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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">Here is another slight adjustment of the test polyhedra that slightly increases the complexity of the intersection. No doubt there are a number of other fundamentally different ways two tetrahedra can intersect that I haven't tried yet. So far so good. Just one failure discovered so far... but it fails on the very first arc segment, so this is no doubt a big fat duh.</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">The algorithm seems to be basically right. Here it is in less summary:</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;"> 0. Remove coplanar domains</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;"> 1. Intersect edges with faces</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;"> 2. Trace out open and closed intersection arcs</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;"> 3. Section mesh(es) along arcs</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;"> 4. Assemble sections according to desired boolean result</p>
<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;"> 5. Triangulate any new non-triangular faces</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">with "open arcs" and "coplanar domains" not done yet, and a new final triangulation step added. Also, the assembly stage is rudimentary, and as I mentioned there is one significant performance issue and a lot of inconsistency handling work to be done. Other than that, it is nearly finished ;)</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">I did notice one unanticipated detail: when an intersection arc lies entirely inside a single face then it makes a hole in that face, or a hole in a hole, nested arbitrarily deeply. It is necessary to detect and handle those nested holes, that is, for each original face, collect together all the closed loops lying entirely inside a given face and triangulate the polygon consisting of all those loops. Not very hard given that we now have a pretty good triangulator, but without this a lot of constructions will break. Image solid2.png is a simple example.</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">I am looking forward to having usable boolean operations in the not enormously distant future.</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">Regards,</p>
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<p style=" margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">Daniel</p>
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