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Copy path[32-1] [Blog 1999] Simple Intersection Tests for Games.html
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[32-1] [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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saved date: Sat Jul 24 2021 02:23:00 GMT+0800 (中国标准时间)
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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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<meta property=og:type content=article>
<meta property=og:url content=https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php>
<meta property=og:title content="Simple Intersection Tests For Games">
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<meta property=og: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 Gomez explains some simple intersection tests for the most useful shapes: spheres and boxes.">
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<meta name=twitter:creator content=@gamasutra>
<meta name=twitter:title content="Simple Intersection Tests For Games">
<meta name=twitter: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 Gomez explains some simple intersection tests for the most useful shapes: spheres and boxes.">
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" 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<strong>Simple Intersection Tests For Games</strong>
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<span style=color:#660000> Page 1 </span>
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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>
<strong>Page 1 of 7</strong>
<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="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-39)!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>
Whether
it's your car crossing the finish line at 180 miles per hour, or a bullet
tearing through the chest of your best friend, all games make use of
collision detection for object interaction. This article describes some
simple intersection tests for the most useful shapes: spheres and boxes.
</p>
<p align=left>
<strong>Sweep
Tests for Moving Objects</strong>
</p>
<div class=hide-phone>
<div class="module_right right bottom30">
<div id=div-gpt-ad-rec1 class=sf-hidden>
</div>
</div>
</div>
<p align=left>
A
common approach to collision detection is to simply test for whether
two objects are overlapping at the end of each frame. The problem with
this method is that quickly moving objects can pass through each other
without detection. To avoid this problem, their trajectories can be
subdivided and the objects checked for overlap at each point; however,
this gets expensive if either object experienced a large displacement.
On the other hand, a sweep test can efficiently determine a lower and
upper bound for the time of overlap, which can then be used as more
optimal starting points for the subdivision algorithm.
</p>
<p align=left>
<strong>A
Sphere-Plane Sweep Test</strong>
</p>
<p align=left>
Figure
1 shows an example of a quickly moving sphere passing through a plane.
It can be seen that <strong>C<sub>0</sub></strong> is on the positive side of
the plane and <strong>C<sub>1</sub></strong> is on its negative side.
</p>
<div align=left>
<table border=0 cellspacing=0 cellpadding=6 width=172 align=center bgcolor=#ffffff>
<tbody>
<tr>
<td>
<div align=center>
<img src=data:image/gif;base64,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 alt=Kuras width=458 height=224 align=absmiddle>
</div>
</td>
</tr>
<tr align=center>
<td height=27><strong>Figure
1. A sphere passes through a plane.</strong></td>
</tr>
</tbody>
</table>
</div>
<p align=left>
</p>
<p align=left>
In
general, if a sphere penetrated a plane at some point during the frame,
then <em>d<sub>0</sub>>r</em> and <em>d<sub>1</sub><r</em>, where
<em>r</em> is the radius of the sphere and <em>d<sub>0</sub></em> and <em>d<sub>1</sub></em>
are the signed distances from the plane to <strong>C<sub>0</sub></strong> and
<strong>C<sub>1</sub></strong>, respectively. The signed distance from a point
<strong>C</strong> to a plane can be calculated with the formula
</p>
<p align=left>
<img src=data:image/gif;base64,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 alt width=186 height=94>
</p>
<p align=left>
More
efficiently, we can store the plane in the form {<strong>n</strong><em>, D</em>},
where
</p>
<p align=left>
<img src="data:image/gif;base64,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" alt width=82 height=28>
</p>
<p align=left>
The
distance <em>d</em> is then calculated
</p>
<p align=left>
<img src=data:image/gif;base64,R0lGODlhZgAcAID/AMDAwAAAACH5BAEAAAAALAAAAABmABwAAAKUhI+py+0Po5y02ouz3rz7D4biSJbmiabqyrauGARsLAO1RdPhfcaHjuHxOMOS71f8PYbJSxNWfD5timnE18wBkbIjgmlNTKOamheHZYrDNm2SHFQy3FGz9QyRLtj7b9m+xGegJ5Zxg1dxhFilNtcA5zTYZQgY6Iez9tclyJjGluPk9jJKWmp6ipqqusra6voKG7tRAAA7 alt width=102 height=28>
</p>
<p align=left>
The
trajectory from <strong>C<sub>0</sub></strong> to <strong>C<sub>1</sub></strong> can be
parameterized with a variable <em>u</em>, which may be thought of as <em>normalized
time,</em> since its value is 0 at <strong>C<sub>0</sub></strong> and 1 at <strong>C<sub>1</sub></strong>.
The normalized time at which the sphere first intersects the plane is
given by
</p>
<p align=left>
<img src=data:image/gif;base64,R0lGODlhYgA4AID/AMDAwAAAACH5BAEAAAAALAAAAABiADgAAALZhI+py+0Po5y02ouz3rz7D4biSEJBUKYiqrYd68YXLNcmSmcnsNu60XuchsHDLuebwJCYYrJCY86eP2BUaqI2rTygF6ptHpdfCjY87aKprPNa1X6z3bUgnTiU/8h6GV+IR9fH8KcReIiYqIi4xRM1WNKGA9mSZydICYKZ6bF5E+I04hkxSlpZ6oAqxLmgmsqKcPQhC6sW2hqoIFlbaGjEG/sSDLvkOuwIjFycRos8aMlXCp1g7BOnWfurNpv9Va3bbQsa7jx7S46err7O3u7+Dh8vP09fb79RAAA7 alt width=98 height=56>
</p>
<p align=left>
The
center of the sphere at this time can then be interpolated with an affine
combination of <strong>C<sub>0</sub></strong> and <strong>C<sub>1</sub></strong>
</p>
<p align=left>
<img src="data:image/gif;base64,R0lGODlhvAAeAID/AMDAwAAAACH5BAEAAAAALAAAAAC8AB4AAAL/hI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuC8fyTNf2jef6zvd1ADQEVkNhqZhAIoBFJcwJYBovQWEV1byKlMFh9Sp9eqNeZNii1R6TJueZvIRK5FQwl/5QR7EKfMdt14fhRxGmR8igh8b0tiCHmGSWd9AFpzgIAdY3xuhx2ea4ySgp6QB1xzF6OTYVauUJmadq+lhRair7gXib+xerm2hL2dvwiZY5HGFs6/YaQvc7lSaY2eysjAyXnGjdSLt0Al346gc5Te6JrswVx2wXPee4HFdGaT33Vulbf13cOL9uSzhwqViBGgSPm8CDe3w1ZLjI4cIRvDboW5MBoCyNHTY4FkoYsY5HHyRLmjyJMqXKlSxbunwJM6bMlwUAADs=" alt width=188 height=30>
</p>
<p align=left>
This
formula interpolates <strong>C<sub>i</sub></strong> correctly as long as <em>d<sub>0</sub></em>
is not equal to <em>d<sub>1</sub></em> (which is the case if displacement
has occurred), even when <em>r </em>= 0 (the case of a line segment).
If desired, the parameter <em>u</em> can also be used to linearly interpolate
the orientation of an object at this point.
</p>
<p align=left>
In
this example, it was assumed that the sphere approached the plane from
the positive side and that the sphere was not already penetrating the
plane at <strong>C<sub>0.</sub></strong>. In the case that there could have been
penetration on the previous frame, the condition |<em>d<sub>0</sub></em>|<=<em>r</em>
should also be checked. Listing 1 gives an implementation of this sphere-plane
sweep test.
</p>
<p align=left>
<em><strong>Listing
1. A sphere-plane sweep test.</strong></em>
</p>
<p align=left>
#include "vector.h"
</p>
<p align=left>
class PLANE
</p>
<p align=left>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
public:<br>
<br>
VECTOR N; <br>
//unit normal<br>
<br>
SCALAR D; <br>
//distance from the plane to the origin
from a <br>
//normal and a point
</blockquote>
</div>
<blockquote>
<p align=left>
PLANE( const VECTOR&
p0, const VECTOR& n ): N(n),
D(-N.dot(p0))<br>
{}<br>
//from 3 points
</p>
<p align=left>
PLANE( const VECTOR&
p0, const VECTOR& p1, <br>
const VECTOR& p2 ): N((p1-p0).cross(p2-p0).unit()),<br>
D(-N.dot(p0))<br>
{}<br>
//signed distance from the
plane topoint 'p' along
<br>
//the unit normal
</p>
<p align=left>
const SCALAR distanceToPoint(
const VECTOR& p ) const<br>
{
</p>
</blockquote>
<p align=left>
</p>
<div align=left>
<blockquote>
</blockquote>
</div>
<blockquote>
<div align=left>
<blockquote>
</blockquote>
</div>
<blockquote>
<p align=left>
return N.dot(p) + D;
</p>
</blockquote>
<p align=left>
}
</p>
</blockquote>
<p align=left>
};
</p>
<p align=left>
const bool SpherePlaneSweep<br>
(<br>
const SCALAR r, //sphere
radius<br>
const VECTOR& C0, //previous
position of sphere<br>
const VECTOR& C1, //current
position of sphere<br>
const PLANE& plane, //the
plane<br>
VECTOR& Ci, //position
of sphere when it first touched the plane<br>
SCALAR& u //normalized
time of collision
</p>
<p align=left>
)
</p>
<p align=left>
{
</p>
<p align=left>
const SCALAR d0
= plane.distanceToPoint( C0 );<br>
const SCALAR d1 = plane.distanceToPoint(
C1 );
</p>
<p align=left>
//check if
it was touching on previous frame<br>
if( fabs(d0) <= r )
</p>
<p align=left>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
Ci = C0;<br>
u = 0;<br>
return true;
</blockquote>
</div>
<p align=left>
}
</p>
<p align=left>
//check if
the sphere penetrated during this frame<br>
if( d0>r && d1<r
)<br>
{
</p>
<p align=left>
</p>
<div align=left>
<blockquote>
u = (d0-r)/(d0-d1); //normalized
time<br>
Ci = (1-u)*C0 + u*C1; //point
of first contact<br>
return true;
</blockquote>
</div>
<p align=left>
}
</p>
<p align=left>
return false;
</p>
<p align=left>
}
</p>
<p align=left>
For
the definition of the VECTOR class, please see [3].
</p>
</div>
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"></a></div>
<div class=title><a href=https://www.gamasutra.com/view/news/385591/How_Naughty_Dog_prototyped_the_interactive_guitar_in_The_Last_of_Us_Part_II.php><strong>How Naughty Dog prototyped the interactive guitar in <i>The Last of Us Part II</i></strong></a></div>
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<div class=thumb><a href=https://www.gamasutra.com/gdc2021><img 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wIro3OOV7knQZ9eKQ05GYDgkDnofXrQKDIRFOR3A6A8ilMXHSninlcAEnORnFDJcivsFMK88mrWwGmtGCaBqR5LE+R1q3HISxJOSecmqEJq1Ga+Rgz7uaNOGTO3gDAxx3q/FJnFZUBNXoWNejTkeZUiaMb1ZjaqMZJq3AeRnnr/Ku6LOCaLyNx1qZHqnGSamQ12Rkccol6M7iAOp9TTgciqyOV6fTkVMCc1oczRMKfnd1OajWnr1oMmSe1G3NIO1Lmgg/9k="></a></div>
<div class=title><a href=https://www.gamasutra.com/gdc2021><strong>GDC 2021: Find all our coverage here!</strong></a></div>
</div>
<div class=stories_item>
<div class=thumb><a href=https://www.gamasutra.com/view/news/385657/Blizzard_president_internally_comments_on_extremely_troubling_harassment_lawsuit.php><img 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"></a></div>
<div class=title><a href=https://www.gamasutra.com/view/news/385657/Blizzard_president_internally_comments_on_extremely_troubling_harassment_lawsuit.php><strong>Blizzard president internally comments on 'extremely troubling' harassment lawsuit</strong></a></div>
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<div class=thumb><a href=https://www.gamasutra.com/view/news/385666/Activision_exec_tells_team_that_California_lawsuit_is_actually_whats_hurting_company.php><img 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<div class=title><a href=https://www.gamasutra.com/view/news/385666/Activision_exec_tells_team_that_California_lawsuit_is_actually_whats_hurting_company.php><strong>Activision exec tells team that California lawsuit is actually what's hurting company</strong></a></div>
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<div id=dynamiccomments><a style=font-weight:bold;font-size:16px name=comments>Comments</a><br><div class=parentComment> <table id=comment142811 cellpadding=0 cellspacing=0 class=commentBox border=0> <tbody><tr> <td colspan=2> <hr noshade size=1 class=hr_comment> </td> </tr> <tr> <td style=background-color:#dcebdc;padding:5px;text-align:left>Dave Moss<br> </td> <td style=background-color:#dcebdc;padding:5px> <div class=date_comment><a href=#comment142811>20 Mar 2012 at 11:23 am PST </a> </div> </td> </table><table cellpadding=0 cellspacing=0 border=0 class=commentBox style=margin-bottom:0px;margin-top:2px> <tbody><tr> <td style=width:80px;text-align:center valign=top> <img style="padding-top:2px;padding-right:5px;padding-bottom:5px;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-51)!important;background-size:100% 100%!important;background-origin:content-box!important;background-repeat:no-repeat!important" alt="profile image" src='data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" width="75" height="75"><rect fill-opacity="0"/></svg>'> </td> <td valign=top style=text-align:left> <div id=comment142811_show class=single_comment>The scaler u0 and u1 represent the time the objects will collide... </div> </td> </tr> <tr> <td style=width:80px;text-align:center valign=top> </td> <td valign=top style=text-align:left> <div id=comment142811_replyLink><div id=no_reply_button><a href="https://www.gamasutra.com/sso/login.php?from=https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php">Login to Reply or Like</a><div style=display:inline;float:right></div></div> </div> <div id=comment142811_replyForm style=display:none> </div> </td> </tr> </table></div><div class=parentComment> <table id=comment248045 cellpadding=0 cellspacing=0 class=commentBox border=0> <tbody><tr> <td colspan=2> <hr noshade size=1 class=hr_comment> </td> </tr> <tr> <td style=background-color:#dcebdc;padding:5px;text-align:left>Petter Oberg<br> </td> <td style=background-color:#dcebdc;padding:5px> <div class=date_comment><a href=#comment248045>5 Aug 2014 at 2:40 pm PST </a> </div> </td> </table><table cellpadding=0 cellspacing=0 border=0 class=commentBox style=margin-bottom:0px;margin-top:2px> <tbody><tr> <td style=width:80px;text-align:center valign=top> <img style="padding-top:2px;padding-right:5px;padding-bottom:5px;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-51)!important;background-size:100% 100%!important;background-origin:content-box!important;background-repeat:no-repeat!important" alt="profile image" src='data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" width="75" height="75"><rect fill-opacity="0"/></svg>'> </td> <td valign=top style=text-align:left> <div id=comment248045_show class=single_comment>Shouldn't SphereSphereSweep() return true only if 0 <= u0 <= 1, since else the collision does not occur within this frame? </div> </td> </tr> <tr> <td style=width:80px;text-align:center valign=top> </td> <td valign=top style=text-align:left> <div id=comment248045_replyLink><div id=no_reply_button><a href="https://www.gamasutra.com/sso/login.php?from=https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php">Login to Reply or Like</a><div style=display:inline;float:right></div></div> </div> <div id=comment248045_replyForm style=display:none> </div> </td> </tr> </table></div><div class=parentComment> <table id=comment294106 cellpadding=0 cellspacing=0 class=commentBox border=0> <tbody><tr> <td colspan=2> <hr noshade size=1 class=hr_comment> </td> </tr> <tr> <td style=background-color:#dcebdc;padding:5px;text-align:left>David Kaplan<br> </td> <td style=background-color:#dcebdc;padding:5px> <div class=date_comment><a href=#comment294106>15 May 2017 at 12:14 pm PST </a> </div> </td> </table><table cellpadding=0 cellspacing=0 border=0 class=commentBox style=margin-bottom:0px;margin-top:2px> <tbody><tr> <td style=width:80px;text-align:center valign=top> <img style="padding-top:2px;padding-right:5px;padding-bottom:5px;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-51)!important;background-size:100% 100%!important;background-origin:content-box!important;background-repeat:no-repeat!important" alt="profile image" src='data:image/svg+xml,<svg xmlns="http://www.w3.org/2000/svg" width="75" height="75"><rect fill-opacity="0"/></svg>'> </td> <td valign=top style=text-align:left> <div id=comment294106_show class=single_comment>Hi! You list this OBB class but the intersects function doesn't use it. </div> </td> </tr> <tr> <td style=width:80px;text-align:center valign=top> </td> <td valign=top style=text-align:left> <div id=comment294106_replyLink><div id=no_reply_button><a href="https://www.gamasutra.com/sso/login.php?from=https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php">Login to Reply or Like</a><div style=display:inline;float:right></div></div> </div> <div id=comment294106_replyForm style=display:none> </div> </td> </tr> </table></div><div id=no_comment_form> <br> <span class=comment_login> <a href="https://www.gamasutra.com/sso/login.php?from=https://www.gamasutra.com/view/feature/131790/simple_intersection_tests_for_games.php"> <img src="data:image/gif;base64,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" width=113 height=16 border=0 alt="Login to Comment"></a> </span> <br></div><br></div>
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" 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