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Creating Anaglyph Images in Java
This document explains the algorithms used to create
the anaglyph graphics displayed in the 3D Cartesian coordinates demo and the
molecules applets.
Two programs that utilize these techniques are
Conic Sections and
3D
Tempest. You'll need red/blue glasses for the 3D effect.
Anaglyph images are graphics that utilize the red/blue glasses to
appear 3 dimensional, similar to cheesy 1950's horror flicks. One image is
created for one eye and colored red while a slightly different image of the
same object is colored blue for the other eye. When the brain combines the
two images they appear 3D. This is useful in educational programs for 2
reasons... "
- Demonstrating and explaining 3 dimensional concepts difficult to
illustrate in 2 dimensions.
- The 'Gee-whiz' effect that may help maintain and pique a students
interest in the remainder of a lesson.
As an example, compare the diagram of nicotene on the left, and the 3D
applet on the right.
The images on the left are what you may find in a chemistry book. Many students
would not be able to glean the true structure of the molecule from these
diagrams, and many would find them just plain boring. The applet on the
right, however, gives an excellent representation of the chemical.
To create two different images of the same object, the method that first
comes to mind is to mimic natural eyesight and chose a common focal point
for both eyes, as shown in this diagram.:
The top view shows two eyes looking at a pyramid, the front view shows
the image that results when the two views are merged.
Another way to get the same effect is to have the viewpoints created
with the as if the eyes are looking parallel with each other and no common
focal point. When the component images are created in this fashion, the
horizontal offset between them can be altered when they are merged with the
effect ofthe object moving out of the screen towards the viewer or into the
screen away from the viewer. This is called HIT, Horizontal Image
Translation.
Initially it would seem that both approaches require twice the amount of
rendering and twice the amount of data as a simple 'flat' 2D rendering.
However, the latter method can let us create anaglyph images in a
mathematically simple and elegant way. Converting 3 dimensional points to 2
dimensional points for on screen display involves scaling and translating
points from the 'data' realm to the 'display' realm. At first glance it
appears each method requires calculating 2 sets of data in the data realm
and converting to the display realm, involving a good bit of calculation and
trigonometry. We'll see how the conversion to anaglyph display can be done
after the points are in the display domain, and how easy it is.
First, let's look at simple single point perspective.
Run the 3D Cartesian coordinate system and turn perspective on, but
leave 3D off. Move the Perspective slider left to right.
The math here is probably obvious - an arbitrary distance along the Z
axis is chosen to represent the vanishing point, and each X and Y coordinate
is moved toward the center of the display area somehow proportional to that
points Z coordinate. Note that a screen Z coordinate had to be calculated,
even though it is not used directly in the display. These next two images
display the measurements used to perform these calculations.
In the above image we are looking 'down' at the bounding box of the display
area with a pyramid in it. Looking at the point that is the far right corner
of the base, its X coordinate is MidX+dX1. B is the distance along the Z
axis from the vanishing point to our reference plane, and C is the distance
from the vanishing point to our point of interest. Calculating the new X
coordinate uses the C/B ratio to move X and Y coordinates towards the
midpoint of the display, mimicing one-point perspective.
This image shows the base of the pyramid
altered after perspective is applied.
The original X coordinate is
X1 = midX + dX1
since we are moving towards the center an amount directly
proportional to the distance from the vanishing point along
the Z axis,
dX2/dX1 = C/B = R
dX2 = R * dX1
X2 = midX + R*dX1
converting these equations to pseudo-code;
For each point,
R = C/B
X2 = MidX + R*(X1-midX)
Y2 = MidY + R*(Y2-midY)
Note that if a point lies on the reference plane the ratio R becomes 1
and the new coordinates are the same as the old.
The neat thing is, the coordinates for the red and blue portions of the
image can be calculated in an equally unsophisticated manner.
But before we get into that, let's take a look at the application of HIT -
Horizontal Image Translation. Turn Perspective off and 3D on, and move the
Perspective slider from side to side. Notice how the two component images
remain the same, the only thing that differs is their horizontal offset from
each other. But this has the net effect of seemingly moving the object into
and out of the screen. Those locations where the points from the red and
blue components are the same will appear to lie directly on the screen.
The display coordinates for the left
and right images differ from the original coordinates only in that the X
value is shifted to the left or right some number of pixels. Turning 3D on
and off will demonstrate this. Similar to the one point perspective
calculations, this amount is proportional to the ratio of the distance from
the points Z coordinate to a reference plane to the distance from the
vanishing point to that reference plane.
for each point,
c = k * a/b
leftX = oldX - c
rightX = oldX + c
Note that if a points lies on the reference plane the ratio a/b becomes 0,
and the new coordinates are the same as the old.
where k is an arbitrary value that scales this ratio to
an aesthetically pleasing distance. Generally if the left and right X
coordinates differ by more than 30 pixels the eyes will have difficulty
reconciling the component images. To see the effect of altering this k
value, turn perspective off, 3D on, and move the L/R separation slider.
It is worthwhile to note that points
that lie on the reference plane will have no perspective applied and the
point for the left and right images will coincide, so that plane will appear
to lie directly on the screen. This, combined with the fact that the two
views were created with parallel points-of-view, allows a plane
perpendicular to one of the X,Y, or Z axis to be viewed undistorted - handy
for those cases where it is necessary to view a 'slice' of a 3D view, such
as when you need to examine what happens when X = 2; For real fun turn
both Perspective and 3D on, click both Spin buttons, and play with the
sliders.
I hope this discourse has shown that often, if you don't go with the
methods that seem obvious, you can do things simply, elegantly and easily.
And cheesily.
A more thorough explanation of these concepts is available in a white
paper written by Lenny Lipton, founder of stereographics, Stereo3D
Handbook is downloadable from
Stereographics.com.
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