coord

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 Go to latest Published: Oct 14, 2018 License: BSD-2-Clause Imports: 2 Imported by: 0

Documentation

Overview

Package coord provides vector types for various coordinates systems.

Floating-point Coordinates

Three structs with float32 fields give access to geometric transformations, and other useful mathematical operations (see subpackages plane and space): 

// 2D cartesian coordinates
var a = XY{1.0, 2.0}

// 3D cartesian coordinates (or 2D projective coordinates)
var b = XYZ{1.0, 2.0, 3.0}

// 3D projective coordinates
var c = XYZW{1.0, 2.0, 3.0, 4.0}

Integer Coordinates

Two structs with int16 fields are used both for on-screen coordinates and in-game grids: 

// 2D cartesian grid coordinates (e.g. pixel coordinates)
var a = CR{1, 2}

// CRD for 3D cartesian grid coordinates (e.g. voxel coordinates)
var b = CRD{1, 2, 3}

Other Coordinate systems

Various structs for hexagonal and triangular grids: 

// Hexagonal grid coordinates
var a = QR{1, 2}

// Axial (hex) coordinates
var b = AL{1.0, 2.0}

// triangular grid coordinates
var c = QRT{1, 2, 0}

And finally structs to manipulate angles: 

// Polar coordinates
var a = RA{1.0, 3.14}

// Cylindrical coordinates
var b = RAZ{1.0, 3.14, 2.0}

// Spherical coordinates
var c = RAS{1.0, 3.14, 6.28}

Index

Constants

This section is empty.

Variables

This section is empty.

Functions

This section is empty.

Types

type CR 

type CR struct {
	C, R int16
}

CR represents 2D integer coordinates. C stands for "column" and corresponds to the x-coordinate, while R stands for "row" and corresponds to the y-coordinate.

func CRof 

func CRof(v Coordinates) CR

CRof returns an integer vector corresponding to the first two coordinates of v.

func (CR) CRD 

func (a CR) CRD(d int16) CRD

CRD returns the integer coordinates of the vector in 3D space, with d as third coordinate.

func (CR) Cartesian 

func (a CR) Cartesian() (x, y, z float32)

Cartesian returns the coordinates of the vector in 3D space. C and R are casted to float32, and the third coordinate is always 0.

func (CR) Col 

func (a CR) Col() CR

Col returns the vector projected on the C axis (i.e. with R nulled).

func (CR) FlipC 

func (a CR) FlipC() CR

FlipC returns the vector with the sign of C flipped.

func (CR) FlipR 

func (a CR) FlipR() CR

FlipR returns the vector with the sign of R flipped.

func (CR) Minus 

func (a CR) Minus(b CR) CR

Minus returns the difference with another vector.

func (CR) MinusS 

func (a CR) MinusS(s int16) CR

MinusS returns the difference with the vector (s, s).

func (CR) Mod 

func (a CR) Mod(s int16) CR

Mod returns the remainder (modulus) of the division by a scalar (which must be non-zero).

func (CR) ModCR 

func (a CR) ModCR(b CR) CR

ModCR returns the remainder (modulus) of the component-wise division by another vector (of which both C and R must be non-zero).

func (CR) Null 

func (a CR) Null() bool

Null returns true if both coordinates are null.

func (CR) Opposite 

func (a CR) Opposite() CR

Opposite returns the opposite of the vector.

func (CR) Perp 

func (a CR) Perp() CR

Perp returns the vector rotated by 90 in counter-clockwise direction.

func (CR) Plus 

func (a CR) Plus(b CR) CR

Plus returns the sum with another vector.

func (CR) PlusS 

func (a CR) PlusS(s int16) CR

PlusS returns the sum with the vector (s, s).

func (CR) RC 

func (a CR) RC() CR

RC returns the vector with coordinates C and R swapped.

func (CR) Row 

func (a CR) Row() CR

Row returns the vector projected on the R axis (i.e. with C nulled).

func (CR) Slash 

func (a CR) Slash(s int16) CR

Slash returns the integer quotient of the division by a scalar (which must be non-zero).

func (CR) SlashCR 

func (a CR) SlashCR(b CR) CR

SlashCR returns the integer quotients of the component-wise division by another vector (of which both C and R must be non-zero).

func (CR) Times 

func (a CR) Times(s int16) CR

Times returns the product with a scalar.

func (CR) TimesCR 

func (a CR) TimesCR(b CR) CR

TimesCR returns the component-wise product with another vector.

func (CR) XY 

func (a CR) XY() XY

XY returns the floating point coordinates of the vector.

func (CR) XYZ 

func (a CR) XYZ(z float32) XYZ

XYZ returns the floating-point coordinates in 3D space, with the third dimension set to z.

func (CR) XYZW 

func (a CR) XYZW(z, w float32) XYZW

XYZW returns the floating-point coordinates in 3D projective space, with the third and fourth dimensions set to z and w.

type CRD 

type CRD struct {
	C, R, D int16
}

CRD represents 3D integer coordinates. C stands for "column" and corresponds to the x-coordinate, R stands for "row" and corresponds to the y-coordinate, and D stands for "depth" and corresponds to the z-coordinate.

func CRDof 

func CRDof(v Coordinates) CRD

CRDof returns the integer coordinates corresponding to v.

func (CRD) Cartesian 

func (a CRD) Cartesian() (x, y, z float32)

Cartesian returns the coordinates of the vector in 3D space. C,R and D are casted to float32.

func (CRD) Col 

func (a CRD) Col() CRD

Col returns the vector projected on the C axis (i.e. with R and D nulled).

func (CRD) Depth 

func (a CRD) Depth() CRD

Depth returns the vector projected on the D axis (i.e. with C and D nulled).

func (CRD) FlipC 

func (a CRD) FlipC() CRD

FlipC returns the vector with the sign of C flipped.

func (CRD) FlipD 

func (a CRD) FlipD() CRD

FlipD returns the vector with the sign of D flipped.

func (CRD) FlipR 

func (a CRD) FlipR() CRD

FlipR returns the vector with the sign of R flipped.

func (CRD) Minus 

func (a CRD) Minus(b CRD) CRD

Minus returns the difference with another vector.

func (CRD) Minuss 

func (a CRD) Minuss(s int16) CRD

Minuss returns the difference with the vector (s, s).

func (CRD) Mod 

func (a CRD) Mod(s int16) CRD

Mod returns the remainder (modulus) of the division by a scalar (which must be non-zero).

func (CRD) Modcr 

func (a CRD) Modcr(b CRD) CRD

Modcr returns the remainder (modulus) of the component-wise division by another vector (of which both C and R must be non-zero).

func (CRD) Opposite 

func (a CRD) Opposite() CRD

Opposite returns the opposite of the vector.

func (CRD) Plus 

func (a CRD) Plus(b CRD) CRD

Plus returns the sum with another vector.

func (CRD) Pluss 

func (a CRD) Pluss(s int16) CRD

Pluss returns the sum with the vector (s, s, s).

func (CRD) Row 

func (a CRD) Row() CRD

Row returns the vector projected on the R axis (i.e. with C and D nulled).

func (CRD) Slash 

func (a CRD) Slash(s int16) CRD

Slash returns the integer quotient of the division by a scalar (which must be non-zero).

func (CRD) Slashcr 

func (a CRD) Slashcr(b CRD) CRD

Slashcr returns the integer quotients of the component-wise division by another vector (of which both C and R must be non-zero).

func (CRD) Times 

func (a CRD) Times(s int16) CRD

Times returns the product with a scalar.

func (CRD) Timescr 

func (a CRD) Timescr(b CRD) CRD

Timescr returns the component-wise product with another vector.

func (CRD) XY 

func (a CRD) XY() XY

XY returns the 3D floating-point vector corresponding to the first two dimensions of the vector.

func (CRD) XYZ 

func (a CRD) XYZ() XYZ

XYZ returns the floating-point version of the vector.

func (CRD) XYZW 

func (a CRD) XYZW(w float32) XYZW

XYZW returns the floating-point vector in 3D projective space, with the fourth dimensions set to w.

type Coordinates 

type Coordinates interface {
	// Cartesian returns the cartesian coordinates of the vector.
	Cartesian() (x, y, z float32)
}

Coordinates represents any three-dimensional vector.

type RA 

type RA struct {
	R float32 // Distance from origin (i.e. radius)
	A float32 // Angle (counter-clockwise from 3 b'clock)
}

RA represents polar coordinates.

Note: incomplete implementation.

func (RA) Cartesian 

func (a RA) Cartesian() (x, y, z float32)

Cartesian returns the cartesian coordinates; z is alwyas 0.

func (RA) XY 

func (a RA) XY() XY

XY returns the cartesian representation of the vector.

type RA64 

type RA64 struct {
	D float64 // Distance from origin (i.e. radius)
	A float64 // Angle //TODO: what angle?
}

RA64 represents a two dimensional vector, defined by its polar coordinates.

func (RA64) Cartesian 

func (a RA64) Cartesian() (x, y float32)

Cartesian returns the cartesian coordinates of the vector. This implements the Vector interface.

func (RA64) XY64 

func (a RA64) XY64() XY64

XY64 returns the cartesian representation of the vector.

type RAB 

type RAB struct {
	R float32 // Distance from origin (i.e. radius)
	A float32 // Angle (counter-clockwise from 3 b'clock)
	S float32 // Second angle
}

RAB represents a three dimensional vector, defined by its spherical coordinates.

Note: not yet implemented.

type RAZ 

type RAZ struct {
	R float32 // Distance from origin (i.e. radius)
	A float32 // Angle (counter-clockwise from 3 b'clock)
	Z float32 // Depth
}

RAZ represents a three dimensional vector, defined by its cylindrical coordinates.

Note: not yet implemented.

type XY 

type XY struct {
	X float32
	Y float32
}

XY represents 2D cartesian coordinates.

func XYof 

func XYof(c Coordinates) XY

XYof converts the first two coordinates of c to XY.

func (XY) CR 

func (a XY) CR() CR

CR return the integer coordinates of the vector.

func (XY) Cartesian 

func (a XY) Cartesian() (x, y, z float32)

Cartesian returns the two coordinates; z is always 0.

func (XY) Distance 

func (a XY) Distance(b XY) float32

Distance returns the distance with another vector.

func (XY) Distance2 

func (a XY) Distance2(b XY) float32

Distance2 returns the square of the distance with another vector.

func (XY) Dot 

func (a XY) Dot(b XY) float32

Dot returns the dot product with another vector.

func (XY) FlipX 

func (a XY) FlipX() XY

FlipX returns the coordinates with the signe of X flipped.

func (XY) FlipY 

func (a XY) FlipY() XY

FlipY returns the coordinates with the signe of Y flipped.

func (XY) IsAlmostEqual 

func (a XY) IsAlmostEqual(b XY, ulps uint32) bool

IsAlmostEqual returns true if the difference between the two vectors is less than the specified ULPs (Unit in the Last Place).

Handle special cases: zero, infinites, denormals.

See also IsNearlyEqual and IsRoughlyEqual.

func (XY) IsNearlyEqual 

func (a XY) IsNearlyEqual(b XY, epsilon float32) bool

IsNearlyEqual Returns true if the relative error between the two vectors is less than epsilon.

Handles special cases: zero, infinites, denormals.

See also IsAlmostEqual and IsRoughlyEqual.

func (XY) IsRoughlyEqual 

func (a XY) IsRoughlyEqual(b XY, epsilon float32) bool

IsRoughlyEqual Returns true if the absolute error between the two vectors is less than epsilon.

See also IsNearlyEqual and IsAlmostEqual.

func (XY) Length 

func (a XY) Length() float32

Length returns the euclidian length of the vector.

func (XY) Length2 

func (a XY) Length2() float32

Length2 returns the square of the euclidian length of the vector.

func (XY) Minus 

func (a XY) Minus(b XY) XY

Minus returns the difference with another vector.

func (XY) Minuss 

func (a XY) Minuss(s float32) XY

Minuss returns the difference with a scalar.

func (XY) Mod 

func (a XY) Mod(s float32) XY

Mod returns the remainder (modulus) of the division by a scalar (which must be non-zero).

func (XY) Modf 

func (a XY) Modf() (intg, frac XY)

Modf returns the integer part and the fractional part of (each component of) the vector.

func (XY) Modxy 

func (a XY) Modxy(b XY) XY

Modxy returns the remainders (modulus) of the component-wise division by another vector (of which both X and Y must be non-zero).

func (XY) Normalized 

func (a XY) Normalized() XY

Normalized return the normalization of the vector (i.e. the vector divided by its length, which must be non-zero).

func (XY) Opposite 

func (a XY) Opposite() XY

Opposite returns the opposite of the vector.

func (XY) PerpDot 

func (a XY) PerpDot(b XY) float32

PerpDot returns the dot product with the perpendicular of v and another vector.

func (XY) Plus 

func (a XY) Plus(b XY) XY

Plus returns the sum with another vector.

func (XY) Pluss 

func (a XY) Pluss(s float32) XY

Pluss returns the sum with a scalar.

func (XY) RoundCR 

func (a XY) RoundCR() CR

RoundCR return the rounded interger coordinates of the vector.

func (XY) Slash 

func (a XY) Slash(s float32) XY

Slash returns the division by a scalar (which must be non-zero).

func (XY) Slashxy 

func (a XY) Slashxy(b XY) XY

Slashxy returns the component-wise division by another vector (of which both X and Y must be non-zero).

func (XY) Times 

func (a XY) Times(s float32) XY

Times returns the product with a scalar.

func (XY) Timesxy 

func (a XY) Timesxy(b XY) XY

Timesxy returns the component-wise product with another vector.

func (XY) XY64 

func (a XY) XY64() XY64

XY64 returns the 64-bit float representation of a.

func (XY) XYZ 

func (a XY) XYZ(z float32) XYZ

XYZ returns the coordinates {X, Y, z}.

type XY64 

type XY64 struct {
	X float64
	Y float64
}

XY64 represents 64-bit 2D cartesian coordinates.

func (XY64) Cartesian 

func (a XY64) Cartesian() (x, y, z float32)

Cartesian returns the cartesian coordinates of the vector.

This function implements the Vector interface.

func (XY64) Distance 

func (a XY64) Distance(b XY64) float64

Distance returns the distance with another vector.

func (XY64) Distance2 

func (a XY64) Distance2(b XY64) float64

Distance2 returns the square of the distance with another vector.

func (XY64) Dot 

func (a XY64) Dot(b XY64) float64

Dot returns the dot product with another vector.

func (XY64) Length 

func (a XY64) Length() float64

Length returns the euclidian length of the vector.

func (XY64) Length2 

func (a XY64) Length2() float64

Length2 returns the square of the euclidian length of the vector.

func (XY64) Minus 

func (a XY64) Minus(b XY64) XY64

Minus returns the difference with another vector.

func (XY64) Minuss 

func (a XY64) Minuss(s float64) XY64

Minuss returns the difference with a scalar.

func (XY64) Mod 

func (a XY64) Mod(s float64) XY64

Mod returns the remainder (modulus) of the division by a scalar (which must be non-zero).

func (XY64) Modf 

func (a XY64) Modf() (intg, frac XY64)

Modf returns the integer part and the fractional part of (each component of) the vector.

func (XY64) Modxy 

func (a XY64) Modxy(b XY64) XY64

Modxy returns the remainders (modulus) of the component-wise division by another vector (of which both X and Y must be non-zero).

func (XY64) Normalized 

func (a XY64) Normalized() XY64

Normalized return the normalization of the vector (i.e. the vector divided by its length, which must be non-zero).

func (XY64) Opposite 

func (a XY64) Opposite() XY64

Opposite returns the opposite of the vector.

func (XY64) PerpDot 

func (a XY64) PerpDot(b XY64) float64

PerpDot returns the dot product with the perpendicular of a and another vector.

func (XY64) Plus 

func (a XY64) Plus(b XY64) XY64

Plus returns the sum with another vector.

func (XY64) Pluss 

func (a XY64) Pluss(s float64) XY64

Pluss returns the sum with a scalar.

func (XY64) Slash 

func (a XY64) Slash(s float64) XY64

Slash returns the division by a scalar (which must be non-zero).

func (XY64) Slashxy 

func (a XY64) Slashxy(b XY64) XY64

Slashxy returns the component-wise division by another vector (of which both X and Y must be non-zero).

func (XY64) Times 

func (a XY64) Times(s float64) XY64

Times returns the product with a scalar.

func (XY64) Timesxy 

func (a XY64) Timesxy(b XY64) XY64

Timesxy returns the component-wise product with another vector.

func (XY64) XY 

func (a XY64) XY() XY

XY returns the 32-bit float version of a.

func (XY64) XYZ64 

func (a XY64) XYZ64() XYZ64

XYZ64 returns the homogenous coordinates of the vector, with Z set to 1.

type XYZ 

type XYZ struct {
	X float32
	Y float32
	Z float32
}

XYZ represents either 3D cartesian coordinates, or 2D projective (homogeneous) coordinates.

func (XYZ) Cartesian 

func (a XYZ) Cartesian() (x, y, z float32)

Cartesian returns the three coordinates.

func (XYZ) Cross 

func (a XYZ) Cross(b XYZ) XYZ

Cross returns the cross product with another vector.

func (XYZ) Distance 

func (a XYZ) Distance(b XYZ) float32

Distance returns the distance with another vector.

func (XYZ) Distance2 

func (a XYZ) Distance2(b XYZ) float32

Distance2 returns the square of the distance with another vector.

func (XYZ) Dot 

func (a XYZ) Dot(b XYZ) float32

Dot returns the dot product with another vector.

func (XYZ) IsAlmostEqual 

func (a XYZ) IsAlmostEqual(b XYZ, ulps uint32) bool

IsAlmostEqual returns true if the difference between the two vectors is less than the specified ULPs (Unit in the Last Place).

Handle special cases: zero, infinites, denormals.

See also IsNearlyEqual and IsRoughlyEqual.

func (XYZ) IsNearlyEqual 

func (a XYZ) IsNearlyEqual(b XYZ, epsilon float32) bool

IsNearlyEqual Returns true if the relative error between the two vectors is less than epsilon.

Handles special cases: zero, infinites, denormals.

See also IsAlmostEqual and IsRoughlyEqual.

func (XYZ) IsRoughlyEqual 

func (a XYZ) IsRoughlyEqual(b XYZ, epsilon float32) bool

IsRoughlyEqual Returns true if the absolute error between the two vectors is less than epsilon.

See also IsNearlyEqual and IsAlmostEqual.

func (XYZ) Length 

func (a XYZ) Length() float32

Length returns the euclidian length of the vector.

func (XYZ) Length2 

func (a XYZ) Length2() float32

Length2 returns the square of the euclidian length of the vector.

func (XYZ) Minus 

func (a XYZ) Minus(b XYZ) XYZ

Minus returns the difference with another vector.

func (XYZ) Mod 

func (a XYZ) Mod(s float32) XYZ

Mod returns the remainder (modulus) of the division by a scalar (which must be non-zero).

func (XYZ) ModCW 

func (a XYZ) ModCW(b XYZ) XYZ

ModCW returns the remainders (modulus) of the component-wise division by another vector (of which X, Y and Z must be non-zero).

func (XYZ) Modf 

func (a XYZ) Modf() (intg, frac XYZ)

Modf returns the integer part and the fractional part of (each component of) the vector.

func (XYZ) Normalized 

func (a XYZ) Normalized() XYZ

Normalized return the normalization of the vector (i.e. the vector divided by its length, which must be non-zero).

func (XYZ) Opposite 

func (a XYZ) Opposite() XYZ

Opposite returns the opposite of the vector.

func (XYZ) Plus 

func (a XYZ) Plus(b XYZ) XYZ

Plus returns the sum with another vector.

func (XYZ) Slash 

func (a XYZ) Slash(s float32) XYZ

Slash returns the division by a scalar (which must be non-zero).

func (XYZ) SlashCW 

func (a XYZ) SlashCW(b XYZ) XYZ

SlashCW returns the component-wise division by another vector (of which X, Y and Z must be non-zero).

func (XYZ) Times 

func (a XYZ) Times(s float32) XYZ

Times returns the product with a scalar.

func (XYZ) TimesCW 

func (a XYZ) TimesCW(b XYZ) XYZ

TimesCW returns the component-wise product with another vector.

func (XYZ) XY 

func (a XYZ) XY() XY

XY returns the planar coordinates {X, Y}.

func (XYZ) XYZW 

func (a XYZ) XYZW(w float32) XYZW

XYZW returns the homogenous coordinates of the vector, with W set to w.

func (XYZ) XYproj 

func (a XYZ) XYproj() XY

XYproj returns the cartesian representation of the vector (i.e. the perspective divide of the homogeneous coordinates). Z must be non-zero.

func (XYZ) XZ 

func (a XYZ) XZ() XY

XZ returns the planar coordinates {X, Z}.

func (XYZ) YX 

func (a XYZ) YX() XY

YX returns the planar coordinates {Y, X}.

func (XYZ) YZ 

func (a XYZ) YZ() XY

YZ returns the planar coordinates {Y, Z}.

func (XYZ) ZX 

func (a XYZ) ZX() XY

ZX returns the planar coordinates {Z, X}.

func (XYZ) ZY 

func (a XYZ) ZY() XY

ZY returns the planar coordinates {Z, Y}.

type XYZ64 

type XYZ64 struct {
	X float64
	Y float64
	Z float64
}

XYZ64 represents a two-dimensional vector, defined by its homogeneous coordinates.

func (XYZ64) Cartesian 

func (a XYZ64) Cartesian() (x, y float32)

Cartesian returns the cartesian coordinates of the vector (i.e. the perspective divide of the homogeneous coordinates). Z must be non-zero.

type XYZW 

type XYZW struct {
	X float32
	Y float32
	Z float32
	W float32
}

XYZW represents 3D projective (homogeneous) coordinates.

func (XYZW) Cartesian 

func (a XYZW) Cartesian() (x, y, z float32)

Cartesian returns the cartesian coordinates of the vector (i.e. the perspective divide of the homogeneous coordinates). W must be non-zero.

func (XYZW) XYZ 

func (a XYZW) XYZ() XYZ

XYZ returns the cartesian representation of the vector (i.e. the perspective divide of the homogeneous coordinates). W must be non-zero.

type XYZW64 

type XYZW64 struct {
	X float64
	Y float64
	Z float64
	W float64
}

XYZW64 represents a two-dimensional vector, defined by its homogeneous coordinates.

func (XYZW64) Cartesian 

func (a XYZW64) Cartesian() (x, y, z float32)

Cartesian returns the cartesian coordinates of the vector (i.e. the perspective divide of the homogeneous coordinates).

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