Quaternion

type

• quaternion .

  • Is the set of all complex numbers with f16 / f32 / f64  real and imaginary ( i , j , & k ) parts.

• Raw_Quaternion .

quaternion64 quaternion128 quaternion256

• Type Conversion .

  • fN               -> quaternion4N  (e.g. f32  -> quaternion128 )

  • complex2N  -> quaternion4N  (e.g. complex64  -> quaternion128 )

Interpretation

• "It's a bit odd that the value is an operation. It's just a very mathematical  approach to it. It's basically an extension of how complex numbers are written mathematically, e.g., 1 + 2i ".

• "It's more just syntax sugar for setting its fields, I think".

rot: quaternion128 = quaternion(x=0, y=0, z=0, w=1)  // arguments must be named, to avoid ambiguity

rot: quaternion128 = 1 + 0i + 0j + 0k                // this is valid.

• rot: quaternion128 = 1 , same as 1 + 0i + 0j + 0k .

  • This is the identity quaternion.

• rot: quaternion128 = 0 , same as 0 + 0i + 0j + 0k .

Procedures

• Quaternion from X :

  • quaternion .

    • (real, imag, jmag, kmag: Float) -> (Quaternion_Type)

  • quaternion_from_scalar .

    • (f: f32) -> (quaternion128)

  • quaternion_from_matrix3 .

    • (m: matrix[3, 3]f32) -> (quaternion128)

  • quaternion_from_matrix4 .

    • (m: matrix[4, 4]f32) -> (quaternion128)

  • to_quaternion .

    • quaternion_from_matrix... .

    • quaternion_from_scalar... .

• Quaternion from angle :

  • quaternion_angle_axis .

    • (angle_radians: f32, axis: [3]f32) -> (quaternion128)

  • Using quaternion_angle_axis , specifying the axis automatically:

    • quaternion_from_euler_angle_x .

      • (angle: f32) -> (quaternion128)

    • quaternion_from_euler_angle_y .

      • (angle: f32) -> (quaternion128)

    • quaternion_from_euler_angle_z .

      • (angle: f32) -> (quaternion128)

  • Using quaternion_from_euler_angle_x/y/z , specifying the operation order:

    • quaternion_from_euler_angles .

      • (t1, t2, t3: f32, order: Euler_Angle_Order) -> (quaternion128)

  • quaternion_from_pitch_yaw_roll .

    • (pitch, yaw, roll: f32) -> (quaternion128)

    • Interestingly, does not use any of the above procedures.

    • .

• Quaternion from vectors3 :

  • quaternion_from_forward_and_up .

    • (forward, up: [3]f32) -> (quaternion128)

  • quaternion_look_at .

    • (eye, centre: [3]f32, up: [3]f32) -> (quaternion128)

  • quaternion_between_two_vector3 .

    • (from, to: [3]f32) -> (quaternion128)

• Quaternion to quaternion

  • quaternion_mul_vector3 .

    • (q: quaternion128, v: [3]f32) -> ([3]f32)

  • quaternion_nlerp .

    • (a, b: quaternion128, t: f32) -> (quaternion128)

  • quaternion_slerp .

    • (x, y: quaternion128, t: f32) -> (quaternion128)

  • quaternion_squad .

    • (q1, q2, s1, s2: quaternion128, h: f32) -> (quaternion128)

  • normalize .

    • (quaternion128) -> (quaternion128)

  • normalize0 .

    • (quaternion128) -> (quaternion128)

• X from quaternion :

  • real .

  • imag .

  • jmag .

  • kmag .

  • conj .

  • angle_from_quaternion .

    • (q: quaternion128) -> (f32)

  • angle_axis_from_quaternion .

    • (q: quaternion128) -> (angle: f32, axis: [3]f32)

  • euler_angles_from_quaternion .

    • (m: quaternion128, order: Euler_Angle_Order) -> (t1, t2, t3: f32)

  • axis_from_quaternion .

    • (q: quaternion128) -> ([3]f32)

  • pitch_yaw_roll_from_quaternion .

    • (q: quaternion128) -> (pitch, yaw, roll: f32)

  • pitch_from_quaternion .

    • (q: quaternion128) -> (f32)

  • yaw_from_quaternion .

    • (q: quaternion128) -> (f32)

  • roll_from_quaternion .

    • (q: quaternion128) -> (f32)