Upcoming Classes

Tuesday, Sept. 4th

Fractal Worlds & Chaotic SystemsAssignments due:

* Topic of first oral presentation or written paper

* Read “Order in Pollock's Chaos”; Scientific American, December 2002

Thursday, Sept. 6th

Motion, in the real world and in animated worlds

Assignment due:

* Read “It’s All in the Timing and the Spacing”, The Animator's Survival Kit, R. Williams, Pages 35-51

* Homework #2

Upcoming Deadlines

Thursday, September 13th

First draft of your first term paper or your

oral presentation

Thursday, September 27th

First Set of Oral Presentations

First term paper (if not giving presentation)

Oral Presentations

The following persons will give oral presentations on Thursday, September 27th :

• Batres, Adan• Boyd, Heidi• Chen, Emily• Kwiatkowski, Dajon• Lebedeff, Christopher• Lipton, ChristopherFor everyone else, your first term paper is due on

that date.

Physical Scale &Geometric

Perspective

Measurement

Measurement is the foundation of modern, quantitative science.

Three fundamental physical measurements:

• Distance

• Time

• Matter (mass)

Today we’ll consider how distance appears in the visual arts, such as in paintings.

Perception of Distance

Visually, we experience distance by• Occultation (objects hide what’s behind them)• Geometric Perspective (objects look smaller as

they get further away)• Atmospheric Perspective (distant objects are

hazy and bluish)• Lighting and shadows• Stereopsis (different view in each eye)• Relative motion (as you move, nearby objects

shift more than distant objects)We’ll discuss some of these today, others in future lectures

Occlusion

The simplest way that we perceive distance is by the fact that closer objects occlude (hide) the objects behind them.

Even in this surreal painting we immediately see the boy as being closer to us than the woman because he partially blocks our view of her.

Detail from The Madonna of Port Lligat, Salvador Dali, 1950

When occlusion is incorrect, we are very cognizant of the distortion.

Distorted Occlusion

Manipulating Occultation

The image is disturbing but the reason isn’t immediately apparent.

Detail from Waterfall, M.C. Escher, 1961

This channel of water needs to be behind the lower part of the right tower.

This distortion is not accidental. The artist carefully designed the composition with this effect in mind.

Pre-15th Century Paintings

Mongol Ruler and consort enthroned, 14th century Road to Calvary, Martini, 1315

Occlusion but no sense of distance

Renaissance PaintingsScenes in these paintings look realistic

The Annunciation, Botticelli, 1489

Marriage of the Virgin, Raphael, 1504

Masaccio

This early fresco by Masaccio is so realistic, we can geometrically analyze it to find the positions of the persons inside the painting.

The Holy Trinity, Masaccio,1425

TopView

Side View

Perspective

The difference is the introduction of visual perspective by Filippo Brunelleschi of Florence.

Objects in the distance look smaller as determined by geometric rules.

Florence, Italy

Perspective Example

The gazelles in this photo appear to be roughly the same physical size.

Thanks to John Clapp for these slides

Move from here…to here

Perspective Example

Let’s move one using cut-and-paste. How big will it be?

Perspective Example

Surprised? Objects appear much smaller with distance!Your brain adjusts and “sees” the animals as equal size.

Perspective Example

Move down

Even a short distance into the background makes a surprising difference.

Move from here…to here

Try to visualize it’s size…

Perspective Example

Now let’s go the other way and move from foreground to background.Again, try to visualize how large the gazelle will be when cut-and-pasted.

Perspective Example

Surprised? Instead of a gazelle it’s now Godzilla.Try this at home with your own photos.

Drawing with Perspective

From that example we see that it’s not easy to predict how large or small objects will be at different distances.

How do artists create images with realistic perspective?By using geometry!

Perspective Demonstration

Start with a blank sheet of paper, draw a thin line close to the top.This is your horizon, the separation between sky and the ground.

Perspective Demonstration

Mark two points, on the line, on opposite sides of the page.These are called vanishing points.

VP VP

Perspective Demonstration

Pick a point near but not quite at the center of the page.Draw light, thin lines from that point to the VPs.

VP VP

Perspective Demonstration

Draw a thick, straight line up from your point, as shown.

VP VP

Perspective Demonstration

Draw a thin lines from the end of this line to your VPs.

VP VP

Perspective Demonstration

Draw a two more vertical lines, as shown, then draw connectinglines to make a pair of rectangles, in perspective.

VP VP

Perspective Demonstration

Draw a two light lines from the corners to the VPs then connectthe rectangle on the top of the box.

VP VP

Perspective Demonstration

This is your little house. Give it a front door.

VP VP

Perspective Demonstration

Draw a person just to the right of the front door.Then draw a second person in the foreground.

VP VP

Perspective Demonstration

But how do we know the second person is the right height?

VP VP

?!?

Perspective Demonstration

Draw thin lines from the VP, passing through head and feet of the person by the house.

VP VP

Perspective Demonstration

Draw a thin horizontal line at the feet of the person in the foreground.A person at that distance should be shorter, as shown.

VP VP

Dude, you’re like 8 feet tall

Perspective Demonstration

Now add the rest of the figures and draw this.

Perspective Demonstration

We can check that the persons in the foreground and backgroundare the same height by drawing lines back to the horizon.

Horizon

SJSU Cafeteria Painting

This painting shows the Business Tower with the Art building on the right.

What’s wrong with it?

SJSU Cafeteria Painting

Horizon

Using geometric perspective, let’s see how tall the red-headed person must be as compared with the door of the Art building.

Pretty tall!

Homework Photo

Are these images at the correct scale?

Homework Photo

Let’s check the scale using the two images on the left side to find the height of a person standing on the sidewalk.

Comparing with the height of the street light shows us that scale is wrong.

Computer Graphics

Geometric perspective can be quickly calculated by computer graphics

Simple objects

Full Rooms

3D worlds

Distorted Perspective

Modern painters sometimes distort the perspective for dramatic effect.

Mystery and Melancholy of a Street, de Chirico, 1914

The two buildings converge to two different horizons. This feels weird and unnatural, which is what the artist intended (note the title of the painting).

Next LectureFractal worlds & Chaotic systems

Remember:

Pick a topic for your first paper/presentation

Read “Order in Pollock’s Chaos”