Math Is Fun Forum

Niels

Guest

How to get the equations of a line in 3D if I have two points?

I should know how to figure this out buy my brain in dead and all my math from school is missing

I have 2 3D points how do I calculated the a,b,c,d in the following equation:

a*x + b*y + c*z + d = 0

What I'm trying to do:

I'm reverse engineering gradients that has been draw as bitmap into SVG. My goal is to approximate the positions of the gradient stops.

My idea is to compare a set of colors, as long they have the same a,b,c and d between them there there should be any stop between them.

Thanks for you help!

/Niels

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: How to get the equations of a line in 3D if I have two points?

You might fiddle with (x,y) separately ignoring z.
then fiddle with (y,z) separaely ignoring x.
then try (x,z) separately ignoring y,
and see if it all goes together.
That would be like looking from orthogonal
angles parallel to the axes without
perspective to get 3 separate views.

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: How to get the equations of a line in 3D if I have two points?

isnt f(x,y,z) = ax + by + cz + d = 0  the equation of a plane? if so then 2 points isnt enough to get a unique set of values for a,b,c,d?

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: How to get the equations of a line in 3D if I have two points?

I am going to explain the 2
points in 3-D question.  If
the line goes in the (2,3,4)
direction and goes through
the point (7,8,9), then the
equation might be:
(x-7)/2 = (y-8)/3 = (z-9)/4

Last edited by John E. Franklin (2008-03-13 10:10:12)

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