Initial due date 9 Oct 98 Revised due date 16 Oct 98 Vague statement: Modify the "Universe" code to do things like you did in project 1 only this time using the power of Java3D. In particular, you need to be able to create Shape3D subclasses for functions z=f(x,y,t) like we had before (corrected) Sample Functions to test: ranges [-1,1]x[-1,1] z = sin(t*x) + sin(t*y) z = sin(t*x*y) z = exp(-x^2-y^2)*sin(t*sqrt(x^2+y^2)) <-- this one is corrected. You need to be able to look at these with various methods. (Keeping the mouseGroupstuff. 1. Lights on (Mathematica lights (perhaps with an additional light) a. Lights rotate with object. b. Lights do not rotate with object. 2. Color ramps (Lights off) a. BlueRed color ramp on Z. b. Something baised on (XY). c. [The normal stuff is ignored as we have the lighting stuff this time.] 3. Texture mode (Lights off) a. BlueRed color ramp on Z b. checkerboard c. contour lines. The program needs to handle user input like one of examples Universe[KMA].java. The program should start without parameters and not prompt for input. Optional: create a Behavoir to animate the objects as t changes from 1 to 4 say.