Path: news.mathworks.com!not-for-mail From: Alan Weiss <aweiss@mathworks.com> Newsgroups: comp.soft-sys.matlab Subject: Re: Intersection of two straight lines in 3D space Date: Wed, 11 Mar 2009 11:33:37 -0400 Organization: The MathWorks, Inc. Lines: 26 Message-ID: <gp8lkh$859$1@fred.mathworks.com> References: <gp8je2$80b$1@fred.mathworks.com> NNTP-Posting-Host: weissa.dhcp.mathworks.com Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: fred.mathworks.com 1236785617 8361 172.31.57.119 (11 Mar 2009 15:33:37 GMT) X-Complaints-To: news@mathworks.com NNTP-Posting-Date: Wed, 11 Mar 2009 15:33:37 +0000 (UTC) User-Agent: Thunderbird 2.0.0.19 (Windows/20081209) In-Reply-To: <gp8je2$80b$1@fred.mathworks.com> Xref: news.mathworks.com comp.soft-sys.matlab:524077 [2.5 2.5 2.5] (you can do this one in your head) Represent each line as A1 + t*(A2 - A1) and B1 + s*(B2 - B1). t = s = 2.5 gets the answer In general, there is no solution to 2 lines in 3-space, and you could instead find the point where the sum of squares is minimized. Represent the sum in terms of t and s as above, differentiate, set to zero, voila! Alan Weiss MATLAB mathematical toolbox documentation James wrote: > Hello, > > I've got two lines in 3D space, each represented by two points (of x,y,z coords) such as: > > A1=[0 0 0]; > A2=[5 5 5]; > > B1=[0 5 5]; > B2=[5 0 0]; > > I would like to be able to calculate the (x,y,z) coordinates at which they intersect. With my own beginners Matlab knowledge and feeble grasp of maths, I have been able to calculate something similar in 2D (by calculating line equations in the form y=mx+c and then solving) but I am stuck at trying to do this in 3D. > > Any help would be greatly appreciated, this is a real road block in my work and it is slowly driving me potty!