package quat
import "gonum.org/v1/gonum/num/quat"
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.
Rotate a cube 120° around the diagonal vector [1, 1, 1].
Code:play
Output:Example (Rotate)¶
package main
import (
"fmt"
"math"
"gonum.org/v1/gonum/floats/scalar"
"gonum.org/v1/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)
}
}
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 Acos(q Number) Number
- func Acosh(q Number) Number
- func Add(x, y Number) Number
- func Asin(q Number) Number
- func Asinh(q Number) Number
- func Atan(q Number) Number
- func Atanh(q Number) Number
- func Conj(q Number) Number
- func Cos(q Number) Number
- func Cosh(q Number) Number
- func Exp(q Number) Number
- func Inf() Number
- func Inv(q Number) Number
- func Log(q Number) Number
- func Mul(x, y Number) Number
- func NaN() Number
- func Parse(s string) (Number, error)
- func Pow(q, r Number) Number
- func PowReal(q Number, r float64) Number
- func Scale(f float64, q Number) Number
- func Sin(q Number) Number
- func Sinh(q Number) Number
- func Sqrt(q Number) Number
- func Sub(x, y Number) Number
- func Tan(q Number) Number
- func Tanh(q Number) Number
- func (q Number) Format(fs fmt.State, c rune)
Examples ¶
Functions ¶
func Abs ¶
Abs returns the absolute value (also called the modulus) of q.
func IsInf ¶
IsInf returns true if any of real(q), imag(q), jmag(q), or kmag(q) is an infinity.
func IsNaN ¶
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 ¶
Acos returns the inverse cosine of q.
func Acosh ¶
Acosh returns the inverse hyperbolic cosine of q.
func Add ¶
Add returns the sum of x and y.
func Asin ¶
Asin returns the inverse sine of q.
func Asinh ¶
Asinh returns the inverse hyperbolic sine of q.
func Atan ¶
Atan returns the inverse tangent of q.
func Atanh ¶
Atanh returns the inverse hyperbolic tangent of q.
func Conj ¶
Conj returns the quaternion conjugate of q.
func Cos ¶
Cos returns the cosine of q.
func Cosh ¶
Cosh returns the hyperbolic cosine of q.
func Exp ¶
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 ¶
Inv returns the quaternion inverse of q.
func Log ¶
Log returns the natural logarithm of q.
func Mul ¶
Mul returns the Hamiltonian product of x and y.
func NaN ¶
func NaN() Number
NaN returns a quaternion “not-a-number” value.
func Parse ¶
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 ¶
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 PowReal ¶
PowReal return q**r, the base-q exponential of r. For generalized compatibility with math.Pow:
PowReal(0, ±0) returns 1+0i+0j+0k PowReal(0, c) for c<0 returns Inf+0i+0j+0k.
func Scale ¶
Scale returns q scaled by f.
func Sin ¶
Sin returns the sine of q.
func Sinh ¶
Sinh returns the hyperbolic sine of q.
func Sqrt ¶
Sqrt returns the square root of q.
func Sub ¶
Sub returns the difference of x and y, x-y.
func Tan ¶
Tan returns the tangent of q.
func Tanh ¶
Tanh returns the hyperbolic tangent of q.
func (Number) Format ¶
Format implements fmt.Formatter.
Source Files ¶
abs.go conj.go doc.go exp.go inf.go nan.go quat.go trig.go util.go
- Version
- v0.15.1 (latest)
- Published
- Aug 16, 2024
- Platform
- linux/amd64
- Imports
- 4 packages
- Last checked
- 12 hours ago –
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