r3

Documentation

Overview

Package r3 implements types and functions for working with geometry in ℝ³.

See ../s2 for a more detailed overview.

Index

• type Axis
• type PreciseVector
  • func NewPreciseVector(x, y, z float64) PreciseVector
  • func PreciseVectorFromVector(v Vector) PreciseVector
  • func (v PreciseVector) Abs() PreciseVector
  • func (v PreciseVector) Add(ov PreciseVector) PreciseVector
  • func (v PreciseVector) Cross(ov PreciseVector) PreciseVector
  • func (v PreciseVector) Dot(ov PreciseVector) *big.Float
  • func (v PreciseVector) Equal(ov PreciseVector) bool
  • func (v PreciseVector) IsUnit() bool
  • func (v PreciseVector) IsZero() bool
  • func (v PreciseVector) LargestComponent() Axis
  • func (v PreciseVector) Mul(f *big.Float) PreciseVector
  • func (v PreciseVector) MulByFloat64(f float64) PreciseVector
  • func (v PreciseVector) Norm2() *big.Float
  • func (v PreciseVector) SmallestComponent() Axis
  • func (v PreciseVector) String() string
  • func (v PreciseVector) Sub(ov PreciseVector) PreciseVector
  • func (v PreciseVector) Vector() Vector
• type Vector
  • func (v Vector) Abs() Vector
  • func (v Vector) Add(ov Vector) Vector
  • func (v Vector) Angle(ov Vector) s1.Angle
  • func (v Vector) ApproxEqual(ov Vector) bool
  • func (v Vector) Cmp(ov Vector) int
  • func (v Vector) Cross(ov Vector) Vector
  • func (v Vector) Distance(ov Vector) float64
  • func (v Vector) Dot(ov Vector) float64
  • func (v Vector) IsUnit() bool
  • func (v Vector) LargestComponent() Axis
  • func (v Vector) Mul(m float64) Vector
  • func (v Vector) Norm() float64
  • func (v Vector) Norm2() float64
  • func (v Vector) Normalize() Vector
  • func (v Vector) Ortho() Vector
  • func (v Vector) SmallestComponent() Axis
  • func (v Vector) String() string
  • func (v Vector) Sub(ov Vector) Vector

Types

type Axis

type Axis int

Axis enumerates the 3 axes of ℝ³.

const (
	XAxis Axis = iota
	YAxis
	ZAxis
)

The three axes of ℝ³.

type PreciseVector

type PreciseVector struct {
	X, Y, Z *big.Float
}

PreciseVector represents a point in ℝ³ using high-precision values. Note that this is NOT a complete implementation because there are some operations that Vector supports that are not feasible with arbitrary precision math. (e.g., methods that need division like Normalize, or methods needing a square root operation such as Norm)

func NewPreciseVector

func NewPreciseVector(x, y, z float64) PreciseVector

NewPreciseVector creates a high precision vector from the given floating point values.

func PreciseVectorFromVector

func PreciseVectorFromVector(v Vector) PreciseVector

PreciseVectorFromVector creates a high precision vector from the given Vector.

func (PreciseVector) Abs

func (v PreciseVector) Abs() PreciseVector

Abs returns the vector with nonnegative components.

func (PreciseVector) Add

func (v PreciseVector) Add(ov PreciseVector) PreciseVector

Add returns the standard vector sum of v and ov.

func (PreciseVector) Cross

func (v PreciseVector) Cross(ov PreciseVector) PreciseVector

Cross returns the standard cross product of v and ov.

func (PreciseVector) Dot

func (v PreciseVector) Dot(ov PreciseVector) *big.Float

Dot returns the standard dot product of v and ov.

func (PreciseVector) Equal

func (v PreciseVector) Equal(ov PreciseVector) bool

Equal reports whether v and ov are equal.

func (PreciseVector) IsUnit

func (v PreciseVector) IsUnit() bool

IsUnit reports whether this vector is of unit length.

func (PreciseVector) IsZero

func (v PreciseVector) IsZero() bool

IsZero reports if this vector is exactly 0 efficiently.

func (PreciseVector) LargestComponent

func (v PreciseVector) LargestComponent() Axis

LargestComponent returns the axis that represents the largest component in this vector.

func (PreciseVector) Mul

func (v PreciseVector) Mul(f *big.Float) PreciseVector

Mul returns the standard scalar product of v and f.

func (PreciseVector) MulByFloat64

func (v PreciseVector) MulByFloat64(f float64) PreciseVector

MulByFloat64 returns the standard scalar product of v and f.

func (PreciseVector) Norm2

func (v PreciseVector) Norm2() *big.Float

Norm2 returns the square of the norm.

func (PreciseVector) SmallestComponent

func (v PreciseVector) SmallestComponent() Axis

SmallestComponent returns the axis that represents the smallest component in this vector.

func (PreciseVector) String

func (v PreciseVector) String() string

func (PreciseVector) Sub

func (v PreciseVector) Sub(ov PreciseVector) PreciseVector

Sub returns the standard vector difference of v and ov.

func (PreciseVector) Vector

func (v PreciseVector) Vector() Vector

Vector returns this precise vector converted to a Vector.

type Vector

type Vector struct {
	X, Y, Z float64
}

Vector represents a point in ℝ³.

func (Vector) Abs

func (v Vector) Abs() Vector

Abs returns the vector with nonnegative components.

func (Vector) Add

func (v Vector) Add(ov Vector) Vector

Add returns the standard vector sum of v and ov.

func (Vector) Angle

func (v Vector) Angle(ov Vector) s1.Angle

Angle returns the angle between v and ov.

func (Vector) ApproxEqual

func (v Vector) ApproxEqual(ov Vector) bool

ApproxEqual reports whether v and ov are equal within a small epsilon.

func (Vector) Cmp

func (v Vector) Cmp(ov Vector) int

Cmp compares v and ov lexicographically and returns:

-1 if v <  ov
 0 if v == ov
+1 if v >  ov

This method is based on C++'s std::lexicographical_compare. Two entities are compared element by element with the given operator. The first mismatch defines which is less (or greater) than the other. If both have equivalent values they are lexicographically equal.

func (Vector) Cross

func (v Vector) Cross(ov Vector) Vector

Cross returns the standard cross product of v and ov.

func (Vector) Distance

func (v Vector) Distance(ov Vector) float64

Distance returns the Euclidean distance between v and ov.

func (Vector) Dot

func (v Vector) Dot(ov Vector) float64

Dot returns the standard dot product of v and ov.

func (Vector) IsUnit

func (v Vector) IsUnit() bool

IsUnit returns whether this vector is of approximately unit length.

func (Vector) LargestComponent

func (v Vector) LargestComponent() Axis

LargestComponent returns the axis that represents the largest component in this vector.

func (Vector) Mul

func (v Vector) Mul(m float64) Vector

Mul returns the standard scalar product of v and m.

func (Vector) Norm

func (v Vector) Norm() float64

Norm returns the vector's norm.

func (Vector) Norm2

func (v Vector) Norm2() float64

Norm2 returns the square of the norm.

func (Vector) Normalize

func (v Vector) Normalize() Vector

Normalize returns a unit vector in the same direction as v.

func (Vector) Ortho

func (v Vector) Ortho() Vector

Ortho returns a unit vector that is orthogonal to v. Ortho(-v) = -Ortho(v) for all v.

func (Vector) SmallestComponent

func (v Vector) SmallestComponent() Axis

SmallestComponent returns the axis that represents the smallest component in this vector.

func (Vector) String

func (v Vector) String() string

func (Vector) Sub

func (v Vector) Sub(ov Vector) Vector

Sub returns the standard vector difference of v and ov.