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<div class="moz-cite-prefix">On 09/23/2016 09:58 PM, wrote:<br>
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<div>Ok I've got that implemented. And now it's onto intersection
checking.
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<div>I've got no idea where to start with that but I'm guessing
there's a matrix there somewhere</div>
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Yep...<br>
<br>
So based on the notes, lets say you have a line segment defined by
the points<br>
<br>
<img style="vertical-align: middle"
src="cid:part1.66FE1660.E5D1C3E5@mercer.edu" alt="$(x_1,y_1)$">
and <img style="vertical-align: middle"
src="cid:part2.DE088597.A34800C7@mercer.edu" alt="$(x_2,y_2)$"><br>
<br>
and another line segment defined by the points<br>
<br>
<img style="vertical-align: middle"
src="cid:part3.6F47A8FF.04C4D687@mercer.edu" alt="$(x_3,y_3)$">
and <img style="vertical-align: middle"
src="cid:part4.FB4063F4.3190DB16@mercer.edu" alt="$(x_4,y_4)$"><br>
<br>
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 <img
style="vertical-align: middle"
src="cid:part5.430840D6.BD812D77@mercer.edu"
alt="$M_{1,1}M_{2,2}-M_{1,2}M_{2,1}$"> where the subscripts refer
to the matrix indices. Once you calculate the determinants then
find <img style="vertical-align: middle"
src="cid:part6.B5C84015.5277A702@mercer.edu" alt="$u_a$"> and <img
style="vertical-align: middle"
src="cid:part7.405ED6CC.4BFBAD21@mercer.edu" alt="$u_b$"> by
division and if both are between 0 and 1 the lines intersect.<br>
<br>
<br>
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<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
<a class="moz-txt-link-freetext" href="http://faculty.mercer.edu/pounds_aj">http://faculty.mercer.edu/pounds_aj</a>
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