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    <p>I am answering this on both MO &amp; SO, expanding the comments I made on MO.</p> <p>My sense is that no computational trick with signed tetrahedra volumes will avoid the precision issues that are your main concern. This is because, if you have tightly twisted segments, the orientation of the triangle depends on the precise positioning of the cutting plane. <br>[image removed; see below]<br> In the above example, the upper plane crosses the segments in the order (<em>a,b,c</em>) [ccw from above]: (<em>red,blue,green</em>), while the lower plane crosses in the reverse order (<em>c,b,a</em>): (<em>green,blue,red</em>). The height of the cutting plane could be determined by your last bit of precision.</p> <p>Consequently, I think it makes sense to just go ahead and compute the points of intersection in the cutting plane, using enough precision to make the computation exact. If your segment endpoints coordinates and plane coefficients have <em>L</em> bits of precision, then there is just a small constant-factor increase needed. Although I am not certain of precisely what that factor is, it is small--perhaps 4. You will not need e.g., <em>L</em><sup>2</sup> bits, because the computation is solving linear equations. So there will not be an explosion in the precision required to compute this exactly.</p> <p>Good luck!</p> <p>(I was prevented from posting the clarifying image because I don't have the reputation. See the <a href="https://mathoverflow.net/questions/31578/computational-geometry-tetrahedron-signed-volume/31695#31695">MO answer</a> instead.)</p> <p><strong>Edit</strong>: Do see the MO answer, but here's the image:</p> <p><img src="https://i.stack.imgur.com/hc2Nm.jpg" alt="Image"></p>
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    1. POComputational geometry, tetrahedron signed volume
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    1. USJoseph O'Rourke
    1. USJoseph O'Rourke
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    1. POComputational geometry, tetrahedron signed volume
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    1. CO@ShreevastaR: Thanks! :-)
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      1. USJoseph O'Rourke
    2. COYou're welcome, professor :-) (and welcome to SO as well!)
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      1. USShreevatsaR
    3. COThanks a lot. I'll get an AP lib from somewhere and do this.
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      1. USmr grumpy
 

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