EXERCISES to EXPLORE with this APPLET
In this applet, you create a cubic Hermite curves by specifying a sequence of points and tangent
vectors at the specified points. For each pair of consective points and associated tangent vectors,
a cubic curve is created that passes through the desired points and has the prescribed tangent
vector.
- Play with the applet to determine the affect of the inputs
for creating one cubic curve.
- How can you create a straight line with a cubic Hermite curve?
- How can you create a closed cubic curve? Can you create a smooth closed cubic
curve?
- Determine rough placements of points (relations between the
points) that guarantee the cubic will self-intersect.
- Determine rough placements of points (relation between the
points) that guarantee the cubic will have a cusp (a place where
the curve has no defined unit tangent vector).
- Classify the possible shapes of cubic curves and the inputs needed
to create them.
- How do you create a smooth closed curve using more than one
cubic arc?
- Describe how to create an approximate circle with n cubic arcs where
n = 1, 2, 3, 4, ...
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