math2d

Two dimensional vector math library for JavaScript. Built for performance in computation-heavy real-time engines without sacrificing usability. Supports tree shaking and dead code removal to avoid bloating client-side bundles. Zero dependencies.

Getting Started

$ yarn add math2d

import { _vec, mat2dFromRotation, vecTransformBy } from "math2d";

const threeFour = _vec(3, 4);
const spin = mat2dFromRotation(Math.PI / 4);
console.log(vecTransformBy(threeFour, spin));

API

Box Functions

• _box: shorthand for defining a Box from minX, minY, maxX, maxY
• boxAlloc: Creates a new Box object in memory, with all values initialized to NaN
• boxClone: Copies values from an existing IBox into a new box
• boxContainsBox: Determines whether the second box is completely enclosed in the first
• boxContainsPoint: Determines whether the box contains a given point
• boxEncapsulate: Grows the box to include a given point
• boxEnclosingPoints: Computes the smallest bounding box that contains all of the provided points
• boxGetOutCode: Determines where the specified point lies in relation to the given box
• boxGrow: Expands a box by a given amount in all directions
• boxIntersection: Computes the area intersection of the two box regions
• boxIntersectsBox: Determines whether two boxes overlap
• boxIsEmpty: Determines whether this box represents an empty area
• boxReset: Construct a new box given minX, minY, maxX, and maxY bounding values
• boxScale: Scales a box by a fixed scalar in both directions
• boxTransformBy: Compute the bounds of the image of this box after applying a 2D affine transformation
• boxTranslate: Translate a box by an offset in the x- and y- directions
• boxUnion: Compute the smallest bounding box that contains both given boxes

Intersection Result Functions

• intersectionResultAlloc: Creates a new IntersectionResult object in memory, with all values initialized to false and NaN
• intersectionResultClone: Copies the values from the given intersection into a new intersection object
• intersectionResultReset: Construct a new intersection given exists, x, y, t0, and t1 values

Mat2d Functions

• _mat2d: shorthand for defining a Mat2d from a, b, c, d, tx, ty
• mat2dAlloc: Creates a new mat2d object in memory, with all values initialized to NaN
• mat2dClone: Copies the values from the given matrix into a new matrix
• mat2dDeterminant: Computes the determinant of the affine matrix
• mat2dFromRotation: Computes the affine transform corresponding to a given rotation, in radians
• mat2dFromTranslation: Computes the affine transform corresponding to a given (tx, ty) translation
• mat2dIdentity: Returns the identity affine matrix, [1 0 0 1 0 0]
• mat2dInvert: Computes the inverse of the given 2d affine matrix
• mat2dIsOrthogonal: Returns whether the matrix is an orthogonal matrix
• mat2dIsTranslationOnly: Returns whether the matrix corresponds to only a translation
• mat2dMulMat2d: Computes the result of affine matrix multiplication m1 × m2
• mat2dReset: Construct a new matrix given component values
• mat2dRotate: Applies a rotation in radians to the given matrix, returning the result
• mat2dScale: Applies a scaling transform on top of the given affine matrix, returning the result
• mat2dTranslate: Applies a translation on top of the given matrix, returning the result

Nearest Point Result Functions

• nearestPointResultAlloc: Creates a new NearestPointResult object in memory, with all values initialized to NaN
• nearestPointResultClone: Copies the values from the given NearestPointResult into a new NearestPointResult object
• nearestPointResultReset: Construct a new intersection given exists, x, y, t0, and t1 values

Polyline Functions

• polylineAlloc: Creates a new Array object in memory to hold Polyline data. Its initial length is 0
• polylineClose: Repeats the polyline's first vertex to form a closed path
• polylineContainsPoint: undefined
• polylineContainsPointInside: Determines whether the point is inside the given polygon, using the even-odd fill rule
• polylineGetBounds: Computes bounding box of polyline's geometry
• polylineGetDistanceAtT: Computes the Euclidean distance traveled along the polyline's geometry to get to the parametric point at t
• polylineGetLength: Computes total length of polyline
• polylineGetNumSegments: Returns the number of individual line segments in this polyline
• polylineGetNumVertices: Returns the number of vertices in this polyline
• polylineGetPointAtT: Computes a point along the polyline, parameterized according to linear interpolation between adjacent vertices
• polylineGetSegment: Returns a polyline's segment by given index, starting at 0
• polylineGetSegmentLength: Computes the length of one of a polyline's segments by index, starting at 0
• polylineGetTAtDistance: Computes the parametric value t along the polyline corresponding to a distance d
• polylineGetVertex: Retrieves a vertex from this polyline's geometry, starting at index 0
• polylineIntersectRay: Computes all locations at which a polyline crosses a given ray
• polylineIntersectSegment: Computes all locations at which a polyline crosses a given line segment
• polylineIsClosed: Returns whether the polyline's last vertex equals its first
• polylineNearestDistanceSqToPoint: Finds the closest the polyline comes to a given reference point
• polylineTransformBy: Transforms a polyline by an affine matrix
• polylineTrim: Trims a polyline to a range of its t parameter

Ray Functions

• _ray: shorthand for defining a Ray from x0, y0, dirX, dirY
• rayAlloc: Creates a new Ray object in memory, with all values initialized to NaN
• rayClone: Copies the values from the given ray into a new ray
• rayContainsPoint: Determines if the point is on the ray
• rayGetPointAtT: Gets a point along the ray, parameterized according to distance along its direction vector
• rayIntersectPolyline: Computes all locations at which a ray crosses a given polyline
• rayIntersectRay: Computes the intersection point between the two rays, if it exists
• rayIntersectSegment: Computes the intersection point between the ray and the segment, if it exists
• rayLookAt: Constructs a ray from an initial point, pointing in the direction of a target point
• rayNearestDistanceSqToPoint: Determines the closest the ray comes to a given reference point
• rayProjectPoint: Projects a point onto the given line, returning the distance t along the line where it falls
• rayReset: Construct a new ray given an (x0, y0) initial point and (dirX, dirY) direction vector
• rayTransformBy: Transforms a ray by an affine matrix
• rayWhichSide: Computes on which side of the ray (as a line) a given point lies

Segment Functions

• _segment: shorthand for defining a Segment from x0, y0, x1, y1
• segmentAlloc: Creates a new Segment object in memory, with all values initialized to NaN
• segmentGetEndpoint0: Retrieves the starting endpoint (t = 0) of the segment, as a vector
• segmentGetEndpoint1: Retrives the ending endpoint (t = 1) of the segment, as a vector
• segmentGetLength: Computes the length of the line segment
• segmentGetLengthSq: Computes the squared length of the line segment
• segmentGetPointAtT: Gets a point along the line segment, parameterized according to linear interpolation between its endpoints
• segmentIntersectPolyline: Computes all locations at which a line segment meets a given polyline
• segmentIntersectRay: Computes the intersection point between the ray and the segment, if it exists
• segmentIntersectSegment: Computes the intersection point between the two line segments, if it exists
• segmentNearestDistanceSqToPoint: Finds the closest the segment comes to a given reference point
• segmentReset: Construct a new line segment given an (x0, y0) starting vertex and (x1, y1) ending vertex. The two points are allowed to be the same
• segmentReverse: Computes the reverse of the segment, i.e. swapping its starting vertex and ending vertex

Vec Functions

• _vec: shorthand for defining a Vec from x, y
• vecAdd: Computes the result of adding the two given vectors
• vecAlloc: Creates a new Vec object in memory, with all values initialized to NaN
• vecClone: Copies the values from the given vector into a new vector
• vecCross: Computes the two-dimensional cross product of the two vectors
• vecDistance: Computes the straight-line (Euclidean) distance between the two points
• vecDistanceSq: Computes the squared straight-line (i.e. Euclidean) distance between the two points
• vecDot: Computes the dot product of the two vectors, i.e. u.x * v.x + u.y * v.y
• vecGetLength: Computes the straight-line length (i.e. Euclidean norm) of the given vector
• vecGetLengthSq: Computes the squared straight-line length (i.e. square of the Euclidean norm) of the given vector
• vecLerp: Performs a linear interpolation between the two vectors. The r parameter is allowed to be outside [0, 1]
• vecNormalize: Normalizes the vector to be length 1. If the given vector is the zero-vector, this method returns (NaN, NaN)
• vecPerp: Computes the perp of the given vector, as defined by vecPerp(a, b) = (-b, a). This is equivalent to a counter-clockwise rotation in the standard plane
• vecReset: Construct a new vector given an x and y value
• vecScale: Scales both coordinates of this vector by a given scalar
• vecSubtract: Computes u - v, i.e. subtracting the second vector from the first
• vecTransformBy: Multiplies the vector by an affine matrix