SAT.js
About
SAT.js is a simple JavaScript library for performing collision detection (and projectionbased collision response) of simple 2D shapes. It uses the Separating Axis Theorem (hence the name)
It supports detecting collisions between:
 Circles (using Voronoi Regions.)
 Convex Polygons (and simple AxisAligned Boxes, which are of course, convex polygons.)
It also supports checking whether a point is inside a circle or polygon.
It's released under the MIT license.
Current version: 0.9.0
.
Nicely compresses with the Google Closure Compiler in Advanced mode to about 6KB (2KB gzipped)
To use it in node.js, you can run npm install sat
and then use it with var SAT = require('sat');
Classes
SAT.js contains the following JavaScript classes:
SAT.Vector (aliased as SAT.V)
This is a simple 2D vector/point class. It is created by calling:
// Create the vector (10,10)  If (x,y) not specified, defaults to (0,0).
var v = new SAT.Vector(10, 10)
It has the following properties:

x
 The xcoordinate of the Vector. 
y
 The ycoordinate of the Vector.
It contains the following methods:

copy(other)
 Copy the value of another Vector to this one. 
clone()
 Return a new vector with the same coordinates as this one. 
perp()
 Change this vector to be perpendicular to what it was before. 
rotate(angle)
 Rotate this vector counterclockwise by the specified number of radians. 
reverse()
 Reverse this Vector. 
normalize()
 Make the Vector unitlengthed. 
add(other)
 Add another Vector to this one. 
sub(other)
 Subtract another Vector from this one. 
scale(x,y)
 Scale this Vector in the X and Y directions. 
project(other)
 Project this Vector onto another one. 
projectN(other)
 Project this Vector onto a unit Vector. 
reflect(axis)
 Reflect this Vector on an arbitrary axis Vector. 
reflectN(axis)
 Reflect this Vector on an arbitrary axis unit Vector. 
dot(other)
 Get the dot product of this Vector and another. 
len2()
 Get the length squared of this Vector. 
len()
 Get the length of this Vector
SAT.Circle
This is a simple circle with a center position and a radius. It is created by calling:
// Create a circle whose center is (10,10) with radius of 20
var c = new SAT.Circle(new SAT.Vector(10,10), 20);
It has the following properties:

pos
 A Vector representing the center of the circle. 
r
 The radius of the circle 
offset
 Offset of center of circle frompos
.
It has the following methods:

setOffset(offset)
 Set the current offset 
getAABB()
 Compute the axisaligned bounding box. Returns a new Polygon every time it is called. 
getAABBAsBox()
 Compute the axisaligned bounding box. Returns a new Box every time it is called.
SAT.Polygon
This is a convex polygon, whose points are specified in a counterclockwise fashion. It is created by calling:
// Create a triangle at (0,0)
var p = new SAT.Polygon(new SAT.Vector(), [
new SAT.Vector(),
new SAT.Vector(100,0),
new SAT.Vector(50,75)
]);
Note: The points are counterclockwise with respect to the coordinate system. If you directly draw the points on a screen that has the origin at the topleft corner it will appear visually that the points are being specified clockwise. This is just because of the inversion of the Yaxis when being displayed.
You can create a line segment by creating a Polygon
that contains only 2 points.
Any identical consecutive points will be combined. (this can happen if you convert a Box
with zero width or height into a Polygon
)
It has the following properties:

pos
 The position of the polygon (all points are relative to this). 
points
 Array of vectors representing the original points of the polygon. 
angle
 Angle to rotate the polgon (affectscalcPoints
) 
offset
 Translation to apply to the polygon before theangle
rotation (affectscalcPoints
) 
calcPoints
 (Calculated) The collision polygon  effectivelypoints
withangle
andoffset
applied. 
edges
 (Calculated) Array of Vectors representing the edges of the calculated polygon 
normals
 (Calculated) Array of Vectors representing the edge normals of the calculated polygon (perpendiculars)
You should not manually change any of the properties except pos
 use the setPoints
, setAngle
, and setOffset
methods to ensure that the calculated properties are updated correctly.
It has the following methods:

setPoints(points)
 Set the original points 
setAngle(angle)
 Set the current rotation angle (in radians) 
setOffset(offset)
 Set the current offset 
rotate(angle)
 Rotate the original points of this polygon counterclockwise (around its local coordinate system) by the specified number of radians. Theangle
rotation will be applied on top of this rotation. 
translate(x, y)
 Translate the original points of this polygon (relative to the local coordinate system) by the specified amounts. Theoffset
translation will be applied on top of this translation. 
getAABB()
 Compute the axisaligned bounding box. Returns a new Polygon every time it is called. Is performed based on thecalcPoints
. 
getAABBAsBox()
 Compute the axisaligned bounding box. Returns a new Box every time it is called. Is performed based on thecalcPoints
. 
getCentroid()
 Compute the Centroid of the polygon. Is performed based on thecalcPoints
.
SAT.Box
This is a simple Box with a position, width, and height. It is created by calling:
// Create a box at (10,10) with width 20 and height 40.
var b = new SAT.Box(new SAT.Vector(10,10), 20, 40);
It has the following properties:

pos
 The bottomleft coordinate of the box (i.e the smallestx
value and the smallesty
value). 
w
 The width of the box. 
h
 The height of the box.
It has the following methods:

toPolygon()
 Returns a new Polygon whose edges are the edges of the box.
SAT.Response
This is the object representing the result of a collision between two objects. It just has a simple new Response()
constructor.
It has the following properties:

a
 The first object in the collision. 
b
 The second object in the collison. 
overlap
 Magnitude of the overlap on the shortest colliding axis. 
overlapN
 The shortest colliding axis (unitvector) 
overlapV
 The overlap vector (i.e.overlapN.scale(overlap, overlap)
). If this vector is subtracted from the position ofa
,a
andb
will no longer be colliding. 
aInB
 Whether the first object is completely inside the second. 
bInA
 Whether the second object is completely inside the first.
It has the following methods:

clear()
 Clear the response so that it is ready to be reused for another collision test.
Note: The clear
ed value for a Response
has what may seem to be strange looking values:
{
a: null,
b: null,
overlap: 1.7976931348623157e+308,
overlapV: Vector(0, 0),
overlapN: Vector(0, 0),
aInB: true,
bInA: true
}
These just make calculating the response simpler in the collision tests. If the collision test functions return false
the values that are in the response should not be examined, and clear()
should be called before using it for another collision test.
Collision Tests
SAT.js contains the following collision tests:
SAT.pointInCircle(p, c)
Checks whether a given point is inside the specified circle.
SAT.pointInPolygon(p, poly)
Checks whether a given point is inside a specified convex polygon.
SAT.testCircleCircle(a, b, response)
Tests for a collision between two Circle
s, a
, and b
. If a response is to be calculated in the event of collision, pass in a clear
ed Response
object.
Returns true
if the circles collide, false
otherwise.
If it returns false
you should not use any values that are in the response
(if one is passed in)
SAT.testPolygonCircle(polygon, circle, response)
Tests for a collision between a Polygon
and a Circle
. If a response is to be calculated in the event of a collision, pass in a clear
ed Response
object.
Returns true
if there is a collision, false
otherwise.
If it returns false
you should not use any values that are in the response
(if one is passed in)
SAT.testCirclePolygon(circle, polygon, response)
The same thing as SAT.testPolygonCircle
, but in the other direction.
Returns true
if there is a collision, false
otherwise.
If it returns false
you should not use any values that are in the response
(if one is passed in)
Note: This is slightly slower than SAT.testPolygonCircle
as it just calls that and reverses the result
SAT.testPolygonPolygon(a, b, response)
Tests whether two polygons a
and b
collide. If a response is to be calculated in the event of collision, pass in a clear
ed Response
object.
Returns true
if there is a collision, false
otherwise.
If it returns false
you should not use any values that are in the response
(if one is passed in)
Note: If you want to detect a collision between Box
es, use the toPolygon()
method
Examples
Test two circles
var V = SAT.Vector;
var C = SAT.Circle;
var circle1 = new C(new V(0,0), 20);
var circle2 = new C(new V(30,0), 20);
var response = new SAT.Response();
var collided = SAT.testCircleCircle(circle1, circle2, response);
// collided => true
// response.overlap => 10
// response.overlapV => (10, 0)
Test a circle and a polygon
var V = SAT.Vector;
var C = SAT.Circle;
var P = SAT.Polygon;
var circle = new C(new V(50,50), 20);
// A square
var polygon = new P(new V(0,0), [
new V(0,0), new V(40,0), new V(40,40), new V(0,40)
]);
var response = new SAT.Response();
var collided = SAT.testPolygonCircle(polygon, circle, response);
// collided => true
// response.overlap ~> 5.86
// response.overlapV ~> (4.14, 4.14)  i.e. on a diagonal
Test two polygons
var V = SAT.Vector;
var P = SAT.Polygon;
// A square
var polygon1 = new P(new V(0,0), [
new V(0,0), new V(40,0), new V(40,40), new V(0,40)
]);
// A triangle
var polygon2 = new P(new V(30,0), [
new V(0,0), new V(30, 0), new V(0, 30)
]);
var response = new SAT.Response();
var collided = SAT.testPolygonPolygon(polygon1, polygon2, response);
// collided => true
// response.overlap => 10
// response.overlapV => (10, 0)
No collision between two Boxes
var V = SAT.Vector;
var B = SAT.Box;
var box1 = new B(new V(0,0), 20, 20).toPolygon();
var box2 = new B(new V(100,100), 20, 20).toPolygon();
var collided = SAT.testPolygonPolygon(box1, box2);
// collided => false
Hit testing a circle and polygon
var V = SAT.Vector;
var C = SAT.Circle;
var P = SAT.Polygon;
var triangle = new P(new V(30,0), [
new V(0,0), new V(30, 0), new V(0, 30)
]);
var circle = new C(new V(100,100), 20);
SAT.pointInPolygon(new V(0,0), triangle); // false
SAT.pointInPolygon(new V(35, 5), triangle); // true
SAT.pointInCircle(new V(0,0), circle); // false
SAT.pointInCircle(new V(110,110), circle); // true
Tests
To run the tests from your console:
npm install
npm run test