EXERCISES to EXPLORE with this APPLET
In this applet, you create C1 cubic Bezier splines. To create a curve with L cubic
segments you need to place 2L+2 control points. The first four points create a Bezier curve, but with the
addition of two more points, you create two cubic Bezier curves using the first three points d-1,
d0, d1 and the point ½d1 + ½d2 for the first
Bezier curve and ½d1 + ½d2, d2, d3, d4.
Adding more points, adds additional Bezier curves using the algorithm outlined in the course notes.
- Play with creating C1 splines.
- Notice how different the curve is from the Bezier curve with the same control points? What is significantly
better about a C1 spline?
- Does a C1 Bezier spline have the same properties as a Bezier curve? (Convex Hull property,
variation diminishing, pseudo local control, endpoing interpolation, prescribed tangent lines)
- Using C1 splines can you create a curve that is approximately a circle? If so how?
- Can you determine conditions on the placement of the control points so that the curvature is
continuous? That is the resulting curve is C2?
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