You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
42 lines
3.7 KiB
42 lines
3.7 KiB
<html>
|
|
<head>
|
|
<title>Magnetic attraction algorithm</title>
|
|
<meta charset='utf-8'/>
|
|
</head>
|
|
<body>
|
|
<h1>Magnetic attraction algorithm</h1>
|
|
<p>The algorithm used to move monitors to the nearest one in "position dialog" is explained here.</p>
|
|
<p>Segment equation is used. Let's explain segment equation in order to understand the proccess:</p>
|
|
<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 straigh line between <b>p<sub>0</sub></b> and <b>p<sub>1</sub></b> is: </p>
|
|
|
|
<b>r</b> = <b>v</b> · t + <b>p<sub>0</sub></b>
|
|
|
|
<p>where <b>v</b> = <b>p<sub>1</sub></b> - <b>p<sub>0</sub></b>, and t ∈ [0,1].</p>
|
|
<p>Algorithm calculates equation of the segment between monitor centers. Then, it gets intersection points with edges of monitors:</p>
|
|
<svg width="343" height="123" xmlns="http://www.w3.org/2000/svg" xmlns:svg="http://www.w3.org/2000/svg">
|
|
<!-- Created with SVG-edit - http://svg-edit.googlecode.com/ -->
|
|
<g>
|
|
<title>Layer 1</title>
|
|
<rect id="svg<sub>1</sub>" height="89" width="117" y="2.5" x="2.5" stroke-width="5" stroke="#000000" fill="#ffffff"/>
|
|
<rect id="svg<sub>2</sub>" height="89" width="117" y="31.5" x="223.5" stroke-width="5" stroke="#000000" fill="#ffffff"/>
|
|
<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"/>
|
|
<text style="cursor: text;" xml:space="preserve" text-anchor="middle" font-family="serif" font-size="24" id="svg_5" y="50.5" x="53.5" stroke-linecap="null" stroke-linejoin="null" stroke-dasharray="null" stroke-width="0" stroke="#000000" fill="#000000">c_0</text>
|
|
<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>
|
|
<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>
|
|
<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>
|
|
<ellipse ry="4" rx="4" id="svg_9" cy="55" cx="119.5" stroke-linecap="null" stroke-linejoin="null" stroke-dasharray="null" stroke-width="5" stroke="#000000" fill="#000000"/>
|
|
<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"/>
|
|
</g>
|
|
</svg>
|
|
<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>
|
|
<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>
|
|
<p>where t<sub>2</sub> the parameter with the c<sub>0</sub> monitor.</p>
|
|
<p>t<sub>1</sub>, t<sub>2</sub> ∈ [0,1].</p>
|
|
|
|
<p>If t<sub>2</sub><t<sub>1</sub>, the monitors are separated, otherwise the monitors are overlapped.</p>
|
|
<p>With the previous information we get:</p>
|
|
<p><b>r<sub>1</sub></b> = <b>v</b>· t<sub>1</sub> + <b>c<sub>0</sub></b></p>
|
|
<p><b>r<sub>2</sub></b> = <b>v</b>· t<sub>2</sub> + <b>c<sub>0</sub></b></p>
|
|
<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>
|
|
</body>
|
|
</html> |