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<title>Magnetic attraction algorithm</title>
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<h1>Magnetic attraction algorithm</h1>
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<p>The algorithm used to move monitors to the nearest one in “position dialog” is explained here.</p>
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<p>Segment equation is used. Let’s explain segment equation in order to understand the proccess:</p>
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<p>If you have two points, <b>p<sub>0</sub></b>, <b>p<sub>1</sub></b> ∈ ℝ <sup>2</sup>, the equation of straight line between <b>p<sub>0</sub></b> and <b>p<sub>1</sub></b> is: </p>
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<b>r</b> = <b>v</b> · t + <b>p<sub>0</sub></b>
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<p>where <b>v</b> = <b>p<sub>1</sub></b> - <b>p<sub>0</sub></b>, and t ∈ [0,1].</p>
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<p>Algorithm calculates equation of the segment between monitor centers. Then, it gets intersection points with edges of monitors:</p>
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<svg width="343" height="123" xmlns="http://www.w3.org/2000/svg" xmlns:svg="http://www.w3.org/2000/svg">
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<g>
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<title>Layer 1</title>
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<rect id="svg<sub>1</sub>" height="89" width="117" y="2.5" x="2.5" stroke-width="5" stroke="#000000" fill="#ffffff"/>
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<rect id="svg<sub>2</sub>" height="89" width="117" y="31.5" x="223.5" stroke-width="5" stroke="#000000" fill="#ffffff"/>
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<line id="svg_4" y2="77.5" x2="286.5" y1="47.5" x1="59.5" stroke-linecap="null" stroke-linejoin="null" stroke-dasharray="null" stroke-width="5" stroke="#000000" fill="none"/>
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<text style="cursor: move;" xml:space="preserve" text-anchor="middle" font-family="serif" font-size="24" id="svg_6" y="70.5" x="288.5" stroke-linecap="null" stroke-linejoin="null" stroke-dasharray="null" stroke-width="0" stroke="#000000" fill="#000000">c_1</text>
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<text style="cursor: move;" xml:space="preserve" text-anchor="middle" font-family="serif" font-size="24" id="svg_7" y="30.5" x="120.5" stroke-linecap="null" stroke-linejoin="null" stroke-dasharray="null" stroke-width="0" stroke="#000000" fill="#000000">t_2</text>
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<text style="cursor: move;" xml:space="preserve" text-anchor="middle" font-family="serif" font-size="24" id="svg_8" y="35.5" x="191.5" stroke-linecap="null" stroke-linejoin="null" stroke-dasharray="null" stroke-width="0" stroke="#000000" fill="#000000">t_1</text>
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<ellipse id="svg<sub>1</sub>1" ry="4" rx="4" cy="69" cx="223.5" stroke-linecap="null" stroke-linejoin="null" stroke-dasharray="null" stroke-width="5" stroke="#000000" fill="#000000"/>
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</g>
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</svg>
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<p>If <b>v</b> = <b>c<sub>1</sub></b> - <b>c<sub>0</sub></b>, <b>c<sub>0</sub></b> and <b>c<sub>1</sub></b> are monitors centers, the equation between them is <b>r</b> = <b>v</b> · t + <b>c<sub>0</sub></b>.</p>
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<p>where t<sub>1</sub> is the parameter of the mentioned equation to get the intersection point with the c<sub>1</sub> monitor.</p>
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<p>where t<sub>2</sub> the parameter with the c<sub>0</sub> monitor.</p>
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<p>t<sub>1</sub>, t<sub>2</sub> ∈ [0,1].</p>
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<p>If t<sub>2</sub><t<sub>1</sub>, the monitors are separated, otherwise the monitors are overlapped.</p>
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<p>With the previous information we get:</p>
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<p><b>r<sub>1</sub></b> = <b>v</b>· t<sub>1</sub> + <b>c<sub>0</sub></b></p>
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<p><b>r<sub>2</sub></b> = <b>v</b>· t<sub>2</sub> + <b>c<sub>0</sub></b></p>
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<p>Iff t<sub>2</sub><t<sub>1</sub>, c<sub>0</sub> monitor must be moved, and its displacement is provided by <b>r</b> = <b>r<sub>1</sub></b>-<b>r<sub>2</sub></b></p>
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</body>
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</html>
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