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Triangulation in three dimensions: Difference between revisions

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== Condition for intersection ==
 
If ''AD'', ''BD'', ''CD'' are assigned according to the arrangement,
 
<br />
:<math>AD \le BD \le CD</math>
 
Then ''AD, BD, CD'' intersect if and only if,<br />
 
:<math>AD+BD \ge AB \ge BD-AD</math>
:<math>AD+CD \ge AC \ge CD-AD</math>
:<math>BD+CD \ge BC \ge CD-BD</math>
 
<br />
Viz, if <br />
 
''AD''=r<sub>A</sub>=radius of sphere centered at '''A''',<br />▼
: ''BDAD'' = ''r''<sub>B''A''</sub> = radius of sphere centered at '''BA''', and <br />
: ''CDBD'' = ''r''<sub>C''B''</sub> = radius of sphere centered at '''CB''',<br />and
▲: ''ADCD'' = ''r''<sub>A''C''</sub> = radius of sphere centered at '''AC''',<br />
such that, <br />
:<math>r_A \le r_B \le r_C</math>
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