Version: v0.0.0-...-740aa86 Latest Latest Go to latest
Published: Feb 11, 2021 License: Apache-2.0 Documentation ¶

Overview ¶

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

See ../s2 for a more detailed overview.

Constants ¶

This section is empty.

Variables ¶

This section is empty.

Functions ¶

This section is empty.

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.

Add returns the standard vector sum of v and ov.

func (PreciseVector) Cross ¶

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) LargestComponent ¶

func (v PreciseVector) LargestComponent() Axis

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

func (PreciseVector) Mul ¶

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 ¶

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 (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.