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Normal, Tangent and Gradient of a Bezier Curve

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I need Normal, Tangent of a bezier curve. Google points me to sites which tells you about finding derivities. like this one http://www.fmi.pu.acad.bg/Education/compgeom/bezier-der.htm But we have just started differentiation in academy two days ago. I just need Normal, Tangent of a simple bezier curve. a simple bezier curve with two points for curve ends and two control points for their curvature.

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The tangent is the derivative.

x(t) = ax³ + bx² + cx + d
x''(t) = 3ax² + 2bx + c
y(t) = ...
y''(y) = ...
...

The tangent is (x''(t), y''(t), z''(t))

A curve does not have a normal in 3D. It has multiple ones. Any vector perpendicular to the tangent is a normal.

Cédric

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