perspective

– parallel lines converge at a single point• Surface Texture Gradient

– more detail for closer objects• Height in the visual field

– Higher the object is (vertically), the further it is

• Atmospheric effects – further away objects are blurrier

• Brightness– further away objects are dimmer

Stereoscopic Display Issues

• Stereopsis

• Stereoscopic Display Technology

• Computing Stereoscopic Images

• Stereoscopic Display and HTDs.

• Works for objects < 5m. Why?

StereopsisThe result of the two slightly different views of the external world that our laterally-displaced eyes receive.

Time-parallel stereoscopic images

• Image quality may also be affected by– Right and left-eye images do not match in

color, size, vertical alignment.– Distortion caused by the optical system– Resolution– HMDs interocular settings– Computational model does not match viewing

geometry.

Disparity

• If an object is closer than the fixation point, the retinal disparity will be a negative value. This is known as crossed disparity because the two eyes must cross to fixate the closer object.

• If an object is farther than the fixation point, the retinal disparity will be a positive value. This is known as uncrossed disparity because the two eyes must uncross to fixate the farther object.

• An object located at the fixation point or whose image falls on corresponding points in the two retinae has a zero disparity.

Convergence Angles

i

f2

f1

D1

D2a b

c d

1

+a+c+b+d = 180

+c+d = 180

- = a+(-b) = 1+2 = Retinal Disparity

2

Stereoscopic Display

• Stereoscopic images are easy to do badly, hard to do well, and impossible to do

correctly.

Stereoscopic Displays

• Stereoscopic display systems create a three-dimensional image (versus a perspective image) by presenting each eye with a slightly different view of a scene.– Time-parallel– Time-multiplexed

Time Parallel Stereoscopic Display

Two Screens• Each eye sees a

different screen• Optical system directs

each eye to the correct view.

• HMD stereo is done this way.

Single Screen• Two different images

projected on the same screen

• Images are polarized at right angles to each other.

• User wears polarized glasses (passive glasses).

Passive Polarized Projection Issues

• Linear Polarization– Ghosting increases when you tilt head– Reduces brightness of image by about ½– Potential Problems with Multiple Screens (next

slide)

• Circular Polarization– Reduces ghosting but also reduces brightness

and crispness of image even more

Problem with Linear Polarization

• With linear polarization, the separation of the left and right eye images is dependent on the orientation of the glasses with respect to the projected image.

• The floor image cannot be aligned with both the side screens and the front screens at the same time.

Time Multiplexed Display

• Left and right-eye views of an image are computed and alternately displayed on the screen.

• A shuttering system occludes the right eye when the left-eye image is being displayed and occludes the left-eye when the right-eye image is being displayed.

Stereographics Shutter Glasses

Motion Depth Cues

• Parallax created by relative head position and object being viewed.

• Objects nearer to the eye move a greater distance

Pulfrich Effect

• Neat trick• Different levels of illumination require

additional time (your frame rates differ base of amount of light)

• What if we darken one image, and brighten another?

• http://dogfeathers.com/java/pulfrich.html• www.cise.ufl.edu/~lok/videos/pulfrich.avi

Physiological Depth Cues

• Accommodation – focusing adjustment made by the eye to change the shape of the lens. (up to 3 m)

• Convergence – movement of the eyes to bring in the an object into the same location on the retina of each eye.

Summary

• Monoscopic – Interposition is strongest.

• Stereopsis is very strong.

• Relative Motion is also very strong (or stronger).

• Physiological is weakest (we don’t even use them in VR!)

• Add as needed– ex. shadows and cartoons

What are some new things we can do?

• Lighting and Shading!

• Texturing!

• Stereo

• Surfaces– Normals– Materials