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Normal, Tangent and Gradient of a Bezier Curve

Started by July 02, 2003 04:22 AM
1 comment, last by DirectXXX 21 years, 7 months ago
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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I got some idea. But im more interested in just pesudo code for now for a simple 4 points bezier.

[edited by - DirectXXX on July 2, 2003 12:36:10 PM]
3D Side-Scroller game demo Project-X2 "playable"Lashkar: A 3D Game & Simulation Project demo @ lashkar.berlios.de

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