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Given a direction vector and a point, how to draw a 3d line?

asked 2012-05-26 04:51:13 -0500

dnizetic gravatar image

updated 2015-01-14 04:00:27 -0500

FrédéricC gravatar image

I have a point

(-e^pi, 0, e^pi)

and a direction vector

tvec = vector((e^t * cos(t) - e^t * sin(t), e^t * sin(t) + e^t * cos(t), e^t))

How would I draw a 3d line based upon these 2 arguments?

I looked over at the documentation but I couldnt find it.

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answered 2012-05-26 09:14:29 -0500

calc314 gravatar image

You can introduce a new parameter s that will parametrize the line. With p=(-e^pi,0,e^pi), the line is then p+s*tvec(t=t0) for some fixed value t0 of the parameter t.

Then, the line can be drawn as follows.

var('s,t')
p=vector([-exp(pi),0,exp(pi)])
tvec = vector((e^t * cos(t) - e^t * sin(t), e^t * sin(t) + e^t * cos(t), e^t))
parametric_plot3d(p+s*tvec(t=pi/2),(s,0,5),thickness=3)
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Asked: 2012-05-26 04:51:13 -0500

Seen: 631 times

Last updated: May 26 '12