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Copy path[85] [Blog 2011] Faster Convex-Convex SAT- Internal Objects.html
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[85] [Blog 2011] Faster Convex-Convex SAT- Internal Objects.html
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<title>Coder Corner » Archivio Blog » Faster convex-convex SAT: internal objects</title>
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<div class=post id=post-461>
<p class=title_post><a href="http://www.codercorner.com/blog/?p=461" rel=bookmark title="Permanent Link: Faster convex-convex SAT: internal objects">Faster convex-convex SAT: internal objects</a></p>
<div class=entrytext>
<div class=mceTemp>I noticed that I had a fairly low amount of posts in the “physics” category, for somebody working in physics & collision detection all day long. So let me try to increase the ratio a bit. <a href="http://www.codercorner.com/blog/?p=24">Last time</a> we talked about partial hulls, today I’ll present another optimization for the same problem.</div>
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<div class=mceTemp>The penetration depth between two convex polytopes can easily be computed using separating-axis tests. But the large number of edge-edge tests often makes this process very slow, and other algorithms such as EPA or Xenocollide are thus often chosen over SAT to compute the MTD between two convexes. There are however a large number of tricks to optimize the SAT version. One of the most efficient ones is to use simple “internal objects”, i.e. simple objects such as a sphere or a box embedded in the convex.</div>
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<div class=mceTemp>Recall that for each candidate axis we do something like:</div>
<blockquote>
<div class=mceTemp>bool testSepAxis(const btVector3& axis, const MyConvex& hull0, const MyConvex& hull1, float& dmin, Vector3& mtd)<br>
{<br>
// Project hull 0 on candidate axis<br>
float Min0,Max0;<br>
hull0.Project(axis, Min0, Max0);</div>
<div class=mceTemp></div>
<div class=mceTemp>// Project hull 1 on candidate axis<br>
float Min1,Max1;<br>
hull1.Project(axis, Min1, Max1);</div>
<div class=mceTemp></div>
<div class=mceTemp>// If the projected intervals don’t overlap, the candidate axis is a separating axis.<br>
// In that case the hulls don’t overlap, we can early exit and return non penetration.<br>
if(Max0<Min1 || Max1<Min0)<br>
return false;</div>
<div class=mceTemp></div>
<div class=mceTemp>// Else compute penetration depth (PD) = how much the intervals overlap<br>
const float d0 = Max0 - Min1;<br>
const float d1 = Max1 - Min0;<br>
const float depth = d0<d1 ? d0:d1;</div>
<div class=mceTemp></div>
<div class=mceTemp>// Then keep track of minimal PD. The axis for which the PD is minimal is the MTD.<br>
if(d<dmin)<br>
{<br>
dmin = d;<br>
mtd = axis;<br>
}<br>
return true;<br>
}</div>
</blockquote>
<div class=mceTemp>So we’re looking for the minimal overlap, and the MTD is the axis for which the overlap is minimal. The idea, then, is to first project the simpler, internal objects on the candidate axis, and use the overlap results to skip the real hull projections if we can.</div>
<div class=mceTemp></div>
<div class=mceTemp>Say our internal objects are spheres (it could also be boxes, but for the sake of the argument let’s use spheres). Let <em>hullOverlap(V)</em> be the overlap value for the hulls on a given axis V, and <em>sphereOverlap(V)</em> be the one for the spheres on the same axis. Since spheres are embedded in the hulls, it should be clear that we always have:</div>
<blockquote>
<div class=mceTemp>hullOverlap(V) >= sphereOverlap(V) (1) (see Figure 1)</div>
</blockquote>
<div class=mceTemp>Now let <em>minHullOverlap</em> be our current best result, i.e. our current minimal penetration depth computed from real hull projections (not sphere projections). It should be obvious that thanks to (1) we have:</div>
<blockquote>
<div class=mceTemp>sphereOverlap(V) > minHullOverlap => hullOverlap(V) > minHullOverlap (2)</div>
</blockquote>
<div class=mceTemp>In other words, if sphereOverlap(V) is already bigger than our current best result, hullOverlap(V) will be bigger as well, and thus there is no need to compute it.</div>
<div class=mceTemp></div>
<div class=mceTemp>
<p style=TEXT-ALIGN:center><a href=http://www.codercorner.com/Pictures/InternalObjects.png><img class=aligncenter title="Internal objects" 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" alt="Internal objects" width=412 height=384></a></p>
</div>
<div class=mceTemp style=TEXT-ALIGN:center>Figure 1</div>
<div class=mceTemp></div>
<div class=mceTemp>This is interesting since, of course, projecting a sphere is a lot faster than projecting a convex hull. Projecting a sphere is one dot product, projecting a hull is one dot product <em><strong>per vertex </strong></em>(plus, we don’t need to even access the vertex memory).</div>
<div class=mceTemp></div>
<div class=mceTemp>As Figure 1 shows, the embedded spheres don’t need to actually touch for this test to be useful - only the spheres’ projections on the candidate axis. In practice, this happens very often, and that single optimization sometimes culls away 90% of the actual hull projections. You can try out <a title=InternalObjects href=http://www.codercorner.com/Code/InternalObjects.rar>this demo</a> for a proof-of-concept.</div>
<div class=mceTemp></div>
<div class=mceTemp>It is also a good idea to test the MTD from the previous frame first, to initialize minHullOverlap to a small value right from the start - discarding candidate axes as early as possible.</div>
<div class=mceTemp></div>
<div class=mceTemp>Finally a note about the internal shapes one should choose. A sphere might not be a great fit for long thin rods, in which case an embedded box might be better. But it might be easier to just use both, and at runtime choose whatever internal shape gives the best results. This is what I do in the above demo.</div>
<div class=mceTemp></div>
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<h3 id=comments>3 Responses to “Faster convex-convex SAT: internal objects”</h3> <br><br>
<ol class=commentlist>
<li class=alt id=comment-12739>
<cite><a href=http://therealdblack.wordpress.com/ rel="external nofollow">David Black</a></cite> Says:
<br><br>
<small class=commentmetadata><a href=#comment-12739 title>January 25th, 2011 at 9:15 am</a> </small>
<p>I tend to find that 95% of convexes I see in my engine are boxes, cylinders from segments and wedges. The only examples I have of more complex polyhedra are those generated by out of control auto generation(which is something I have been meaning to remove from my levels)…</p>
<p>I would be very tempted to just decompose everything into tetra(and wedges + boxes as an optimization) and let the broad/mid phase deal with the culling. (this seems like the logical extension of your last post…)</p>
<p>I think this approach would also be the best way to approach doing RBs on GPUs as it avoids most of the divergant flow control, has a fixed size for each primitive type and increases the amount of parallel work.</p>
</li>
<li id=comment-12788>
<cite>admin</cite> Says:
<br><br>
<small class=commentmetadata><a href=#comment-12788 title>January 27th, 2011 at 1:14 am</a> </small>
<p>Well people use more complex convexes in a lot of different places, for example to approximate the shape of a car in a racing game, or around ragdoll bones, etc. John’s old decomposer also approximates arbitrary meshes with several convexes, and these can have a fair amount of vertices. So we need to optimize the worst case anyway.</p>
</li>
<li class=alt id=comment-12795>
<cite><a href=http://therealdblack.wordpress.com/ rel="external nofollow">David Black</a></cite> Says:
<br><br>
<small class=commentmetadata><a href=#comment-12795 title>January 27th, 2011 at 7:10 am</a> </small>
<p>I hope you guys release a GPU rigid body system soon, and also some details about how well it works and how you adapt such things to work within the constraints of the GPU(maybe just using software for some things, like big convexes).</p>
<p>Just using collections of connected spheres seems a bit lame… (as in Batman:-) and I only found one brief mention and no analysis in a slide.</p>
<p>I am tempted to to experiment my self with something in OpenCL, but I have more practical useful things to do(from my perspective anyway).</p>
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<li><a href="http://www.codercorner.com/blog/?m=200907" title="July 2009">July 2009</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200906" title="June 2009">June 2009</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200905" title="May 2009">May 2009</a></li>
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<li><a href="http://www.codercorner.com/blog/?m=200811" title="November 2008">November 2008</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200810" title="October 2008">October 2008</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200809" title="September 2008">September 2008</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200808" title="August 2008">August 2008</a></li>
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<li><a href="http://www.codercorner.com/blog/?m=200806" title="June 2008">June 2008</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200805" title="May 2008">May 2008</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200804" title="April 2008">April 2008</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200803" title="March 2008">March 2008</a></li>
<li><a href="http://www.codercorner.com/blog/?m=200802" title="February 2008">February 2008</a></li>
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</li>
<li><h2>Categories</h2>
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</li>
<li>
<ul>
<li id=linkcat-2 class=linkcat><h2>Blogroll</h2>
<ul>
<li><a href=http://www.moravanszky.com/>Adam Moravanszky</a></li>
<li><a href=http://www.atari-forum.com/>Atari forums</a></li>
<li><a href=http://www.bulletphysics.com/Bullet/phpBB3/>Bullet Physics forums</a></li>
<li><a href=http://www.cbloom.com/>Charles Bloom</a></li>
<li><a href=http://realtimecollisiondetection.net/blog/>Christer Ericson</a></li>
<li><a href=http://tuxedolabs.blogspot.com/ title="Physics blog from Dennis">Dennis Gustafsson</a></li>
<li><a href=http://digestingduck.blogspot.com/ title="Home of Recast library">Digesting Duck</a></li>
<li><a href=http://www.iquilezles.org/blog/ title=iq>El Trastero</a></li>
<li><a href=https://fgiesen.wordpress.com/ title=Ryg>Fabian Giesen</a></li>
<li><a href="http://www.humus.name/index.php?page=News">Humus</a></li>
<li><a href=http://castano.ludicon.com/blog/>Ignacio Castano</a></li>
<li><a href=http://www.iguanademos.com/Jare/jblog_main.php title="Jare / Iguana">Jare</a></li>
<li><a href=http://jratcliffscarab.blogspot.com/>John Ratcliff</a></li>
<li><a href=http://msinilo.pl/blog/>Maciej Sinilo</a></li>
<li><a href="https://mollyrocket.com/forums/index.php?sid=8a25506e2e63ebc6dbba67402cddb996">Molly Rocket</a></li>
<li><a href=http://oni.bungie.org/community/forum/index.php>Oni forums</a></li>
<li><a href=http://patapom.com/blog/>Patapom’s blog</a></li>
<li><a href=http://randomascii.wordpress.com/ title="Bruce Dawson">Random Ascii</a></li>
<li><a href=http://timmoss.blogspot.com/>Tim Moss</a></li>
<li><a href=https://tomforsyth1000.github.io/blog.wiki.html>Tom Forsyth</a></li>
<li><a href=http://www.valvesoftware.com/publications.html>Valve Publications</a></li>
<li><a href=http://blog.wolfire.com/ title="Home of Lugaru & Overgrowth">Wolfire blog</a></li>
</ul>
</li>
</ul>
</li>
<li><h2>Calendar</h2>
<table id=wp-calendar summary=Calendar>
<caption>July 2021</caption>
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<th abbr=Thursday scope=col title=Thursday>T</th>
<th abbr=Friday scope=col title=Friday>F</th>
<th abbr=Saturday scope=col title=Saturday>S</th>
<th abbr=Sunday scope=col title=Sunday>S</th>
</tr>
</thead>
<tfoot>
<tr>
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</tr>
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</tr>
<tr>
<td>19<td>20<td>21<td>22<td id=today>23<td>24<td>25</td>
</tr>
<tr>
<td>26<td>27<td>28<td>29<td>30<td>31</td>
<td class=pad colspan=1> </td>
</tr>
</tbody>
</table> </li>
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