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# SAT.js

SAT.js is a simple JavaScript library for performing collision detection (and projection-based 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 Axis-Aligned 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: `0.8.0`.

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 x-coordinate of the Vector.
• `y` - The y-coordinate 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 counter-clockwise by the specified number of radians.
• `reverse()` - Reverse this Vector.
• `normalize()` - Make the Vector unit-lengthed.
• `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 from `pos`.

It has the following methods:

• `setOffset(offset)` - Set the current offset

### SAT.Polygon

This is a convex polygon, whose points are specified in a counter-clockwise 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 counter-clockwise with respect to the coordinate system. If you directly draw the points on a screen that has the origin at the top-left corner it will appear visually that the points are being specified clockwise. This is just because of the inversion of the Y-axis 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 (affects `calcPoints`)
• `offset` - Translation to apply to the polygon before the `angle` rotation (affects `calcPoints`)
• `calcPoints` - (Calculated) The collision polygon - effectively `points` with `angle` and `offset` 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 counter-clockwise (around its local coordinate system) by the specified number of radians. The `angle` 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. The `offset` translation will be applied on top of this translation.
• `getAABB()` - Compute the axis-aligned bounding box. Returns a new Polygon every time it is called. Is performed based on the `calcPoints`.
• `getCentroid()` - Compute the Centroid of the polygon. Is performed based on the `calcPoints`.

### 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 bottom-left coordinate of the box (i.e the smallest `x` value and the smallest `y` 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 (unit-vector)
• `overlapV` - The overlap vector (i.e. `overlapN.scale(overlap, overlap)`). If this vector is subtracted from the position of `a`, `a` and `b` 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
``````