# js-2dmath

Fast 2d geometry math: Vector2, Rectangle, Circle, Matrix2x3 (2D transformation), Circle, BoundingBox, Line2, Segment2, Intersections, Distances, Transitions (animation/tween), Random numbers, Noise

``npm install js-2dmath``

# js-2dmath

Fast 2d geometry math: Vector2, Rectangle, Circle, Matrix2x3 (2D transformation), Circle, BoundingBox, Line2, Segment2, Intersections, Distances, Transitions (animation/tween), Noise, Random numbers.

So the objective is "Be fast"

## Help needed / TODO LIST

• API completeness
• Testing
• did I miss anything useful?

## Performance? HOW?/TIPS

• avoid new
• use arrays instead of objects, this is huge performance boost!
• avoid creating unnecessary variables.
• cache every function call to a single variable. example: Vec2.add -> vec2_add
• avoid return new arrays (except for create/clone)
• if you access two time an array, cache it

I'm sure i miss some of my own performance tips, PR if you find any error or find a better way!

## Browser

``````npm run-script browserify
``````

Will generate js-2dmath-browser.js that you can include in any browser.

## API

This doc is autogenerated with falafel see doc.js for more fun! :)

## Vec2

• create (x: Number, y: Number): Vec2

Create a Vec2 given two coords

• dFromPolar (length: Number, degrees: Number (Degrees)): Vec2

Create a Vec2 given length and angle

• fromPolar (length: Number, radians: Number (Radians)): Vec2

Create a Vec2 given length and angle

• zero (): Vec2

Create an empty Vec2

• clone (v1: Vec2): Vec2

Clone given vec2

• equals (v1: Vec2, v2: Vec2): Boolean

Returns true if both vectors are equal(same coords)

• equalsEpsilon (v1: Vec2, v2: Vec2): Boolean

Returns true if both vectors are "almost(Math.EPS)" equal

• gt (v1: Vec2, v2: Vec2): Boolean

Returns true both coordinates of v1 area greater than v2

• lt (v1: Vec2, v2: Vec2): Boolean

Returns true both coordinates of v1 area lesser than v2

• near (v1: Vec2, v2: Vec2, dist: Number): Boolean

Returns true if the distance between v1 and v2 is less than dist.

• isValid (v1: Vec2): Boolean

The vector does not contain any not number value: ±Infinity || NaN

• isNaN (v1: Vec2): Boolean

Any coordinate is NaN

• copy (out: Vec2, v1: Vec2): Vec2

Copy v1 into out

• negate (out: Vec2, v1: Vec2): Vec2

Negate v1 and return it into out

• perpendicular (out: Vec2, v1: Vec2): Vec2

Negate v1 and return it into out

• normalize (out: Vec2, v1: Vec2): Vec2

• rperpendicular (out: Vec2, v1: Vec2): Vec2
• lerp (out: Vec2, v1: Vec2, v2: Vec2, t: Number): Vec2

Linearly interpolate between a and b.

• lerpconst (out: Vec2, v1: Vec2, v2: Vec2, d: Number): Vec2

Linearly interpolate between v1 towards v2 by distance d.

• slerp (out: Vec2, v1: Vec2, v2: Vec2, t: Number): Vec2

Spherical linearly interpolate between v1 and v2.

• slerpconst (out: Vec2, v1: Vec2, v2: Vec2, radians: Number (Radians)): Vec2

Spherical linearly interpolate between v1 towards v2 by no more than angle a in radians.

• forAngle (v1: Vec2, radians: Number (Radians)): Vec2

Returns the unit length vector for the given angle(in radians).

• project (out: Vec2, v1: Vec2, v2: Vec2): Vec2

Returns the vector projection of v1 onto v2.

• rotate (out: Vec2, v1: Vec2, radians: Number (Radians), center: Vec2): Vec2

Rotates the point by the given angle around an optional center point.

The object itself is not modified.

Read more about angle units and orientation in the description of the

• rotateVec (out: Vec2, v1: Vec2, v2: Vec2): Vec2

• unrotateVec (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• midPoint (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• reflect (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• subtract (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• subtract2 (out: Vec2, v1: Vec2, x: Number, y: Number): Vec2
• add (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• add2 (out: Vec2, v1: Vec2, x: Number, y: Number): Vec2
• multiply (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• multiply2 (out: Vec2, v1: Vec2, x: Number, y: Number): Vec2
• divide (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• divide2 (out: Vec2, v1: Vec2, x: Number, y: Number): Vec2
• scale (out: Vec2, v1: Vec2, factor: Number): Vec2
• max (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• min (out: Vec2, v1: Vec2, v2: Vec2): Vec2
• abs (out: Vec2, v1: Vec2): Vec2
• scaleAndAdd (out: Vec2, v1: Vec2, v2: Vec2, factor: Number): Vec2
• clamp (out: Vec2, v1: Vec2, length: Number): Vec2
• magnitude (v1: Vec2, v2: Vec2): Number
• compare (v1: Vec2, v2: Vec2): Number

0 equal, 1 top, 2 top-right, 3 right, 4 bottom right, 5 bottom, 6 bottom-left, 7 left, 8 top-left

• dot (v1: Vec2, v2: Vec2): Number

Vector dot product.

• cross (v1: Vec2, v2: Vec2): Number

• toAngle (v1: Vec2): Number
• distance (v1: Vec2, v2: Vec2): Number

Returns the distance between v1 and v2.

• sqrDistance (v1: Vec2, v2: Vec2): Number

you length only need to compare lengths.

• length (v1: Vec2): Number

Returns the length.

• sqrLength (v1: Vec2): Number

• within (v1: Vec2, v2: Vec2, v3: Vec2): Number

Return true if v2 is between v1 and v3(inclusive)

• \$within (px: Number, py: Number, qx: Number, qy: Number, rx: Number, ry: Number): Number

Return true if q is between p and r(inclusive)

## Line2

• create (x: Number, y: Number, m: Number): Line2
• fromPoints (x1: Number, y1: Number, x2: Number, y2: Number): Line2
• fromSegment2 (seg2: Segment2): Line2
• copy (out: Line2, l1: Line2): Line2
• clone (l1: Line2): Line2
• add (out: Line2, l1: Line2, v1: Vec2): Line2
• subtract (out: Line2, l1: Line2, v1: Vec2): Line2
• parallel (out: Line2, l1: Line2): Line2

## Segment2

• create (x1: Number, y1: Number, x2: Number, y2: Number): Segment2
• clone (seg2: Segment2): Segment2
• copy (out: Segment2, seg2: Segment2): Segment2
• translate (out: Segment2, seg2: Segment2, vec2: Vec2): Segment2
• length (seg2: Segment2): Number
• sqrLength (seg2: Segment2): Number
• cross (seg2: Segment2, vec2: Vec2): Number
• collinear (seg2: Segment2, vec2: Vec2): Boolean
• inside (seg2: Segment2, vec2: Vec2): Boolean
• closestPoint (out_vec2: Segment2, seg2: Segment2, vec2: Vec2): Vec2
• \$closestPoint (out_vec2: Segment2, x1: Number, y1: Number, x2: Number, y2: Number, x3: Number, y3: Number): Vec2
• \$collinear (x1: Number, y1: Number, x2: Number, y2: Number, x3: Number, y3: Number): Boolean
• \$inside (x1: Number, x2: Number, y1: Number, y2: Number, x3: Number, y3: Number): Boolean

## Rectangle

• create (x1: Number, y1: Number, x2: Number, y2: Number): Rectangle

Rectangle is an array with [a: Vec2, b: Vec2, normalized: Boolean]

• fromBB (bb2: BB2): Rectangle

• zero (): Rectangle
• clone (rect: Rectangle): Rectangle
• copy (out: Rectangle, rect: Rectangle): Rectangle
• normalize (out: Rectangle, rect: Rectangle, force: Boolean): Rectangle

a -> bottom-left

a -> top-right

• center (out_vec2: Vec2, rect: Rectangle): Vec2

• translate (out: Rectangle, rect: Rectangle, vec2: Vec2): Rectangle
• distance (rect: Rectangle, rect2: Rectangle): Number
• area (rect: Rectangle): Number

## BB2

• create (l: Number, b: Number, r: Number, t: Number): BB2

BoundingBox2 is an array [left: Number, bottom: Number, right: Number, top: Number, nomalized: Boolean]

• fromCircle (circle: Circle): BB2

• fromRectangle (rect: Rectangle): BB2
• zero (): BB2
• clone (bb2: BB2): BB2
• copy (out: BB2, bb2: BB2): BB2
• merge (out: BB2, bb2_1: BB2, bb2_2: BB2): BB2
• offsetMerge (out: BB2, bb2_1: BB2, bb2_2: BB2, vec2_offset: Vec2): BB2
• osMerge (out: BB2, bb2_1: BB2, bb2_2: BB2, vec2_offset: Vec2, vec2_scale: Vec2): BB2

offset & scale merge

• area (bb2: BB2): Number

• normalize (out: BB2, bb2: BB2): BB2
• translate (out: BB2, bb2: BB2, vec2: Vec2): BB2
• clampVec (out_vec2: Vec2, bb2: BB2, vec2: Vec2): Vec2
• align (out_vec2: Vec2, bb2: BB2, alignament: Number): Vec2

alignament values: BB2.TOPLEFT, BB2.TOPMIDDLE, BB2.TOPRIGHT, BB2.CENTERLEFT, BB2.CENTER, BB2.CENTERRIGHT, BB2.BOTTOMLEFT, BB2.BOTTOM, BB2.BOTTOMRIGH

## Circle

• create (x: Number, y: Number, radius: Number): Circle
• clone (circle: Circle): Circle
• copy (out: Circle, circle: Circle): Circle
• translate (out: Circle, circle: Circle, vec2: Vec2): Circle
• distance (circle: Circle, circle_2: Circle): Number
• length (circle: Circle): Number
• area (circle: Circle): Number

## Matrix2D

• create (): Matrix2D

Creates a new identity 2x3 matrix

• fromPoints (): Matrix2D

Creates a new matrix given 4 points(a Rectangle)

• copy (out: Matrix2D, m2d: Matrix2D): Matrix2D

Copy m2d into out

• identity (out: Matrix2D): Matrix2D

Copy m2d into out

• dRotate (out: Matrix2D, m2d: Matrix2D, degrees: Number (Degrees)): Matrix2D

Rotates a Matrix2D by the given angle in degrees(increment rotation)

@note increment rotation

• rotate (out: Matrix2D, m2d: Matrix2D, radians: Number (Radians)): Matrix2D

Rotates a Matrix2D by the given angle in radians(increment rotation)

@note increment rotation

• dRotation (out: Matrix2D, m2d: Matrix2D, degrees: Number (Degrees)): Matrix2D

Set rotation of a Matrix2D by the given angle in degrees(set rotation)

@note set rotation

• rotation (out: Matrix2D, m2d: Matrix2D, radians: Number (Radians)): Matrix2D

Set rotation of a Matrix2D by the given angle in radians(set rotation)

@note set rotation

• translate (out: Matrix2D, m2d: Matrix2D, vec2: Vec2): Matrix2D

Translates given Matrix2D by the dimensions in the given vec2

@note This translation is affected by rotation/skew

@note increment position

@see * gtranslate

• gTranslate (out: Matrix2D, m2d: Matrix2D, vec2: Vec2): Matrix2D

Translates given Matrix2D by the dimensions in the given vec2

@note This translation is NOT affected by rotation/skew

@note increment position

@see * translate

• position (out: Matrix2D, m2d: Matrix2D, vec2: Vec2): Matrix2D

Set Matrix2D position

@note This translation is NOT affected by rotation/skew

@note set position

@see gtranslate @see translate

• scale (out: Matrix2D, m2d: Matrix2D, vec2: Vec2): Matrix2D

Scales the Matrix2D by the dimensions in the given vec2

@note incremental scale

@note do not affect position

@see * scalation

• scalation (out: Matrix2D, m2d: Matrix2D, vec2: Vec2): Matrix2D

Set the Matrix2D scale by the dimensions in the given vec2

@note set scale

@note do not affect position

@see * scalation

• dSkewX (out: Matrix2D, m2d: Matrix2D, degrees: Number (Degrees)): Matrix2D

Increment the Matrix2D x-skew by given degrees

@note increment skewX

@see * scalation

• skewX (out: Matrix2D, m2d: Matrix2D, radians: Number (Radians)): Matrix2D

Increment the Matrix2D x-skew by given radians

@note increment skewX

@see * scalation

• dSkewY (out: Matrix2D, m2d: Matrix2D, degrees: Number (Degrees)): Matrix2D

Increment the Matrix2D y-skew by given degrees

@note increment skewY

@see * scalation

• skewY (out: Matrix2D, m2d: Matrix2D, radians: Number (Radians)): Matrix2D

Increment the Matrix2D y-skew by given radians

@note increment skewY

@see * scalation

• dSkew (out: Matrix2D, m2d: Matrix2D, vec2_degrees: Vec2 (Degrees)): Matrix2D

Increment the Matrix2D skew y by given degrees in vec2_degrees

@note increment skew

@see * dSetSkew

• skew (out: Matrix2D, m2d: Matrix2D, vec2: Vec2): Matrix2D

Increment the Matrix2D skew y by given radians in vec2

@note increment skew

@see * scalation

• dSetSkew (out: Matrix2D, m2d: Matrix2D, vec2_degrees: Vec2 (Degrees)): Matrix2D

Set the Matrix2D skew y by given degrees in vec2_degrees

@note set skew

@see * setSkew

• setSkew (out: Matrix2D, m2d: Matrix2D, vec2: Vec2): Matrix2D

Set the Matrix2D skew y by given radians in vec2

@note set skew

@see * skew

• multiply (out: Matrix2D, m2d: Matrix2D, m2d_2: Matrix2D): Matrix2D

Multiplies two Matrix2D's

• multiplyVec2 (out_vec2: Vec2, m2d: Matrix2D, vec2: Vec2): Vec2

Multiplies a Matrix2D and a Vec2

• getPosition (out_vec2: Vec2, m2d: Matrix2D): Vec2

Retrieve current position as Vec2

• getScale (out_vec2: Vec2, m2d: Matrix2D): Vec2

Retrieve current scale as Vec2

• getSkew (out_vec2: Vec2, m2d: Matrix2D): Vec2

Retrieve current skew as Vec2

• reflect (out: Matrix2D, m2d: Matrix2D): Matrix2D

Alias of rotate 180º(PI)

• inverse (out: Matrix2D, m2d: Matrix2D)

• transpose (out: Matrix2D, m2d: Matrix2D)
• determinant (out: Matrix2D, m2d: Matrix2D)
• translationMatrix (x: Number, y: Number): Matrix2D

Returns a 3x2 2D column-major translation matrix for x and y.

• dSkewXMatrix (degrees: Number (Degrees)): Matrix2D

Returns a 3x2 2D column-major y-skew matrix for the given degrees.

Returns a 3x2 2D column-major y-skew matrix for the given radians.

• dSkewYMatrix (degrees: Number (Degrees)): Matrix2D

Returns a 3x2 2D column-major y-skew matrix for the given degrees.

Returns a 3x2 2D column-major y-skew matrix for the given radians.

• scalingMatrix (x: Number, y: Number)

Returns a 3x2 2D column-major scaling matrix for sx and sy.

## Polygon

• create (): Polygon
• centroid (out_vec2: Segment2, poly: Polygon): Vec2
• recenter (out: Polygon, poly: Polygon): Polygon
• area (poly: Polygon): Number

## Beizer

• cubic (cp0x: Number, cp0y: Number, cp1x: Number, cp1y: Number, cp2x: Number, cp2y: Number, cp3x: Number, cp3y: Number)

@return {Beizer}

• quadric (cp0x: Number, cp0y: Number, cp1x: Number, cp1y: Number, cp2x: Number, cp2y: Number)

@return {Beizer}

• get (out_vec2: Segment2, curve: Beizer, t: Number)

@return {Vec2}

• length (curve: Beizer, step: Number): Number

Calculate the curve length by incrementally solving the curve every substep=CAAT.Curve.k. This value defaults

to .05 so at least 20 iterations will be performed.

@todo some kind of cache maybe it's needed!

## Triangle

• create (x1: Number, y1: Number, x2: Number, y2: Number, x3: Number, y3: Number): Triangle
• zero (): Triangle
• clone (tri: Triangle): Triangle
• copy (out: Triangle, tri: Triangle): Triangle
• centroid (out_vec2: Vec2, tri: Triangle): Vec2
• incenter (out_vec2: Vec2, tri: Triangle): Vec2
• circumcenter (out_vec2: Vec2, tri: Triangle): Vec2
• area (tri: Triangle): Number
• translate (out: Triangle, tri: Triangle, vec2: Vec2): Triangle

### Intersection

• OUTSIDE 1
• INSIDE 2
• PARALLEL 1
• COLLIDE 4
• COINCIDENT 5
• TANGENT 6
• bb2_bb2 (bb1, bb2, collision, distance)
• bb2_vec2 (bb, vec2, collision, distance)
• vec2_bb2 (vec2, bb, collision, distance)
• rectangle_rectangle (rectangle_1, rectangle_2, collision, distance)
• bb2_rectangle (rectangle_2, bb2, collision, distance)
• rectangle_vec2 (rectangle, vec2, collision, distance)
• vec2_rectangle (vec2, rectangle, collision, distance)
• circle_vec2 (circle, vec2, collision, distance)
• vec2_circle (vec2, circle, collision, distance)
• circle_circle (acircle, bcircle, collision, distance)
• circle_bb2 (circle, bb, collision, distance)
• bb2_circle (bb, circle, collision, distance)
• circle_rectangle (circle, rect, collision, distance)
• rectangle_circle (rect, circle, collision, distance)
• circle_segment2 (circle, segment2, collision, distance)
• segment2_circle (segment2, circle, collision, distance)
• line2_line2 (aline, bline, collision, distance)
• segment2_segment2 (asegment, bsegment, collision, distance)
• segment2_vec2 (seg2, vec2)
• vec2_segment2 (vec2, seg2)

### Transitions

• linear (zero)
• create (name, transition)
• Pow (pos)
• PowIn (pos)
• PowOut (pos)
• PowInOut (pos)
• Expo (pos)
• ExpoIn (pos)
• ExpoOut (pos)
• ExpoInOut (pos)
• Circ (pos)
• CircIn (pos)
• CircOut (pos)
• CircInOut (pos)
• Sine (pos)
• SineIn (pos)
• SineOut (pos)
• SineInOut (pos)
• Back (pos)
• BackIn (pos)
• BackOut (pos)
• BackInOut (pos)
• Bounce (pos)
• BounceIn (pos)
• BounceOut (pos)
• BounceInOut (pos)
• Elastic (pos)
• ElasticIn (pos)
• ElasticOut (pos)
• ElasticInOut (pos)
• Cubic (pos)
• CubicIn (pos)
• CubicOut (pos)
• CubicInOut (pos)
• Quart (pos)
• QuartIn (pos)
• QuartOut (pos)
• QuartInOut (pos)
• Quint (pos)
• QuintIn (pos)
• QuintOut (pos)
• QuintInOut (pos)