quat

package

v0.8.13 Latest Latest Go to latest Published: Dec 1, 2023 License: BSD-3-Clause Imports: 4 Imported by: 0

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Valid go.mod file
Redistributable license
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Stable version
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Repository

github.com/ArkaGPL/gonum

Links

Open Source Insights

Documentation ¶

Overview ¶

Package quat provides the quaternion numeric type and functions.

For a good treatment of uses and behaviors of quaternions, see the interactive videos by Ben Eater and Grant Sanderson here https://eater.net/quaternions.

Example (Rotate) ¶

Rotate a cube 120° around the diagonal vector [1, 1, 1].

package main

import (
	"fmt"
	"math"

	"github.com/ArkaGPL/gonum/floats/scalar"
	"github.com/ArkaGPL/gonum/num/quat"
)

// point is a 3-dimensional point/vector.
type point struct {
	x, y, z float64
}

// raise raises the dimensionality of a point to a quaternion.
func raise(p point) quat.Number {
	return quat.Number{Imag: p.x, Jmag: p.y, Kmag: p.z}
}

// rotate performs the quaternion rotation of p by the given quaternion
// and scaling by the scale factor.
func rotate(p point, by quat.Number, scale float64) point {
	// Ensure the modulus of by is correctly scaled.
	if len := quat.Abs(by); len != scale {
		by = quat.Scale(math.Sqrt(scale)/len, by)
	}

	// Perform the rotation/scaling.
	pp := quat.Mul(quat.Mul(by, raise(p)), quat.Conj(by))

	// Extract the point.
	return point{x: pp.Imag, y: pp.Jmag, z: pp.Kmag}
}

// Rotate a cube 120° around the diagonal vector [1, 1, 1].
func main() {
	alpha := 2 * math.Pi / 3
	q := raise(point{1, 1, 1})
	scale := 1.0

	q = quat.Scale(math.Sin(alpha/2)/quat.Abs(q), q)
	q.Real += math.Cos(alpha / 2)

	for i, p := range []point{
		{x: 0, y: 0, z: 0},
		{x: 0, y: 0, z: 1},
		{x: 0, y: 1, z: 0},
		{x: 0, y: 1, z: 1},
		{x: 1, y: 0, z: 0},
		{x: 1, y: 0, z: 1},
		{x: 1, y: 1, z: 0},
		{x: 1, y: 1, z: 1},
	} {
		pp := rotate(p, q, scale)

		// Clean up floating point error for clarity.
		pp.x = scalar.Round(pp.x, 2)
		pp.y = scalar.Round(pp.y, 2)
		pp.z = scalar.Round(pp.z, 2)

		fmt.Printf("%d %+v -> %+v\n", i, p, pp)
	}

}

Output:


0 {x:0 y:0 z:0} -> {x:0 y:0 z:0}
1 {x:0 y:0 z:1} -> {x:1 y:0 z:0}
2 {x:0 y:1 z:0} -> {x:0 y:0 z:1}
3 {x:0 y:1 z:1} -> {x:1 y:0 z:1}
4 {x:1 y:0 z:0} -> {x:0 y:1 z:0}
5 {x:1 y:0 z:1} -> {x:1 y:1 z:0}
6 {x:1 y:1 z:0} -> {x:0 y:1 z:1}
7 {x:1 y:1 z:1} -> {x:1 y:1 z:1}

Index ¶

func Abs(q Number) float64
func IsInf(q Number) bool
func IsNaN(q Number) bool
type Number
- func (q Number) Format(fs fmt.State, c rune)

Examples ¶

Package (Rotate)

Constants ¶

This section is empty.

Variables ¶

This section is empty.

Functions ¶

func Abs ¶

func Abs(q Number) float64

Abs returns the absolute value (also called the modulus) of q.

func IsInf ¶

func IsInf(q Number) bool

IsInf returns true if any of real(q), imag(q), jmag(q), or kmag(q) is an infinity.

func IsNaN ¶

func IsNaN(q Number) bool

IsNaN returns true if any of real(q), imag(q), jmag(q), or kmag(q) is NaN and none are an infinity.

Types ¶

type Number ¶

type Number struct {
	Real, Imag, Jmag, Kmag float64
}

Number is a float64 precision quaternion.

func Acos ¶

func Acos(q Number) Number

Acos returns the inverse cosine of q.

func Acosh ¶

func Acosh(q Number) Number

Acosh returns the inverse hyperbolic cosine of q.

func Add ¶

func Add(x, y Number) Number

Add returns the sum of x and y.

func Asin ¶

func Asin(q Number) Number

Asin returns the inverse sine of q.

func Asinh ¶

func Asinh(q Number) Number

Asinh returns the inverse hyperbolic sine of q.

func Atan ¶

func Atan(q Number) Number

Atan returns the inverse tangent of q.

func Atanh ¶

func Atanh(q Number) Number

Atanh returns the inverse hyperbolic tangent of q.

func Conj ¶

func Conj(q Number) Number

Conj returns the quaternion conjugate of q.

func Cos ¶

func Cos(q Number) Number

Cos returns the cosine of q.

func Cosh ¶

func Cosh(q Number) Number

Cosh returns the hyperbolic cosine of q.

func Exp ¶

func Exp(q Number) Number

Exp returns e**q, the base-e exponential of q.

func Inf ¶

func Inf() Number

Inf returns a quaternion infinity, quaternion(+Inf, +Inf, +Inf, +Inf).

func Inv ¶

func Inv(q Number) Number

Inv returns the quaternion inverse of q.

func Log ¶

func Log(q Number) Number

Log returns the natural logarithm of q.

func Mul ¶

func Mul(x, y Number) Number

Mul returns the Hamiltonian product of x and y.

func NaN ¶

func NaN() Number

NaN returns a quaternion “not-a-number” value.

func Parse ¶

func Parse(s string) (Number, error)

Parse converts the string s to a Number. The string may be parenthesized and has the format [±]N±Ni±Nj±Nk. The order of the components is not strict.

func Pow ¶

func Pow(q, r Number) Number

Pow return q**r, the base-q exponential of r. For generalized compatibility with math.Pow:

Pow(0, ±0) returns 1+0i+0j+0k
Pow(0, c) for real(c)<0 returns Inf+0i+0j+0k if imag(c), jmag(c), kmag(c) are zero,
    otherwise Inf+Inf i+Inf j+Inf k.

func Scale ¶

func Scale(f float64, q Number) Number

Scale returns q scaled by f.

func Sin ¶

func Sin(q Number) Number

Sin returns the sine of q.

func Sinh ¶

func Sinh(q Number) Number

Sinh returns the hyperbolic sine of q.

func Sqrt ¶

func Sqrt(q Number) Number

Sqrt returns the square root of q.

func Sub ¶

func Sub(x, y Number) Number

Sub returns the difference of x and y, x-y.

func Tan ¶

func Tan(q Number) Number

Tan returns the tangent of q.

func Tanh ¶

func Tanh(q Number) Number

Tanh returns the hyperbolic tangent of q.

func (Number) Format ¶

func (q Number) Format(fs fmt.State, c rune)

Format implements fmt.Formatter.

Source Files ¶

View all Source files

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