Axis enumerates the 3 axes of ℝ³.
type Axis int
The three axes of ℝ³.
const (
XAxis Axis = iota
YAxis
ZAxis
)
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)
type PreciseVector struct {
X, Y, Z *big.Float
}
func NewPreciseVector(x, y, z float64) PreciseVector
NewPreciseVector creates a high precision vector from the given floating point values.
func PreciseVectorFromVector(v Vector) PreciseVector
PreciseVectorFromVector creates a high precision vector from the given Vector.
func (v PreciseVector) Abs() PreciseVector
Abs returns the vector with nonnegative components.
func (v PreciseVector) Add(ov PreciseVector) PreciseVector
Add returns the standard vector sum of v and ov.
func (v PreciseVector) Cross(ov PreciseVector) PreciseVector
Cross returns the standard cross product of v and ov.
func (v PreciseVector) Dot(ov PreciseVector) *big.Float
Dot returns the standard dot product of v and ov.
func (v PreciseVector) Equal(ov PreciseVector) bool
Equal reports whether v and ov are equal.
func (v PreciseVector) IsUnit() bool
IsUnit reports whether this vector is of unit length.
func (v PreciseVector) IsZero() bool
IsZero reports if this vector is exactly 0 efficiently.
func (v PreciseVector) LargestComponent() Axis
LargestComponent returns the axis that represents the largest component in this vector.
func (v PreciseVector) Mul(f *big.Float) PreciseVector
Mul returns the standard scalar product of v and f.
func (v PreciseVector) MulByFloat64(f float64) PreciseVector
MulByFloat64 returns the standard scalar product of v and f.
func (v PreciseVector) Norm2() *big.Float
Norm2 returns the square of the norm.
func (v PreciseVector) SmallestComponent() Axis
SmallestComponent returns the axis that represents the smallest component in this vector.
func (v PreciseVector) String() string
func (v PreciseVector) Sub(ov PreciseVector) PreciseVector
Sub returns the standard vector difference of v and ov.
func (v PreciseVector) Vector() Vector
Vector returns this precise vector converted to a Vector.
Vector represents a point in ℝ³.
type Vector struct {
X, Y, Z float64
}
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 (v Vector) Angle(ov Vector) s1.Angle
Angle returns the angle between v and ov.
func (v Vector) ApproxEqual(ov Vector) bool
ApproxEqual reports whether v and ov are equal within a small epsilon.
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 (v Vector) Cross(ov Vector) Vector
Cross returns the standard cross product of v and ov.
func (v Vector) Distance(ov Vector) float64
Distance returns the Euclidean distance between v and ov.
func (v Vector) Dot(ov Vector) float64
Dot returns the standard dot product of v and ov.
func (v Vector) IsUnit() bool
IsUnit returns whether this vector is of approximately unit length.
func (v Vector) LargestComponent() Axis
LargestComponent returns the axis that represents the largest component in this vector.
func (v Vector) Mul(m float64) Vector
Mul returns the standard scalar product of v and m.
func (v Vector) Norm() float64
Norm returns the vector's norm.
func (v Vector) Norm2() float64
Norm2 returns the square of the norm.
func (v Vector) Normalize() Vector
Normalize returns a unit vector in the same direction as v.
func (v Vector) Ortho() Vector
Ortho returns a unit vector that is orthogonal to v. Ortho(-v) = -Ortho(v) for all v.
func (v Vector) SmallestComponent() Axis
SmallestComponent returns the axis that represents the smallest component in this vector.
func (v Vector) String() string
func (v Vector) Sub(ov Vector) Vector
Sub returns the standard vector difference of v and ov.