Kraus Java LiveGraphics3D

The Java LiveGraphics3D images were generated with Mathematica and made "live" using the LiveGraphics3D Java 1.1 applet by Martin Kraus. The LiveGraphics3D applet allows you to grab and rotate the image. As each page of graphics is viewed it may take up to 30 seconds for the plot to become "live", but then you can click and drag the mouse over the image to rotate it.

LiveGraphics3D has the capability of displaying stereo pictures. Pressing "s" when the cursor is on the picture will toggle between a single picture, two pictures for diverge fusing, two pictures for cross fusing, a single picture again, and so on. Diverge fusing means to view the left picture with your left eye and the right picture with your right eye. Cross fusing is to view the left picture with your right eye and vice versa.

Zernike Polynomials

Surface of Revolution (m=0)

n = 1, 2, 3 (Zernikes 3, 8, 15)

n = 4, 5, 6 (Zernikes 24, 35, 48)

Cylindrical Plot 3D

n = 1, m = 1, 0 terms (Zernikes 1, 2, 3)

n = 2, m = 2 terms (Zernikes 4, 5)

n = 2, m = 1, 0 terms (Zernikes 6, 7, 8)

n = 3, m = 3 terms (Zernikes 9, 10)
n = 3, m = 2 terms (Zernikes 11, 12)
n = 3, m = 1, 0 terms (Zernikes 13, 14, 15)

n = 4, m = 4 terms (Zernikes 16, 17)
n = 4, m = 3 terms (Zernikes 18, 19)
n = 4, m = 2 terms (Zernikes 20, 21)
n = 4, m = 1, 0 terms (Zernikes 22, 23, 24)

n = 5, m = 5 terms (Zernikes 25, 26)
n = 5, m = 4 terms (Zernikes 27, 28)
n = 5, m = 3 terms (Zernikes 29, 30)
n = 5, m = 2 terms (Zernikes 31, 32)
n = 5, m = 1, 0 terms (Zernikes 33, 34, 35)

n = 6, m = 6 terms (Zernikes 36, 37)
n = 6, m = 5 terms (Zernikes 38, 39)
n = 6, m = 4 terms (Zernikes 40, 41)
n = 6, m = 3 terms (Zernikes 42, 43)
n = 6, m = 2 terms (Zernikes 44, 45)
n = 6, m = 1, 0 terms (Zernikes 46, 47, 48)