0:00

So when we use three dimensional computer graphics for data visualization.

We need to queue the viewer that they're looking at a three dimensional scene

even though they're seeing a two dimensional image.

That means we need to add three dimensional perceptional queues to

an image, but those perceptional queues can interfere with our perception if three

dimensions or two dimensions.

0:22

So we'll learn how we perceive a 3D world from the two dimensional image on

our retina and how that ability to perceive the 3D world can interfere

with the visual presentation of two dimensional data.

And what we can do to avoid that misperception.

So again, we'll look at the visual part of the model human processor.

Basically, our eye is going to be sensing data that's going to be processed by

this perceptual processor.

And as perceptual processor has been developed to

1:07

It includes things like foreshortening.

The fact that three dimensional objects are projected onto an image plane or

onto our retinal hemisphere.

And that projection creates foreshortening, so if I look at a unit

cube, when I look at a projection of the unit cube on an image plane.

Some of the edges are shorter than the others.

The edges in the depth direction are going to be shorter than the edges

in the transverse directions.

And so that's foreshortening,

the effect that this edge is shorter than this edge in the projection,

even though in the three-dimensional scene they're the same length.

1:45

And so lengths in a projection are not necessarily accurate compared

to the lengths in the real world, but perceptually we've grown

to understand that these lengths could be the same length.

And the differences are the result of the projection onto the image plane.

And then there's Linear Perspective, and

you can see that here we have a projector which is basically aligned

from the object to a focal point through an image plane here.

That's being used by this early artist in order to create

a perspective drawing of this object as a,

2:31

When we were first understanding how perspective worked.

Basically, linear perspective said that object that are further away

appears smaller and you can see that here.

And then we have size constancy.

We know that object like this musical instrument aren't going to change size.

And so if an object appears to be changing size,

it must be moving farther away from us or closer to us, and

that objects that appear smaller than other objects must be farther away.

That's a size constancy expectation we have, and

our perceptual system depends on that.

So it can also malfunction.

And so here I've got a very simple line drawing.

With two parallel lines, A and B, and then I've got two lines that

are receding in the distance, that are, kind of sloped against each other.

And these two lines can set up the appearance of, for example,

railroad tracks or some two lines that are converging to

a vanishing point in a perspective drawing.

And if that's the case, then line A, if this was a perspective rendering of

a three-dimensional scene, line A should be farther away from us than line B.

And if that's the case, line A should be much bigger.

And in fact, A looks bigger in this image because of that.

But actually line A and line B are the same size.

But, when we add these additional lines in here, when we add a perspective

context to these lines, line A looks bigger, because it's farther away.

4:12

Similarly, I could have two equal length vertical lines here.

And if I add a few other decorations, suddenly I've changed the length and

now this line looks shorter and

this line looks taller even though I know that they are the same length.

After adding these additional lines, I've decreased the size of this line and

increase the size of this line perceptually.

And the reason is if I follow these out further I'm thinking of

this line in perspective as being the front corner of a cube.

And this line is being the back corner of for example a room if this is the floor

and the ceiling and this is to the wall this is the back corner of the room.

And this is the closest corner of an external cube, if that's the case then

I would expect this line to be farther away because it's the back corner and

this line to be closer to me, because it's the front corner.

And in perspective, if I have two lines, but this line is closer to me, and

this line is farther away, even though these two lines are the same length,

this one looks bigger, because it's farther away.

Perspective can also confuse us just from foreshortening,

not from linear perspectives.

So, here I've got a parallelogram, and

anytime you have parallel lines that aren't meeting at ninety degree angles,

we expect them to be receding in other distance.

And so here, even though this is just a parallelogram,

you want it to be a quadrilateral with right angles or rectangle.

That just happens to be receding Into the distance and that it's being foreshortened

into a parallelogram because it's being projected on to our retina.

5:58

If that as the case, then if this is receding into the distance,

then the fact that B is closer to this point than it is to this point,

would make this line A shorter than line C.

And just looking at the figure it looks like line AB is shorter than line BC,

when in fact line AB and BC are the same length for this is an isosceles triangle.

6:25

This also works with texture.

Here I just have an arrangement of lipsoids,

a two dimensional arrangement of lipsoids.

We tend to perceive it as for

example the tops of oil barrels receding off in the distance.

Because I've smaller features and more features in the distance and

so I've got a higher frequency of smaller features in the distance and

they lower frequency of fewer larger features.

In the foreground, and

we tend to attribute that to a projection of linear perspective, as well.

7:02

And we also have certain lighting assumptions.

So we're used to the sun being over head.

And so we're used to objects, seeing the front sides of objects, and

those objects are illuminated from above.

And so we see this dot illuminated from above as a convex sphere,

and we see this dot illuminated from below with the illumination

on the bottom side as being a concave indentation.

Because we don't expect illumination to come from the bottom,

we expect illumination to come from the top.

And the only way for this to be illuminated from the top like this,

is if it was an indentation instead of a bulge, as it is on the left side.

So when we use three dimensional graphics for data visualization, our perception

of size is based on our perception of how far the object is away from us.

And that can sometimes mislead us to what the actual size of the object is.