[b]Project Goals[/b][br][br]In this project, we will work simultaneously on several fundamental mathematical concepts: the parameterization of the sphere, longitude and latitude, the tangent vector to a parametric curve, and rotations in space.[br][br]
What are the value ranges for longitude (u) and latitude (v)?
[left][/left]What value ranges should longitude and latitude take if we only want to draw the northern hemisphere? And what if we want to draw only a vertical hemisphere?
In the following applet, define a point [b]P[/b] and modify the parameterization of the sphere so that it is centered at [b]P[/b]
In the next applet, create [b]6 copies[/b] of the sphere’s parameterization and adjust the longitude and latitude ranges in each copy to draw a [b]basketball[/b] painted in [b]6 different colors[/b].
In the next applet, rotate each of the six sections of the sphere around the given axis. Use the command:[br][code]Rotate(object, angle, axis)[/code][br]
[justify][/justify]Modify the following applet so that the [b]basketball[/b] moves along the given [b]helix[/b].
Combine everything you’ve learned so far to make the basketball [b]move along the helix[/b] while simultaneously [b]rotating around the tangent line[/b] to the helix at each point.