Tangent Vector
Author
What is a tangent vector and how would I calculate such a vector? Thanks for any information.
Todd
A tangent vector of a curve is a vector which starts at one point of the curve and has the same direction as the curve at this point. If you''ve got a parametrized curve in 3D space, curve(t) = (x(t),y(t),z(t)), you get the tangent vector if you derive x(t), y(t) and z(t): tangent vector(t) = (dx(t)/dt,dy(t)/dt,dz(t)/dt).
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GA
Visit our homepage: www.rarebyte.de.st
GA
Hey,
Yeah, you''d need to know calculus for that. Or if you give the equation of the curve, maybe someone here (including me) could give you the differentiated equation. Basically, you take the equation of the curve/line, find the derivative, and evaluate the derivative at the point of tangency. This is the direction of the vector (actually its the slope of any line, but... here it could be considered the direction).
Now the magnitutde of the vector is what you''d need to have. A true tangent vector doesn''t need a specific magnitude... I think a unit vector would do fine as a tangent.
Hope this helps, but give the equation of a curve so we could better help you.
OldManDave.
Yeah, you''d need to know calculus for that. Or if you give the equation of the curve, maybe someone here (including me) could give you the differentiated equation. Basically, you take the equation of the curve/line, find the derivative, and evaluate the derivative at the point of tangency. This is the direction of the vector (actually its the slope of any line, but... here it could be considered the direction).
Now the magnitutde of the vector is what you''d need to have. A true tangent vector doesn''t need a specific magnitude... I think a unit vector would do fine as a tangent.
Hope this helps, but give the equation of a curve so we could better help you.
OldManDave.
doesn''t deriving just give you the gradient?
Although I suppose you you could work out the rest from that...
-Mezz
Although I suppose you you could work out the rest from that...
-Mezz
quote:Original post by Mezz
doesn''t deriving just give you the gradient?
Although I suppose you you could work out the rest from that...
-Mezz
I think the gradient is the derivation of a scalar function with more than one parameter, e.g. f(x,y,z) gives a scalar value, e.g. f(x,y,z) = sqrt(x^2 + y^2 + z^2) for the length of a vector. Then the gradient is
(df(x,y,z)/dx, df(x,y,z)/dy,df(x,y,z)/dz)
It gives us the direction in whích the value of the scalar function has the biggest change.
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GA
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