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.

Getting Started

$ yarn add math2d

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

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

// or, re-use existing memory to avoid potentially expensive heap allocations.
const tmp = vecReset(3, 4);
vecTransformBy(tmp, rotation, tmp);

API

Documentation for Math2d's API is available at https://crazytoucan.github.io/math2d/api/.

Box Functions

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.
boxComputeIntersection: Computes the area intersection of the two box regions.
boxComputeUnion: Compute the smallest bounding box that contains both given boxes.
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.
boxGetOutCode: Determines where the specified point lies in relation to the given box.
boxGrow: Expands a box by a given amount in all directions.
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.

Line Functions

lineAlloc: Creates a new Line object in memory, with all values initialized to NaN.
lineClone: Copies the values from the given line into a new line.
lineContainsPoint: Determines if the point is on the line
lineGetPointAt: Gets a point along the line, parameterized according to distance along its direction vector.
lineIntersectLine: Computes the intersection point between the two given lines, if it exists.
lineIntersectPolylineIterator: Computes all locations at which a line crosses a given polyline.
lineIntersectRay: Computes the intersection point between the given line and ray, if it exists.
lineIntersectSegment: Computes the intersection point between the given line and segment, if it exists.
lineNearestDistanceToPoint: Determines the closest the line comes to a given point
lineNearestSignedDistanceToPoint: Determines the closest signed distance the line comes to a given point
lineProjectPoint: Projects a point onto the given line, returning the distance t along the line where it falls.
lineReset: Construct a new line given an (x0, y0) initial point and (dirX, dirY) direction vector.
lineThroughPoints: Construct a line that passes through two given points.
lineTransformBy: Transforms a line by an affine matrix.
lineWhichSide: Computes on which side of the line a given point lies.

Mat2d Functions

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.

Polygon Functions

polygonAlloc: Creates a new Array object in memory to hold Polygon data. Its initial length is 0.
polygonContainsPointInside: Determines whether the point is inside the given polygon, using the even-odd fill rule.
polygonGetBounds: Calculate the smallest bounding box that contains this polygon's geometry
polygonGetNumSides: Return the number of sides of this polygon, which is poly.length / 2.
polygonGetPerimeterLength: Computes the total perimeter length of this polygon.
polygonGetPerimeterPointAt: Computes a point along the polygon's perimeter, parameterized according to linear interpolation between adjacent vertices, cycling back to the start after its last vertex.
polygonGetSideLength: Returns the length of a polygon's side by index, starting at 0.
polygonGetSideSegment: Returns a polygon's side by given index as a segment, starting at 0.
polygonIntersectLineIterator: Computes all locations at which a polygon crosses a given line.
polygonIntersectRayIterator: Computes all locations at which a polygon crosses a given ray.
polygonIntersectSegmentIterator: Computes all locations at which a polygon crosses a given line segment.
polygonNearestDistanceSqToPoint: Computes the closest the polygon's perimeter comes to a given reference point.
polygonTransformBy: Transforms a polygon by an affine matrix.

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.
polylineGetBounds: Computes bounding box of polyline's geometry
polylineGetLength: Computes total length of polyline
polylineGetNumSegments: Returns the number of individual line segments in this polyline
polylineGetPointAt: 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.
polylineGetVertex: Retrieves a vertex from this polyline's geometry, starting at index 0
polylineIntersectLineIterator: Computes all locations at which a polyline crosses a given line.
polylineIntersectRayIterator: Computes all locations at which a polyline crosses a given ray.
polylineIntersectSegmentIterator: 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

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
rayGetPointAt: Gets a point along the ray, parameterized according to distance along its direction vector.
rayIntersectLine: Computes the intersection point between the given ray and line, if it exists.
rayIntersectPolylineIterator: 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
rayReset: Construct a new ray given an (x0, y0) initial point and (dirX, dirY) direction vector.
rayTransformBy: Transforms a ray by an affine matrix.

Segment Functions

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
segmentGetPointAt: Gets a point along the line segment, parameterized according to linear interpolation between its endpoints.
segmentIntersectLine: Computes the intersection point between the given segment and line, if it exists.
segmentIntersectPolylineIterator: 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

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.
vecGetManhattanLength: Computes the Manhattan length of the given vector, i.e. |v.x| + |v.y|.
vecLerp: Performs a linear interpolation between the two vectors. The r parameter is allowed to be outside [0, 1].
vecManhattanDistance: Computes the Manhattan distance between the two points.
vecNormalize: Normalizes the vector to be length 1. If the given vector is the zero-vector, this method returns (NaN, NaN).
vecOrigin: Returns the 2d origin vector, (0, 0).
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.

cmslewis / math2d