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Thread: Using the determinant to decide which side of a line a point is on

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    Using the determinant to decide which side of a line a point is on

    I have attached a photo of the complete problem description below. I really donít understand what a determinant is other then a strange formula. Not even sure where to start with this one
    Attached Thumbnails Attached Thumbnails Using the determinant to decide which side of a line a point is on-13cd408b-1e90-4908-9d19-7f6210affffa.jpeg  
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    Re: Using the determinant to decide which side of a line a point is on

    Why don't you start by using your formula?
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    Re: Using the determinant to decide which side of a line a point is on

    Quote Originally Posted by mdm508 View Post
    I have attached a photo of the complete problem description below. I really don’t understand what a determinant is other then a strange formula. Not even sure where to start with this one
    Many universities maintain course specific help webpages. However this site does not attempt to do that. Therefore, you must post all relevant axioms & definitions for any questions. Otherwise, we have no way of knowing the nature of the problem.

    For example: I have never seen the term "directed line". I know about sides of a line, about rays, about half-lines, but nothing about directed lines. It appears that this question is very specific to a particular set of course notes. In courses I have given, I have used the text by Varberg&Roberts, Convex Functions. This question is similar to some there, but the vocabulary is off. So please give us some idea of your course material.
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    Re: Using the determinant to decide which side of a line a point is on

    I apolagize for the ambiguity, I will try and give more background in future posts. The class I am taking is computational geometry. We are studying an algorithm called the Graham Scans which takes a set of (x,y)s and outputs the Convex Hull of the input set.

    The details of the algorithm are explained on wikipedia, the crucial step is deciding if a new point is also in the hull.
    Suppose you have added points $x,y$ already to the hull and know you want to consider if $z$ is also in the hull. $z$ is only in the hull if a ‘clockwise’ turn is made from $y$ to $z$. That is, if you have a line segment $\overline{xy}$ does $\overline{yz}$ form a counter clockwise turn w.r.t $\overline{x,y}$ if so it is not in otherwise it is
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    Re: Using the determinant to decide which side of a line a point is on

    Hey mdm508.

    You should consider finding out how to link a dot product with the normal of the line to the determinant.

    Consider finding the connection between <n,r-r0> < 0 and <n,r-r0> > 0 and what you have above [but for two dimensions only].
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