Your thought is correct - this does (in a sense) move along the curve to produce new control points, and the subset does match the curve exactly. And the new control points are non-linear too! (The inner ones, anyway.) Pay attention to how the new control points are chosen - to split you take one control point from each level of the lerp tree.
That is a really neat demo to play with. With some thinking, I can intuit and see visually in that what you mean by 'each level of the lerp tree'. Thankyou :)
The cool part about this is that you can see the control points of the two split curves in this diagram. The original control points are the bottom edge of the triangle. The left split is the left edge of the triangle, and the right split is the right edge of the triangle.
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Here’s an interactive picture of how the splitting with lerps works: https://pomax.github.io/bezierinfo/#splitting
Did you ever doodle parabolas on graph paper by drawing straight lines? That’s one way to see why you can form nonlinear curves using only lerps. (For example https://mathcraft.wonderhowto.com/how-to/create-parabolic-cu...)
Your thought is correct - this does (in a sense) move along the curve to produce new control points, and the subset does match the curve exactly. And the new control points are non-linear too! (The inner ones, anyway.) Pay attention to how the new control points are chosen - to split you take one control point from each level of the lerp tree.
That is a really neat demo to play with. With some thinking, I can intuit and see visually in that what you mean by 'each level of the lerp tree'. Thankyou :)
I hope it helps, Bézier curves are so simple and fun.
I found a picture of the ‘lerp tree’ that might help even more: https://www.researchgate.net/figure/De-Casteljau-algorithm-t...
The cool part about this is that you can see the control points of the two split curves in this diagram. The original control points are the bottom edge of the triangle. The left split is the left edge of the triangle, and the right split is the right edge of the triangle.
That is neat, and yes, does help! I have learned a lot in this thread. Thanks for taking the time to share this.