Pixar in a Box
- Start here!
- Weighted average of two points
- Weighted averages
- 2. Where is the touching point?
- Exploring the parabola construction
- 3. Compute the touching point
- Calculating the touching point
- 4. How can we prove this?
- Touching point
- Bonus: Completing the proof
Ready to dive into some math?
In this lesson we are going to develop a powerful formula which allows us to easily calculate points along a parabolic arc:
To get there we are first going to develop our understanding of weighted averages. This is really important to understand as several other lessons will build on it (you can do this step without finishing the entire lesson).
Next we'll discover de Casteljau's algorithm which will allow us to calculate points on any parabolic curve. This results in a really simple set of equations computers can use to draw parabolic arcs: