Instructions

  1. After the applet is running, select Blue-Red Anaglyth, and look through the three-D glasses.
  2. Adjust the separation slider until the image melds into one 3-D image. Each slider works by clicking on the handle once, then moving it up and down to the desired position. Once you get the desired result, click the mouse once again to let go)
  3. Answer question 1 below.
  4. Now change the distance to a large value. You may have to adjust the separation. Answer Question 2 below.
  5. Now make the image appear large (Adjust separation again if you need to.)
  6. Use the rotation slider. Answer questions 3 and 4 below.
  7. Click the "dots" box. (If the dots do not appear, you need to install Java.) Try turning off the "box". Answer Question 5.
  8. Change the 2 "view" sliders. Answer the remaining questions.

Questions

  1. What is the best separation for you? (note the number on the bottom of the slider)
  2. Does a greater distance make the object look smaller or larger?
  3. Are the two images identical?
  4. Are the images more different the closer or further the distance?
  5. Is there a particular shape to the group of dots?
  6. What does the third slider from the left control?
  7. What does the forth slider from the left control?
  8. Try to match these 5 controls (rotation, distance, view 1, view 2, separation) with the variables A, B, C, D and E in the diagram below.
  9. If a point was at (1, 1, 0), and it was rotated 90 degrees counterclockwise, what are the new coordinates?
  10. If the point at (1,1,0) was rotated 10 degrees counterclockwise, what are the new coordinates?
  11. A tree that is 10 feet away apears to be the same height as a tree that is 25 feet away. How much taller (in %) is the distant tree?

The Rotation & Perspective Formulas

 As the point revolves around the y axis, it follows the path of a circle, always at the same height(y) and distance (the radius of the circle) from the turning point (the y axis).

A green right triangle can be formed from the turning point, the original location (x,y,z) and the axes.

Since

sin a°= opposite/hypotenuse,
then
sin a° = z/d,
where d is the distance of the point to the turning point (or the radius of the circle).

Solving the equation for z,

z= d * sin a°

Therefore, to get the new location (x', y, z') we can see the red triangle can be formed, and

z' = d * sin a'°

By similar means the new x' will be

x' = d cos a'°,

Since cos a° = adjacent/hypotenuse and in the green triangle

cos a° = x/d

so that
x = d * cos a°

The adjustment for perspective takes advantage of the similar triangles that are formed between the object, the eye and the image in between. The diagram above shows only how to find the vertical adjustment y' (the corresponding vertical coordinate on the image would be y+y'), but the horizontal coordinate is found in exactly the same way. The ratios between the similar triangles are the same, and so solving for y', it is found to be the ratio between the product of the Distance and observer's height and the total distance between the object and the observer.

What's next?

The wonderful brain you have helps you to see two images as one, with an intuitive sense of the geometry of two view points. The closer the object the more different the view on the left is from the view on the right. Another explanation is here

3D Anaglyphs Links