Bézier Curves 5: Continous Path
- Ryan Hirst
- Parametric Curves
We often argue that a result holds for any continuous curve (with, say, continuous first- or second- ... derivatives). I'd like to use splines in these demonstrations. I will flesh out the properties of 3rd order curves to make them more serviceable in examples, demonstrations, proofs.
Concatenated 3rd order curves. By construction, curve and first derivative are continuous across the connecting points (blue). To make them continuous in t, offset t by one unit for each appended curve. To Do: *The moving point is oriented, but I would like it to turn and face the direction of motion (next..) *Path parameter s (arc length). *Self-intersections ____________________ Bézier Curves 1. Construction: http://www.geogebratube.org/material/show/id/27320 2. Higher Order Curves: http://www.geogebratube.org/material/show/id/27627 3. Basic Implementation: http://www.geogebratube.org/material/show/id/27631 4. Weights: http://www.geogebratube.org/material/show/id/28313 →5. Continuous path 6. ...