math

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v0.15.0 Latest Latest
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 Go to latest Published: Aug 26, 2026 License: GPL-3.0 Imports: 10 Imported by: 0

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Index

Constants

View Source 
const (
	Pi         = gomath.Pi
	InvPi      = 0.31830988618379067154
	Inv2Pi     = 0.15915494309189533577
	Inv4Pi     = 0.07957747154594766788
	PiOver2    = 1.57079632679489661923
	PiOver4    = 0.78539816339744830961
	FourOverPi = 1.27323949337005615234375
	Sqrt2      = 1.41421356237309504880
)

Mathematical Constants

View Source 
const FeetToNauticalMiles = 1 / NauticalMilesToFeet
View Source 
const NMPerLatitude = 60
View Source 
const NauticalMilesToFeet = 6076.12
View Source 
const StatuteMilesToNauticalMiles = 1 / 1.15078

Variables

View Source 
var Infinity float32 = float32(gomath.Inf(1))

Functions

func Abs 

func Abs[V constraints.Integer | constraints.Float](x V) V

Abs returns the absolute value of x

func Add2f 

func Add2f(a [2]float32, b [2]float32) [2]float32

a+b

func AngleBetween 

func AngleBetween(v1, v2 [2]float32) float32

Equivalent to acos(Dot(a, b)), but more numerically stable. via http://www.plunk.org/~hatch/rightway.html

func Atan 

func Atan(xFull float32) float32

Atan computes atan(x) for a single float32 value Ported from syrah/FixedVectorMath.h:289

func Atan2 

func Atan2(y, x float32) float32

Atan2 computes atan2(y, x) for single float32 values Ported from syrah/FixedVectorMath.h:327

func BitsToFloat 

func BitsToFloat(ui uint32) float32

BitsToFloat converts a bit representation to float32

func Ceil 

func Ceil(v float32) float32

func CirclePoints 

func CirclePoints(nsegs int) [][2]float32

CirclePoints returns the vertices for a unit circle at the origin with the given number of segments; it creates the vertex slice if this tessellation rate hasn't been seen before and otherwise returns a preexisting one.

func Clamp 

func Clamp[T cmp.Ordered](x T, low T, high T) T

Clamp restricts x to the range [low, high]

func ClosestPointOnLine 

func ClosestPointOnLine(line [2][2]float32, p [2]float32) [2]float32

ClosestPointOnLine returns the closest point on the (infinite) line to the given point p.

func Compass 

func Compass[T HeadingT](heading T) string

compass converts a heading expressed into degrees into a string corresponding to the closest compass direction.

func ConvexHull 

func ConvexHull(points [][2]float32) [][2]float32

https://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain

func Cos 

func Cos(x float32) float32

func DMEDistance added in v0.14.3 

func DMEDistance(a Point2LL, aAltitude float32, b Point2LL, bAltitude float32) float32

DMEDistance returns the straight-line distance in nautical miles between two lat-long positions at the given altitudes in feet.

func DecodePathBytes added in v0.14.4 

func DecodePathBytes(stream []byte, out []Point2LL) (int, error)

DecodePathBytes reads len(out)*8 bytes from stream and writes the decoded path into out. It returns the number of bytes consumed, or an error if stream is too short.

func Degrees 

func Degrees(r float32) float32

Degrees converts an angle expressed in degrees to radians

func Distance2f 

func Distance2f(a [2]float32, b [2]float32) float32

Distance between two points

func Dot 

func Dot(a, b [2]float32) float32

func EncodePathBytes added in v0.14.4 

func EncodePathBytes(b []byte, pts []Point2LL) []byte

EncodePathBytes appends the encoded representation of pts to b and returns the extended slice. The output length is 8*len(pts).

func EquilateralTriangleVertices 

func EquilateralTriangleVertices(height float32) [3][2]float32

Returns the vertex coordinates of an equilateral triangle centered at the origin with specified height.

func Exponent 

func Exponent(v float32) int

Exponent returns the exponent of a float32

func FastExp 

func FastExp(x float32) float32

FastExp computes e^x using a fast approximation Based on https://stackoverflow.com/a/10792321, translated from pbrt-v4's FastExp.

func FloatToBits 

func FloatToBits(f float32) uint32

FloatToBits converts a float32 to its bit representation

func Floor 

func Floor(v float32) float32

func HeadingAsHour 

func HeadingAsHour[T HeadingT](heading T) int

headingAsHour converts a heading expressed in degrees into the closest "o'clock" value, with an integer result in the range [1,12].

func HeadingDifference 

func HeadingDifference[T HeadingT](a, b T) float32

HeadingDifference returns the minimum difference between two headings. (i.e., the result is always in the range [0,180].) The result is a plain angular delta, not a heading.

func HeadingInTurnArc added in v0.14.3 

func HeadingInTurnArc[T HeadingT](from, heading, to T, turn TurnDirection) bool

func HeadingSignedTurn 

func HeadingSignedTurn[T HeadingT](cur, target T) float32

HeadingSignedTurn returns the signed angular delta to turn from cur to target. Positive is a right turn, negative is a left turn.

func HeadingVector added in v0.13.0 

func HeadingVector(hdg TrueHeading) [2]float32

func IsHeadingBetween added in v0.13.0 

func IsHeadingBetween[T HeadingT](h, h1, h2 T) bool

IsHeadingBetween checks if heading h is between h1 and h2 (clockwise from h1 to h2). Returns true if h is in the clockwise arc from h1 to h2, inclusive of both endpoints.

func LL2NM 

func LL2NM(p Point2LL, nmPerLongitude float32) [2]float32

LL2NM converts a point expressed in latitude-longitude coordinates to nautical mile coordinates; this is useful for example for reasoning about distances, since both axes then have the same measure.

func Length2f 

func Length2f(v [2]float32) float32

Length of v

func Lerp 

func Lerp(x, a, b float32) float32

Lerp performs linear interpolation between a and b using factor x in [0,1]

func Lerp2f 

func Lerp2f(x float32, a [2]float32, b [2]float32) [2]float32

Linearly interpolate x of the way between a and b. x==0 corresponds to a, x==1 corresponds to b, etc.

func LineLineIntersect 

func LineLineIntersect(p1f, p2f, p3f, p4f [2]float32) ([2]float32, bool)

LineLineIntersect returns the intersection point of the two lines specified by the vertices (p1f, p2f) and (p3f, p4f). An additional returned Boolean value indicates whether a valid intersection was found. (There's no intersection for parallel lines, and none may be found in cases with tricky numerics.)

func Log added in v0.13.0 

func Log(x float32) float32

Log computes the natural logarithm (ln) for a single float32 value Ported from syrah/FixedVectorMath.h:495

func Mid2f 

func Mid2f(a [2]float32, b [2]float32) [2]float32

midpoint of a and b

func Mod 

func Mod(a, b float32) float32

func NMDistance2LL 

func NMDistance2LL(a Point2LL, b Point2LL) float32

NMDistance2LL returns the distance in nautical miles between two provided lat-long coordinates.

func NMDistance2LLFast 

func NMDistance2LLFast(a Point2LL, b Point2LL, nmPerLongitude float32) float32

Fast but approximate distance between latlongs.

func NMDistanceToSegment2LL added in v0.15.0 

func NMDistanceToSegment2LL(p, a, b Point2LL) float32

NMDistanceToSegment2LL returns the distance in nautical miles from p to the great-circle segment between a and b: the spherical cross-track distance where p lies abeam the segment and otherwise the distance to the nearer endpoint.

func NMLength2LL 

func NMLength2LL(a Point2LL, nmPerLongitude float32) float32

NMLength2ll returns the length of a vector expressed in lat-long coordinates.

func NMPerLongitudeAt 

func NMPerLongitudeAt(p Point2LL) float32

NMPerLongitudeAt returns the number of nautical miles spanned by one degree of longitude at the given lat-long point.

func Normalize2f 

func Normalize2f(a [2]float32) [2]float32

Normalizes the given vector.

func NormalizeHeading 

func NormalizeHeading[T HeadingT](h T) T

Reduces it to [0,360).

func OffsetHeading added in v0.14.2 

func OffsetHeading[T ~float32, D ~float32 | ~int](h T, delta D) T

OffsetHeading adds an angular delta to a heading and normalizes the result, preserving the heading's type.

func OppositeHeading 

func OppositeHeading[T HeadingT](h T) T

func Overlaps 

func Overlaps(a Extent2D, b Extent2D) bool

Overlaps returns true if the two provided Extent2Ds overlap.

func PointInPolygon 

func PointInPolygon(p [2]float32, pts [][2]float32) bool

PointInPolygon checks whether the given point is inside the given polygon; it assumes that the last vertex does not repeat the first one, and so includes the edge from pts[len(pts)-1] to pts[0] in its test.

func PointInPolygon2LL 

func PointInPolygon2LL(p Point2LL, pts []Point2LL) bool

func PointLineDistance 

func PointLineDistance(p, p0, p1 [2]float32) float32

PointLineDistance returns the minimum distance from the point p to the infinite line defined by (p0, p1).

func PointSegmentDistance 

func PointSegmentDistance(p, v, w [2]float32) float32

Return minimum distance between line segment vw and point p https://stackoverflow.com/a/1501725

func Pow 

func Pow(a, b float32) float32

func Radians 

func Radians[T ~float32](d T) float32

Radians converts an angle expressed in degrees to radians

func RayRayMinimumDistance 

func RayRayMinimumDistance(p0, d0, p1, d1 [2]float32) float32

RayRayMinimumDistance takes two rays p0+d0*t and p1+d1*t and returns the value of t where their distance is minimized.

func RaySegmentIntersect added in v0.14.3 

func RaySegmentIntersect(org, dir, p0, p1 [2]float32) ([2]float32, float32, float32, bool)

RaySegmentIntersect returns the intersection point of the ray org+dir*t with the segment p0+(p1-p0)*u. The returned values include the ray parameter t and the segment parameter u.

func Rotator2f 

func Rotator2f(angle float32) func([2]float32) [2]float32

rotator2f returns a function that rotates points by the specified angle (given in degrees).

func Round 

func Round(v float32) float32

func SafeACos 

func SafeACos(a float32) float32

func SafeASin 

func SafeASin(a float32) float32

func Scale2f 

func Scale2f(a [2]float32, s float32) [2]float32

a*s

func SegmentSegmentIntersect 

func SegmentSegmentIntersect(p1, p2, p3, p4 [2]float32) ([2]float32, bool)

SegmentSegmentIntersect returns the intersection point of the two line segments specified by the vertices (p1, p2) and (p3, p4). An additional returned Boolean value indicates whether a valid intersection was found within both segments.

func SetLocationResolver 

func SetLocationResolver(r LocationResolver)

func ShortCompass 

func ShortCompass[T HeadingT](heading T) string

ShortCompass converts a heading expressed in degrees into an abbreviated string corresponding to the closest compass direction.

func Sign 

func Sign(v float32) float32

Sign returns 1 if v > 0, -1 if v < 0, or 0 if v == 0

func SignBit 

func SignBit(v float32) bool

SignBit returns true if the given float32's sign bit is set. (i.e., it's non-negative)

func SignedPointLineDistance 

func SignedPointLineDistance(p, p0, p1 [2]float32) float32

SignedPointLineDistance returns the signed distance from the point p to the infinite line defined by (p0, p1) where points to the right of the line have negative distances.

func Significand 

func Significand(v float32) int

Significand returns the significand of a float32

func Sin 

func Sin(x float32) float32

func SinCos 

func SinCos(xFull float32) [2]float32

SinCos computes sin(x) and cos(x) simultaneously for a single float32 value Ported from syrah/FixedVectorMath.h:152, which is via Abramowitz and Stegun.

func SplitSelfIntersectingPolygon added in v0.14.1 

func SplitSelfIntersectingPolygon(poly []Point2LL) [][]Point2LL

SplitSelfIntersectingPolygon decomposes a possibly self-intersecting polygon into a slice of simple (non-self-intersecting) polygons. If the polygon is already simple, it is returned as a single-element slice.

func Sqr 

func Sqr[V constraints.Integer | constraints.Float](v V) V

func Sqrt 

func Sqrt(a float32) float32

func Sub2f 

func Sub2f(a [2]float32, b [2]float32) [2]float32

a-b

func Tan 

func Tan(xFull float32) float32

Tan computes tan(x) for a single float32 value, via syrah/FixedVectorMath.h:206

Types

type CardinalOrdinalDirection 

type CardinalOrdinalDirection int
const (
	North CardinalOrdinalDirection = iota
	NorthEast
	East
	SouthEast
	South
	SouthWest
	West
	NorthWest
)

func ParseCardinalOrdinalDirection 

func ParseCardinalOrdinalDirection(s string) (CardinalOrdinalDirection, error)

func (CardinalOrdinalDirection) Heading 

func (co CardinalOrdinalDirection) Heading() float32

func (CardinalOrdinalDirection) ShortString 

func (co CardinalOrdinalDirection) ShortString() string

type Extent2D 

type Extent2D struct {
	P0, P1 [2]float32
}

Extent2D represents a 2D bounding box with the two vertices at its opposite minimum and maximum corners.

func BoundLatLongCircle 

func BoundLatLongCircle(c Point2LL, r float32) Extent2D

func EmptyExtent2D 

func EmptyExtent2D() Extent2D

EmptyExtent2D returns an Extent2D representing an empty bounding box.

func Extent2DFromP2LLs 

func Extent2DFromP2LLs(pts []Point2LL) Extent2D

Extent2DFromP2LLs returns an Extent2D that bounds all of the provided points.

func Extent2DFromPoints 

func Extent2DFromPoints(pts [][2]float32) Extent2D

Extent2DFromPoints returns an Extent2D that bounds all of the provided points.

func Extent2DFromSeq added in v0.13.0 

func Extent2DFromSeq(it iter.Seq[Point2LL]) Extent2D

func Intersect added in v0.14.3 

func Intersect(a, b Extent2D) Extent2D

Intersect returns the rectangle that is the intersection of a and b. If the inputs do not overlap, the returned extent has P1 < P0 and IsEmpty returns true.

func Union 

func Union(e Extent2D, p [2]float32) Extent2D

func (Extent2D) Center 

func (e Extent2D) Center() [2]float32

func (Extent2D) ClosestPointInBox 

func (e Extent2D) ClosestPointInBox(p [2]float32) [2]float32

ClosestPointInBox returns the closest point to p that is inside the Extent2D. (If p is already inside it, then it is returned.)

func (Extent2D) Corners added in v0.14.6 

func (e Extent2D) Corners() [][2]float32

Corners returns the 4 corners of the associated box in counter-clockwise order.

func (Extent2D) Expand 

func (e Extent2D) Expand(d float32) Extent2D

Expand expands the extent by the given distance in all directions.

func (Extent2D) Height 

func (e Extent2D) Height() float32

func (Extent2D) Inside 

func (e Extent2D) Inside(p [2]float32) bool

func (Extent2D) IntersectRay 

func (e Extent2D) IntersectRay(org, dir [2]float32) (bool, float32, float32)

IntersectRay find the intersections of the ray with given origin and direction with the Extent2D. The returned Boolean value indicates whether an intersection was found. If true, the two returned floating-point values give the parametric distances along the ray where the intersections occurred.

func (Extent2D) IsEmpty added in v0.14.3 

func (e Extent2D) IsEmpty() bool

IsEmpty returns true if the extent has no positive area; i.e., its width or height is zero or negative.

func (Extent2D) Lerp 

func (e Extent2D) Lerp(p [2]float32) [2]float32

func (Extent2D) Offset 

func (e Extent2D) Offset(p [2]float32) Extent2D

func (Extent2D) Scale 

func (e Extent2D) Scale(s float32) Extent2D

func (Extent2D) Width 

func (e Extent2D) Width() float32

type HeadingT 

type HeadingT interface{ ~int | ~float32 }

type LocationResolver 

type LocationResolver interface {
	Resolve(s string) (Point2LL, error)
}

type MagneticHeading added in v0.14.2 

type MagneticHeading float32

func TrueToMagnetic added in v0.14.2 

func TrueToMagnetic(h TrueHeading, magneticVariation float32) MagneticHeading

type Matrix3 

type Matrix3 [3][3]float32

func Identity3x3 

func Identity3x3() Matrix3

func MakeMatrix3 

func MakeMatrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22 float32) Matrix3

func (Matrix3) Determinant 

func (m Matrix3) Determinant() float32

func (Matrix3) Inverse 

func (m Matrix3) Inverse() Matrix3

func (Matrix3) Ortho 

func (m Matrix3) Ortho(x0, x1, y0, y1 float32) Matrix3

func (Matrix3) PostMultiply 

func (m Matrix3) PostMultiply(m2 Matrix3) Matrix3

func (Matrix3) Rotate 

func (m Matrix3) Rotate(theta float32) Matrix3

func (Matrix3) Scale 

func (m Matrix3) Scale(x, y float32) Matrix3

func (Matrix3) TransformPoint 

func (m Matrix3) TransformPoint(p [2]float32) [2]float32

func (Matrix3) TransformVector 

func (m Matrix3) TransformVector(p [2]float32) [2]float32

func (Matrix3) Translate 

func (m Matrix3) Translate(x, y float32) Matrix3

type Point2LL 

type Point2LL [2]float32

Point2LL represents a 2D point on the Earth in latitude-longitude. Important: 0 (x) is longitude, 1 (y) is latitude

func Add2LL 

func Add2LL(a Point2LL, b Point2LL) Point2LL

func Mid2LL 

func Mid2LL(a Point2LL, b Point2LL) Point2LL

func NM2LL 

func NM2LL(p [2]float32, nmPerLongitude float32) Point2LL

NM2LL converts a point expressed in nautical mile coordinates to lat-long.

func Offset2LL 

func Offset2LL(pll Point2LL, hdg TrueHeading, dist float32, nmPerLongitude float32) Point2LL

Offset2LL returns the point at distance dist along the vector with true heading hdg from the given point. It assumes a (locally) flat earth.

func ParseLatLong 

func ParseLatLong(llstr []byte) (Point2LL, error)

func Sub2LL 

func Sub2LL(a Point2LL, b Point2LL) Point2LL

func (Point2LL) DDString 

func (p Point2LL) DDString() string

DDString returns the position in decimal degrees, e.g.: (39.860901, -75.274864)

func (Point2LL) DMSString 

func (p Point2LL) DMSString() string

DMSString returns the position in degrees minutes, seconds, e.g. N039.51.39.243,W075.16.29.511

func (Point2LL) IsZero 

func (p Point2LL) IsZero() bool

func (Point2LL) Latitude 

func (p Point2LL) Latitude() float32

func (Point2LL) Longitude 

func (p Point2LL) Longitude() float32

func (Point2LL) MarshalJSON 

func (p Point2LL) MarshalJSON() ([]byte, error)

Store Point2LLs as strings is JSON, for compactness/friendliness...

func (*Point2LL) UnmarshalJSON 

func (p *Point2LL) UnmarshalJSON(b []byte) error

type RayRouteIntersection added in v0.14.3 

type RayRouteIntersection struct {
	Index    int
	SegT     float32
	Location Point2LL
}

RayRouteIntersection describes a single point where a ray crosses a polyline segment. Index is the segment index in the polyline (the segment runs from route[Index] to route[Index+1]); SegT is the 0..1 parameter along that segment. Callers that need the nautical-mile distance from the ray origin compute it from (origin, Location) via NMDistance2LL.

func IntersectRayWithRoute added in v0.14.3 

func IntersectRayWithRoute(origin Point2LL, heading TrueHeading, route []Point2LL) []RayRouteIntersection

IntersectRayWithRoute returns all segments of the polyline route that the ray from origin along the given true heading crosses, in route order. Internally converts to a local NM frame anchored at origin so the caller does not need to supply nmPerLongitude.

type TrueHeading added in v0.14.2 

type TrueHeading float32

func GreatCircleHeading added in v0.15.0 

func GreatCircleHeading(from, to Point2LL) TrueHeading

GreatCircleHeading returns the initial true heading from one point toward another along a great circle. The flat approximation Heading2LL uses is fine over a TRACON but not over an ocean: Tokyo is west of Anchorage the way an airplane flies and southeast of it the way a flat map draws, and it is the airplane that matters when the question is where traffic comes from.

func Heading2LL 

func Heading2LL(from Point2LL, to Point2LL, nmPerLongitude float32) TrueHeading

Heading2LL returns the true heading from the point |from| to the point |to| in degrees. The provided points should be in latitude-longitude coordinates.

func MagneticToTrue added in v0.14.2 

func MagneticToTrue(h MagneticHeading, magneticVariation float32) TrueHeading

func VectorHeading 

func VectorHeading(v [2]float32) TrueHeading

type TurnDirection added in v0.14.3 

type TurnDirection int

TurnDirection specifies the direction of a turn. 

const (
	TurnClosest TurnDirection = iota // default: turn the shortest direction
	TurnLeft
	TurnRight
)

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