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].

      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

      Examples

      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.