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
