You have already seen the general structure of an animation in Mathematica in previous labs. In this section, several different 3-space animations are discussed. You will be referred to separate notebooks which contain the already calculated animations for viewing. This procedure will save you a lot of time since you won't have to wait for the frames of the animation to be calculated. You can find these animation notebooks in the same folder as this lab.
Remember that animations can require a lot of free RAM, so you may need to shut down the Mathematica kernel to view the animations smoothly.
Another point to keep in mind when computing an animation is that each frame of the animation is stored in a page description language called PostScript. If you would like to view the PostScript commands which describe a graphic, you can unformat the graphics cell by toggling the Formatted option in the Attributes option of the Style menu. For images of surfaces, you can save a lot of memory by converting the description of the graphic from PostScript to Bitmap PICT (use the Graph menu). A bitmap of a graphic is simply a pixel by pixel description of the image. As such, it does not resize well, and does not print well since the printer has a much higher resolution than the computer screen. But for animations, converting to Bitmap PICT usually frees up a lot of badly needed memory to allow the animation to be viewed more smoothly. Thus the tradeoff is usually a good one.
When we graphed the twisted cubic curve in an earlier section in this lab, we proposed two animations which would help us to see the details of the curve. One was to animate the unit tangent and unit normal vectors moving along the curve. This animation is contained in the notebook named twisted cubic animation.
The other animation discussed earlier for the twisted cubic was simply to rotate the curve around in 3-space. This type of animation is located in the notebook twisted cubic rotation.
The monkey saddle surface was discussed and graphed earlier in this lab. A notebook named monkey_saddle_rotation.nb contains an animation of the surface rotating in space.