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Thread: Rhombus inside Rectangle : testing coordinates

  1. #1
    Oct 2008

    Rhombus inside Rectangle : testing coordinates

    Hi, I am building a web game, and I came across a small issue you might help me with:

    I have a rhombus inside a rectangle, and some random coordinates inside the rectangle. I have to test if these coordinates are inside the rhombus or outside of it. That’s it!

    I know everything about the rectangle and rhombus (angles & length)
    I could devise an ugly switch case to determine this, but I was wondering if they’re wasn’t a better (and faster ) approach to this problem.
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  2. #2
    Senior Member pankaj's Avatar
    Jul 2008
    New Delhi(India)
    Consider centre of the rectangle as origin and let the diagonals of the rhombus lie along the $\displaystyle x-$axis and the $\displaystyle y-$axis.The coordinates of the vertices of the rhombus are $\displaystyle A(\frac{-d}{2},0),D(0,\frac{-D}{2}),C(\frac{d}{2},0), B(0,\frac{D}{2}).$

    The cartesian equations of the sides $\displaystyle AD,DC,CB, BA $ are respectively

    $\displaystyle \frac{X}{\frac{-d}{2}}+\frac{Y}{\frac{-D}{2}}-1=0$

    $\displaystyle \frac{X}{\frac{d}{2}}+\frac{Y}{\frac{-D}{2}}-1=0$

    $\displaystyle \frac{X}{\frac{d}{2}}+\frac{Y}{\frac{D}{2}}-1=0$

    $\displaystyle \frac{X}{\frac{-d}{2}}+\frac{Y}{\frac{D}{2}}-1=0$

    When we substitute $\displaystyle (0,0)$ in the LHS of the above equations we get $\displaystyle -1$ i.e. a negative quantity is obtained in all the four cases.Therefore all points inside the rhombus when substituted in the LHS of the above equations must yield a negative quantity.

    Hope this helps.
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