0:00

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

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

Â even though they're seeing a two dimensional image.

Â That means we need to add three dimensional perceptional queues to

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

Â dimensions or two dimensions.

Â 0:22

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

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

Â with the visual presentation of two dimensional data.

Â And what we can do to avoid that misperception.

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

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

Â this perceptual processor.

Â And as perceptual processor has been developed to

Â 1:07

It includes things like foreshortening.

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

Â onto our retinal hemisphere.

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

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

Â Some of the edges are shorter than the others.

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

Â in the transverse directions.

Â And so that's foreshortening,

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

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

Â 1:45

And so lengths in a projection are not necessarily accurate compared

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

Â to understand that these lengths could be the same length.

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

Â And then there's Linear Perspective, and

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

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

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

Â a perspective drawing of this object as a,

Â 2:31

When we were first understanding how perspective worked.

Â Basically, linear perspective said that object that are further away

Â appears smaller and you can see that here.

Â And then we have size constancy.

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

Â And so if an object appears to be changing size,

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

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

Â That's a size constancy expectation we have, and

Â our perceptual system depends on that.

Â So it can also malfunction.

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

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

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

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

Â railroad tracks or some two lines that are converging to

Â a vanishing point in a perspective drawing.

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

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

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

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

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

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

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

Â 4:12

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

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

Â now this line looks shorter and

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

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

Â increase the size of this line perceptually.

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

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

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

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

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

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

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

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

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

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

Â Perspective can also confuse us just from foreshortening,

Â not from linear perspectives.

Â So, here I've got a parallelogram, and

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

Â we expect them to be receding in other distance.

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

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

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

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

Â 5:58

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

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

Â would make this line A shorter than line C.

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

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

Â 6:25

This also works with texture.

Â Here I just have an arrangement of lipsoids,

Â a two dimensional arrangement of lipsoids.

Â We tend to perceive it as for

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

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

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

Â they lower frequency of fewer larger features.

Â In the foreground, and

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

Â 7:02

And we also have certain lighting assumptions.

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

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

Â those objects are illuminated from above.

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

Â and we see this dot illuminated from below with the illumination

Â on the bottom side as being a concave indentation.

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

Â we expect illumination to come from the top.

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

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

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

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

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

Â