[CSC 315] Intersecting Line Segments

[Andrew J. Pounds]

On 09/23/2016 09:58 PM,  wrote:
> Ok I've got that implemented. And now it's onto intersection checking.
>
> I've got no idea where to start with that but I'm guessing there's a 
> matrix there somewhere
>
>
>
Yep...

So based on the notes, lets say you have a line segment defined by the 
points

$(x_1,y_1)$ and $(x_2,y_2)$

and another line segment defined by the points

$(x_3,y_3)$ and $(x_4,y_4)$

You need to calculate the determinants that are shown on page 16 of the 
lecture slides.  There are only three determinants to be calculated 
because the denominators are the same.   Calculating the determinants in 
the 2D case is really easy as it equals $M_{1,1}M_{2,2}-M_{1,2}M_{2,1}$ 
where the subscripts refer to the matrix indices.  Once you calculate 
the determinants then find $u_a$ and $u_b$ by division and if both are 
between 0 and 1 the lines intersect.






-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-4.png
Type: image/png
Size: 812 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-3.png
Type: image/png
Size: 855 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment-0001.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-2.png
Type: image/png
Size: 854 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment-0002.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-1.png
Type: image/png
Size: 835 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment-0003.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-5.png
Type: image/png
Size: 1350 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment-0004.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-7.png
Type: image/png
Size: 551 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment-0005.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tblatex-6.png
Type: image/png
Size: 556 bytes
Desc: not available
URL: <http://theochem.mercer.edu/pipermail/csc315/attachments/20160924/2995885b/attachment-0006.png>