Curve Driving Generator

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Curve Driving Generator

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#12

30-03-2012, 21:01

Ether

systems engineer (retired)

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Join Date: Nov 2009

Rookie Year: 1969

Location: US

Posts: 8,087

Re: Curve Driving Generator

Quote:

Originally Posted by theNerd

what if the current heading angle was a slope of infinity?

Pick a coordinate system whose origin is the starting point and whose positive X axis aligns with the starting direction of motion.

Compute the ending point (X₂,Y₂) and slope m₂ in that coordinate system.

Then the cubic becomes simply Y = aX³ + bX²

and the formulas for a and b are simply

a = (m₂X₂ - 2Y₂)/X₂³

b = (3Y₂ - m₂X₂)/X₂²

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