EXERCISES to EXPLORE with this APPLET
In this applet, you place control points to create a smooth piecewise circular
curve. The first two control points specify the tangent line of the first circular arc.
After that applet creates a circular curve that interpolates the control points.
- You can easily create a circle with two circular arcs. Place
the zeroth control point p0somewhere. Make
the next two p1 and p2 anywhere
so p0, p1 and p2
are non collinear. Then place the control point p3
on top of p1. How does the choice of the tangent
line affect the circle?
- Can you create a circle with three circular arcs? If so, how?
- Create a closed curve with n arcs. (n being
3, 4, 5, 6, etc). Can you always create a smooth piecewise circular
curve? What must be true to create a smooth piecewise circular
curve.
- Once you have created a smooth piecewise circular curve using
an odd number of arcs, does it remain smooth once you change
the defining tangent line? Why or why not?
- Once you have created a smooth piecewise circular curve using
an even number of arcs, does it remain smooth once you change
the defining tangent line? Why or why not?
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