Hello, I have trouble understanding the math behind the formal equation of quadratic and cubic Bézier curves, I need someone who can explain the math behind them in a fairly primitive way, thank you.
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Imagine 3 dots; A, B, and C. These dots are connected like so:
Now imagine two other dots traveling along the lines. One goes from A to B, and the other goes from B to C.
Now connect the moving dots.
Once again, imagine a dot traveling along that line.
The path that the yellow dot takes is your quadratic Bezier curve.
You should recognize the pattern by now; traveling dots, connect with lines, and repeat. A quadratic Bezier is just the same thing but with four dots to start with instead of three.
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That’s not my issue, I know how a Bézier curve works, I just don’t understand the formula behind it in the formal way ( (1 - t)^2 * p0 + 2 * (1 - t) * t * p1 + t^2 * p2 ) , I know the basic way of just doing repetitive lerps.
This is a linear Bezier. It is essentially just linear interpolation.
Focus on the underlined terms of the expression.
This is a quadratic Bezier.
Compare the corresponding terms. Do you see any similarities? Red is the same as red, and blue is the same as blue. Both green and brown are similar to the entire expression of the linear Bezier. The expression you stated is just that but rearranged/simplified. The cubic Bezier merely just repeats this pattern of recursion, where the points become their own linear Bezier as you move up in degree.
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Thanks, this really answers my questions, thank you again for putting time into trying to make me understand!