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Copy path[32-3] [Blog 1999] Simple Intersection Tests for Games.html
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[32-3] [Blog 1999] Simple Intersection Tests for Games.html
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<!DOCTYPE html> <html lang=en class=hb-loaded style><!--
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url: https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php?page=3
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<title>Gamasutra - Simple Intersection Tests For Games</title>
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<meta name=keywords content="game development, game developer, game programming, game programmer, videogame, artificial intelligence, 3D animation, game design, 3D modeling, game business, game jobs, game directory, game development software, game technology, 3D technology, game producer, game audio, game animation, virtual reality, digital entertainment, PC game, Xbox game, game news, new game, arcade development, Nintendo development, Playstation development, Playstation 2, PS2, Dreamcast development, Game Developer magazine, Computer Game Developers Conference, Game Developers Conference, Independent Game Developers Conference, CMP Game Media Group, game industry research, online game development, digital assets, free textures, free 3D models, free shaders, Gamasutra Exchange, 3D Studio Max textures"><meta name=description content="A key component to virtually any graphical game, 2D or 3D, is a collision detection system for game objects. In this article, Looking Glass's Miguel G"><link rel=image_src href=https://twimgs.com/gamasutra//images/questionmark.jpg>
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" 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<strong>Simple Intersection Tests For Games</strong>
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" 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<h1 class=item_title>Simple Intersection Tests For Games</h1>
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<span class=newsAuth>by <a href=https://www.gamasutra.com/view/authors/751407/miguel_gomez.php>miguel gomez</a></span><span class=pageNav> [<span class=category_links><a class=category_links href=https://www.gamasutra.com/features//></a></span>]</span><br>
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<title>Error 404 (Not Found)!!1</title>
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<p><b>404.</b> <ins>That’s an error.</ins>
<p>The requested URL <code>/u/0/se/0/_/+1/fastbutton</code> was not found on this server. <ins>That’s all we know.</ins>
</p>'></iframe></div><g:plusone size=medium count=false data-gapiscan=true data-onload=true data-gapistub=true></g:plusone>
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<a href=http://feeds.feedburner.com/GamasutraFeatureArticles><img src=data:image/gif;base64,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 width=15 height=15 border=0 alt=RSS></a>
</div>
<hr>
<strong>October 18, 1999</strong>
<a href=https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php><img src='data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" width="91" height="16"><rect fill-opacity="0"/></svg>' width=91 height=16 border=0 alt="Article Start" style="background-blend-mode:normal!important;background-clip:content-box!important;background-position:50% 50%!important;background-color:rgba(0,0,0,0)!important;background-image:var(--sf-img-38)!important;background-size:100% 100%!important;background-origin:content-box!important;background-repeat:no-repeat!important"></a>
<a href="https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php?page=2">
<img src='data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" width="68" height="16"><rect fill-opacity="0"/></svg>' width=68 height=16 border=0 alt=Previous style="background-blend-mode:normal!important;background-clip:content-box!important;background-position:50% 50%!important;background-color:rgba(0,0,0,0)!important;background-image:var(--sf-img-39)!important;background-size:100% 100%!important;background-origin:content-box!important;background-repeat:no-repeat!important">
</a>
<strong>Page 3 of 7</strong>
<a href="https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php?page=4">
<img src='data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" width="44" height="16"><rect fill-opacity="0"/></svg>' width=44 height=16 border=0 alt=Next style="background-blend-mode:normal!important;background-clip:content-box!important;background-position:50% 50%!important;background-color:rgba(0,0,0,0)!important;background-image:var(--sf-img-40)!important;background-size:100% 100%!important;background-origin:content-box!important;background-repeat:no-repeat!important">
</a>
<hr>
<div class="item_body mobile_image_transform">
<div class=clear> </div>
<p align=left>
<strong>An
Axis-Aligned Bounding Box (AABB) Sweep Test</strong><strong>
</strong><strong> </strong>
</p>
<p align=left>
Just
like the name says, the faces of an axis-aligned bounding box are aligned
with the coordinate axes of its parent frame (see Figure 3). In most
cases AABBs can fit an object more tightly than a sphere, and their
overlap test is extremely fast.
</p>
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<div class="module_right right bottom30">
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</div>
</div>
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<p align=left>
To
see if A and B overlap, a separating axis test is used along the x,
y, and z-axes. If the two boxes are disjoint, then at least one of these
will form a separating axis. Figure 4 illustrates an overlap test in
one dimension.
</p>
<p align=left>
</p>
<p align=left>
<img src=data:image/gif;base64,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 alt width=432 height=186 align=middle>
</p>
<p align=left>
</p>
<p align=center>
<img src="data:image/gif;base64,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" alt width=408 height=106>
</p>
<p align=left>
In
this example the x-axis forms a separating axis because
</p>
<p align=center>
<img src=data:image/gif;base64,R0lGODlhagAmAID/AMDAwAAAACH5BAEAAAAALAAAAABqACYAAALBhI+py+0Po5y02ouz3rz7D4biSJbmiabqypIB9bYyEkv1LN+Qjq9xAAwGEzxA8QRE/Q413fFogn5etyWxIcVIsx2nYxuCcrtX7ENMnYiN44zXfF78uMIh0Tqqxr9yJoyh50KzB9jnp1Z4mDfIl6jQ1GbwpLgoueP4KJmmARmlmaRpRDl6R9UZyQQainqJFeihyhFLBkfKCcIasfYqK0qWS5jJu7HZC9xo06O8zNzs/AwdLT1NXW19jZ2tvc3d7R1SAAA7 alt width=106 height=38>
</p>
<p align=left>
Note
that the separating axis test will return true even if one box fully
contains the other. A more general separating axis test is given in
the section below on oriented bounding boxes (OBB’s). Listing 3 defines
an AABB class that implements this overlap test.
</p>
<p align=left>
<em><strong>Listing
3. An AABB class.</strong></em>
</p>
<p align=left>
#include
"vector.h"
</p>
<p align=left>
// An
axis-aligned bounding box
</p>
<p align=left>
class
AABB<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
public:
</blockquote>
</div>
<blockquote>
<p align=left>
VECTOR P; //position<br>
VECTOR E;
//x,y,z extents<br>
</p>
<blockquote>
<p align=left>
AABB(
const VECTOR& p, <br>
const VECTOR& e ): P(p),
E(e)
</p>
<p align=left>
{}
</p>
</blockquote>
</blockquote>
<p align=left>
//returns
true if this is overlapping b<br>
const bool
overlaps( const AABB& b ) const<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
const
VECTOR T = b.P - P;//vector from A to B<br>
return fabs(T.x)
<= (E.x + b.E.x)
</blockquote>
</div>
<blockquote>
<p align=left>
&&
</p>
<p align=left>
fabs(T.y)
<= (E.y + b.E.y)
</p>
<p align=left>
&&
</p>
<p align=left>
fabs(T.z)
<= (E.z + b.E.z);
</p>
</blockquote>
<p align=left>
}
</p>
<p align=left>
//NOTE:
since the vector indexing operator is not const,<br>
//we must cast
away the const of the this pointer in the<br>
//following
min() and max() functions<br>
//min x,
y, or z
</p>
<p align=left>
const
SCALAR min( long i ) const
</p>
<p align=left>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
return
((AABB*)this)->P[i] - ((AABB*)this)->E[i];
</blockquote>
</div>
<p align=left>
}
</p>
<p align=left>
//max
x, y, or z<br>
const SCALAR
max( long i ) const
</p>
<p align=left>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
return
((AABB*)this)->P[i] + ((AABB*)this)->E[i];
</blockquote>
</div>
<p align=left>
}
</p>
<p align=left>
};
</p>
<p align=left>
For
more information on AABBs and their applications, please see [8].
</p>
<p align=left>
Just
like spheres, AABBs can be swept to find the first and last occurrence
of overlap. In Figure 5(a), A and B experienced displacements <strong>v<sub>a</sub></strong>
and <strong>v<sub>b</sub></strong>, respectively, while Figure 5(b) shows B's
displacement as observed by A.
</p>
<p align=left>
<img src=data:image/gif;base64,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 alt width=478 height=156>
</p>
<p align=left>
</p>
<p align=left>
Figure 6 shows
B's displacement as observed by A.
</p>
<p align=left>
<img src="data:image/gif;base64,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" alt width=368 height=208>
</p>
<p align=left>
In
this example, the normalized times it took for the x-extents and y-extents
to overlap are given by
</p>
<p align=left>
<img src=data:image/gif;base64,R0lGODlhOAE8AID/AMDAwAAAACH5BAEAAAAALAAAAAA4ATwAAAL/hI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuC8fyTNf2jef6zvf+DwwKh8Si8YhMKpfMpvMJjUqn1Kr1is1qY4EuwAvrBr7j7QNM5pbTZgd6JI4z3u0Geh2Kixf3ut2G5/f3RVMWKHhwGIZ4ZqDYYsiYMPbIQul2Vql0WUg4aKdZFCkzmhGKRKfGcSoE5qXnSCnLlxrhKrtH9krLKooAm/aqmIuBByw3XOt0acg859nhTLg7Cb2sIL37yHlxmB2MbR3lzLnt+PFdei4O0uvB/Tstz77unkifvn5Pf00+X20PQj5x8PIE3KDMnzSA3cyV8xSoIBQ9woTFA4aQIixX//pIHIRDUdesexgzatzDkZ+gj3lWsJzxsp2qjm5CSuJFMqLEPhI03vQILebPeOdyrWnGkObQTkpBlVwaS586b/t62oSKruqqk1y7ev0KNizXTBD3GQvX1JTYtWzbuiUGlA1WU2braq0ndO67qHmXIg1q9g3Svno1oDwqsbBcXSJxJSp4+FdixZAIb7FsSyVlFZizdBaoefOJyaI5fy7dMzTqEqdXu96h7LWkO61hB6EtGwXP3KyP8h5993fLtMKjES++6jhyw6qXF2vu3ELs6IZrL9cJnfqzSaS1S7d+Pbv3RuNlgufdvXyF6eozny/+vr18svPrL7KPP7/+/fz7+xf/D2CAAg5IYIEGHohgggouyGCDDjpQAAA7 alt width=312 height=60>
</p>
<p align=left>
and
it can be seen that the x-extents will cross before the y-extents. The
two boxes cannot overlap until all the extents are overlapping, and
the boxes will cease to overlap when any one of these extents becomes
disjoint. If <em>u<sub>0,x</sub></em>, <em>u<sub>0,y</sub></em>, and <em>u<sub>0,z</sub></em>
were the times at which the x, y, and z-extents began to overlap, then
the earliest time at which the boxes could have begun to overlap was
</p>
<p align=left>
<img src=data:image/gif;base64,R0lGODlhrgAcAID/AMDAwAAAACH5BAEAAAAALAAAAACuABwAAAL/hI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuC8fyTNf2jedkoIt8P/oBQcJhp2j0IJOYJVPjtASEUcX0OrUCstvi1fANW6kb7rZMvlQlvDTn2wXL52lk+7CG3OfNM7+SF+Gmh2WGd/gXJzfIF6iHCAUp9SZJ2Yi397fEqFbZmUjh+PBjaDh56ZeauQnmJYpA6npa+vrKEOtHmuGmq1iXgNtrG0wX2poLeovW9quWFfYcDd3byowoS5VtXYyZ6ht9DQvn+UEN42iuSA6cmJkMq+n9fjS/EphuJ9jufb/PXpLu3Kh4trh1A0QQ3glTRrg8k8cGF8SI1cY9mVFwFMM+Dxc7fvIIMqTIkSRLmjRRAAA7 alt width=174 height=28>
</p>
<p align=left>
Likewise,
if <em>u<sub>1,x</sub></em>, <em>u<sub>1,y</sub></em>, and <em>u<sub>1,z</sub></em>
are the times at which the x, y, and z-extents become disjoint, then
the earliest time at which the boxes could have become disjoint was
</p>
<p align=left>
<img src="data:image/gif;base64,R0lGODlhqgAeAID/AMDAwAAAACH5BAEAAAAALAAAAACqAB4AAAL/hI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuC8drANGyad9prpN8P/oBRcKhp2g8EnNIROAJFdKeBmr1agUgs80aU8O1dMXawzgCrdqm7PVVMTVj4u8LvVw55+XeqJSP5/a2BWhXaFhHoad4mPE1WCcI18iYiIi3B7K2WAMo+EioxbmwuVFK9lF6egkaaTlIl4WmFjhaezubSiVra7b76wf8msbrpcbmhLaJTDmp0tsx+sdz9rObUI2d1hwEw1kU1omNSd5gTQ7tGLMIjprc+8ftk0Q6aSsFfZ7OsU1/LBpIkZVrYgZG8edvHxyFyRAm1KXEocSJFCtavIgxo8aNCBw7evwIckIBADs=" alt width=170 height=30>
</p>
<p align=left>
In
order for the two boxes to have overlapped during their displacement,
the condition
</p>
<p align=left>
<img src="data:image/gif;base64,R0lGODlhPgAaAID/AMDAwAAAACH5BAEAAAAALAAAAAA+ABoAAAJghI+py+0Po5y02ouz3rzb4IULKJYGaYpoqgTo6sDtu4G0JB+2zt1TfuL1hBSgT0NyIZSQXPIFfDwByeDntLNWXLabk8tNhJnaTlWFppail3OI3YZ/yKy6/Y7P6/f8vqQAADs=" alt width=62 height=26>
</p>
<p align=left>
must
have been met. Just like in the sphere sweep test, the positions of
first and last overlap can be linearly interpolated with <em>u</em>. Listing
4 gives an implementation of this AABB sweep algorithm.
</p>
<p align=left>
<em><strong>Listing
4. An AABB sweep algorithm.</strong></em>
</p>
<p align=left>
#include
"aabb.h"
</p>
<p align=left>
//Sweep
two AABB's to see if and when they first<br>
//and last
were overlapping
</p>
<p align=left>
const
bool AABBSweep<br>
(
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
const
VECTOR& Ea, //extents of AABB A<br>
const VECTOR& A0, //its
previous position<br>
const VECTOR& A1, //its
current position<br>
const VECTOR& Eb, //extents
of AABB B<br>
const VECTOR& B0, //its
previous position<br>
const VECTOR& B1, //its
current position<br>
SCALAR& u0, //normalized
time of first collision<br>
SCALAR& u1 //normalized
time of second collision
</blockquote>
</div>
<p align=left>
)
</p>
<p align=left>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
const
AABB A( A0, Ea );//previous state of AABB A<br>
const AABB
B( B0, Eb );//previous state of AABB B<br>
const VECTOR
va = A1 - A0;//displacement of A<br>
const VECTOR
vb = B1 - B0;//displacement of B
</blockquote>
</div>
<blockquote>
<p align=left>
//the
problem is solved in A's frame of reference
</p>
<p align=left>
VECTOR
v = vb - va;<br>
//relative
velocity (in normalized time)
</p>
<p align=left>
VECTOR
u_0(0,0,0);<br>
//first times of overlap along each axis
</p>
<p align=left>
VECTOR
u_1(1,1,1);<br>
//last times of overlap along each axis
</p>
<p align=left>
//check
if they were overlapping <br>
// on the
previous frame<br>
if( A.overlaps(B)
)<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
</blockquote>
</div>
<blockquote>
<p align=left>
u0
= u1 = 0;<br>
return
true;
</p>
</blockquote>
<p align=left>
}
</p>
<p align=left>
//find
the possible first and last times<br>
//of overlap
along each axis<br>
for( long
i=0 ; i<3 ; i++ )<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
</blockquote>
</div>
<blockquote>
<p align=left>
if(
A.max(i)<B.min(i) && v[i]<0 )<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
u_0[i]
= (A.max(i) - B.min(i)) / v[i];
</blockquote>
</div>
<p align=left>
}
</p>
<p align=left>
else
if( B.max(i)<A.min(i) && v[i]>0 )<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
u_0[i]
= (A.min(i) - B.max(i)) / v[i];
</blockquote>
</div>
<p align=left>
}
</p>
<p align=left>
if(
B.max(i)>A.min(i) && v[i]<0 )<br>
{
</p>
<div align=left>
<blockquote>
u_1[i] = (A.min(i)
- B.max(i)) / v[i];
</blockquote>
</div>
<p align=left>
}
</p>
<p align=left>
else
if( A.max(i)>B.min(i) && v[i]>0 )<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
u_1[i]
= (A.max(i) - B.min(i)) / v[i];
</blockquote>
</div>
<p align=left>
}
</p>
</blockquote>
<p align=left>
}
</p>
<p align=left>
//possible
first time of overlap<br>
u0 = MAX(
u_0.x, MAX(u_0.y, u_0.z) );
</p>
<p align=left>
//possible
last time of overlap<br>
u1 = MIN(
u_1.x, MIN(u_1.y, u_1.z) );
</p>
<p align=left>
//they
could have only collided if<br>
//the first
time of overlap occurred<br>
//before
the last time of overlap<br>
return u0
<= u1;
</p>
</blockquote>
<p align=left>
}
</p>
</div>
<hr>
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