Plotting Surfaces and Curves

This lab covers commands useful in plotting curves and surfaces. Surfaces are usually given in one of the following forms - explicitly as z=f(x,y), parametrically as , or implicitly as f(x,y,z)=c. Use the appropriate commands to complete the task given below. You will need the following commands

plot3d, implicitplot3d, spacecurve, display

If you are not familiar with any of these commands please use Maple's help command to learn their syntax and see some examples. Also see the Maple tutorial distributed in class.

Please submit your work as a Maple report. If you have never prepared a Maple report please see the Maple tutorial for instructions. Be sure to load the Plots package in Maple with the command with(plots): before starting your work.

1. In the same picture display the paraboloid and the plane x+y+z=1. Adjust the parameters so that the solid bounded by these surfaces occupies most of the picture. Color the two surfaces differently.
2. In one picture display the hemisphere (parametric equation)
   
   and the curve
   
   Adjust the parameters to get the best picture and color the two objects differently. Use the appropriate option to thicken the curve.
3. Draw the two cylinders and in the same picture coloring them differently. Adjust the parameters to get a nice smooth picture of the intersecting solids.

 
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