Class: Numerix::Quaternion

Inherits:

Structure

• Object
• Structure
• Numerix::Quaternion

Defined in:

lib/numerix/quaternion.rb

Overview

A structure encapsulating a four-dimensional vector (x,y,z,w), which is used to efficiently rotate an object about the (x,y,z) vector by the angle theta, where w = cos(theta / 2).

Instance Attribute Summary

• #w ⇒ Float

  The rotation component of the quaternion.

• #x ⇒ Float

  The X-value of the quaternion component of the quaternion.

• #y ⇒ Float

  The Y-value of the quaternion component of the quaternion.

• #z ⇒ Float

  The Z-value of the quaternion component of the quaternion.

Class Method Summary

• .from_axis_angle(axis, angle) ⇒ Quaternion

  Creates a quaternion from a vector and an angle to rotate about the vector.

• .from_rotation_matrix(matrix) ⇒ Quaternion

  Creates a quaternion from the given rotation matrix.

• .from_yaw_pitch_roll(yaw, pitch, roll) ⇒ Quaternion

  Creates a new quaternion from the given yaw, pitch, and roll, in radians.

• .identity ⇒ Quaternion

  A quaternion representing no rotation.

• .lerp(quaternion1, quaternion2, amount) ⇒ Quaternion

  Linearly interpolates between two quaternions based on the given weighting.

• .slerp(quaternion1, quaternion2, amount) ⇒ Quaternion

  Interpolates between two quaternions, using spherical linear interpolation.

Instance Method Summary

• #*(other) ⇒ Quaternion

  Quaternion multiplication.

• #+(other) ⇒ Quaternion

  Adds this quaternion with another.

• #-(other) ⇒ Quaternion

  Gets the difference of this quaternion and another.

• #-@ ⇒ Quaternion

  Performs unary negation on this quaternion instance.

• #/(other) ⇒ Quaternion

  Quaternion division.

• #==(other) ⇒ Boolean

  Returns flag if this quaternion instance is equal to the given object.

• #concatenate(other) ⇒ Quaternion

  Concatenates this quaternion and another, the result represents the this rotation followed by the given quaternion's rotation.

• #concatenate!(other) ⇒ self

  Concatenates this quaternion and another, the result represents the this rotation followed by the given quaternion's rotation.

• #conjugate ⇒ Quaternion

  Creates the conjugate of this quaternion.

• #conjugate! ⇒ self

  Alters this instance to be its conjugate.

• #dot(other) ⇒ Float

  Calculates the dot product of two quaternions.

• #identity? ⇒ Boolean

  true if the quaternion is the identity quaternion, otherwise false.

• #initialize(*args) ⇒ Quaternion constructor

  A new instance of Quaternion.

• #inverse ⇒ Quaternion

  The inverse of this quaternion.

• #length ⇒ Float (also: #magnitude)

  The length of the quaternion.

• #length_squared ⇒ Float

  The length of the quaternion squared.

• #lerp(quaternion, amount) ⇒ Quaternion

  Linearly interpolates between this quaternion and another based on the given weighting.

• #lerp!(quaternion, amount) ⇒ self

  Linearly interpolates between this quaternion and another based on the given weighting, altering the values of this quaternion.

• #normalize ⇒ Quaternion

  Returns a new quaternion with the same direction as the given quaternion, but with a length of 1.0.

• #normalize! ⇒ self

  Alters this quaternion instance to maintain same direction, but adjust values so that quaternion has a length of 1.0.

• #slerp(quaternion, amount) ⇒ Quaternion

  Interpolates between this quaternion and another using spherical linear interpolation.

• #slerp!(quaternion, amount) ⇒ self

  Interpolates between this quaternion and another using spherical linear interpolation.

• #to_a ⇒ Array<Float> (also: #elements)

  An Array representation of this instance.

• #to_h ⇒ Hash{Symbol => Float}

  A Hash representation of this instance.

• #to_s ⇒ String

  A String representation of this instance.

• #to_vec4 ⇒ Vector4

  A Vector4 representation of this instance.

Methods inherited from Structure

#[], #[]=, #address, #dup, #each, #pack, #ptr, size, unpack

Constructor Details

#initialize ⇒ Quaternion #initialize(x, y, z, w) ⇒ Quaternion #initialize(vector, scalar) ⇒ Quaternion

Returns a new instance of Quaternion.

Overloads:

• #initialize ⇒ Quaternion

  Constructs a default quaternion with all components set to 0.0.
• #initialize(x, y, z, w) ⇒ Quaternion

  Constructs a Quaternion from the given components.

  Parameters:

  • x (Float) —

    The X component of the quaternion.

  • y (Float) —

    The Y component of the quaternion.

  • z (Float) —

    The Z component of the quaternion.

  • w (Float) —

    The W component of the quaternion.

• #initialize(vector, scalar) ⇒ Quaternion

  Constructs a Quaternion from the given vector and rotation parts.

  Parameters:

  • vector (Vector3) —

    The vector part of the quaternion.

  • scalar (Float) —

    The rotation part of the quaternion.

# File 'lib/numerix/quaternion.rb', line 43

def initialize(*args) # TODO

end

Instance Attribute Details

#w ⇒ Float

Returns the rotation component of the quaternion.

Returns:

• (Float) —

  the rotation component of the quaternion.

# File 'lib/numerix/quaternion.rb', line 23

def w
  @w
end

#x ⇒ Float

Returns the X-value of the quaternion component of the quaternion.

Returns:

• (Float) —

  the X-value of the quaternion component of the quaternion.

# File 'lib/numerix/quaternion.rb', line 11

def x
  @x
end

#y ⇒ Float

Returns the Y-value of the quaternion component of the quaternion.

Returns:

• (Float) —

  the Y-value of the quaternion component of the quaternion.

# File 'lib/numerix/quaternion.rb', line 15

def y
  @y
end

#z ⇒ Float

Returns the Z-value of the quaternion component of the quaternion.

Returns:

• (Float) —

  the Z-value of the quaternion component of the quaternion.

# File 'lib/numerix/quaternion.rb', line 19

def z
  @z
end

Class Method Details

.from_axis_angle(axis, angle) ⇒ Quaternion

Creates a quaternion from a vector and an angle to rotate about the vector.

Parameters:

• axis (Vector3) —

  The vector to rotate around.

• angle (Float) —

  The angle, in radians, to rotate around the vector.

Returns:

• (Quaternion) —

  the created quaternion.

# File 'lib/numerix/quaternion.rb', line 304

def from_axis_angle(axis, angle)
end

.from_rotation_matrix(matrix) ⇒ Quaternion

Creates a quaternion from the given rotation matrix.

Parameters:

• matrix (Matrix4x4) —

  The rotation matrix

Returns:

• (Quaternion) —

  the created quaternion.

# File 'lib/numerix/quaternion.rb', line 325

def from_rotation_matrix(matrix)
end

.from_yaw_pitch_roll(yaw, pitch, roll) ⇒ Quaternion

Creates a new quaternion from the given yaw, pitch, and roll, in radians.

Parameters:

• yaw (Float) —

  The yaw angle, in radians, around the Y-axis.

• pitch (Float) —

  The pitch angle, in radians, around the X-axis.

• roll (Float) —

  The roll angle, in radians, around the Z-axis.

Returns:

• (Quaternion) —

  the created quaternion.

# File 'lib/numerix/quaternion.rb', line 316

def from_yaw_pitch_roll(yaw, pitch, roll)
end

.identity ⇒ Quaternion

Returns a quaternion representing no rotation.

Returns:

• (Quaternion) —

  a quaternion representing no rotation.

# File 'lib/numerix/quaternion.rb', line 293

def identity
end

.lerp(quaternion1, quaternion2, amount) ⇒ Quaternion

Linearly interpolates between two quaternions based on the given weighting.

Parameters:

• quaternion1 (Quaternion) —

  The first source quaternion.

• quaternion2 (Quaternion) —

  The second source quaternion.

• amount (Float) —

  Value between 0.0 and 1.0 indicating the weight of the second source quaternion.

Returns:

• (Quaternion) —

  the interpolated quaternion.

# File 'lib/numerix/quaternion.rb', line 351

def lerp(quaternion1, quaternion2, amount)
end

.slerp(quaternion1, quaternion2, amount) ⇒ Quaternion

Interpolates between two quaternions, using spherical linear interpolation.

Parameters:

• quaternion1 (Quaternion) —

  The first source quaternion.

• quaternion2 (Quaternion) —

  The second source quaternion.

• amount (Float) —

  Value between 0.0 and 1.0 indicating the weight of the second source quaternion.

Returns:

• (Quaternion) —

  the interpolated quaternion.

# File 'lib/numerix/quaternion.rb', line 338

def slerp(quaternion1, quaternion2, amount)
end

Instance Method Details

#*(scalar) ⇒ Quaternion #*(other) ⇒ Quaternion

Quaternion multiplication.

Overloads:

• #*(scalar) ⇒ Quaternion

  Scalar quaternion multiplication.

  Parameters:

  • scalar (Float) —

    The scalar value.

• #*(other) ⇒ Quaternion

  Multiplies this quaternion by another.

  Parameters:

  • other (Quaternion) —

    The source quaternion to multiply.

Returns:

• (Quaternion) —

  the product quaternion.

# File 'lib/numerix/quaternion.rb', line 260

def *(other)
end

#+(other) ⇒ Quaternion

Adds this quaternion with another.

Parameters:

• other (Quaternion) —

  The quaternion to add.

Returns:

• (Quaternion) —

  the sum of the quaternions.

# File 'lib/numerix/quaternion.rb', line 235

def +(other)
end

#-(other) ⇒ Quaternion

Gets the difference of this quaternion and another.

Parameters:

• other (Quaternion) —

  The quaternion to subtract.

Returns:

• (Quaternion) —

  the difference of the quaternions.

# File 'lib/numerix/quaternion.rb', line 243

def -(other)
end

#-@ ⇒ Quaternion

Performs unary negation on this quaternion instance.

Returns:

• (Quaternion) —

  the vector with swapped +/- values.

# File 'lib/numerix/quaternion.rb', line 226

def -@
end

#*(scalar) ⇒ Quaternion #*(other) ⇒ Quaternion

Quaternion division.

Overloads:

• #*(scalar) ⇒ Quaternion

  Scalar quaternion division.

  Parameters:

  • scalar (Float) —

    The scalar value.

• #*(other) ⇒ Quaternion

  Divides this quaternion by another.

  Parameters:

  • other (Quaternion) —

    The source quaternion to divide.

Returns:

• (Quaternion) —

  the resulting quaternion.

# File 'lib/numerix/quaternion.rb', line 277

def /(other)
end

#==(other) ⇒ Boolean

Returns flag if this quaternion instance is equal to the given object.

Parameters:

• other (Object) —

  The object to compare.

Returns:

• (Boolean) —

  true if objects are equal, otherwise false.

# File 'lib/numerix/quaternion.rb', line 286

def ==(other)
end

#concatenate(other) ⇒ Quaternion

Concatenates this quaternion and another, the result represents the this rotation followed by the given quaternion's rotation.

Parameters:

• other (Quaternion) —

  The rotation to add in the series.

Returns:

• (Quaternion) —

  a new quaternion representing the concatenation this rotation followed by the other rotation.

See Also:

• #concatenate!

# File 'lib/numerix/quaternion.rb', line 122

def concatenate(other)
end

#concatenate!(other) ⇒ self

Note:

This function is identical to #concatenate, but alters the values of this instance without creating a new object.

Concatenates this quaternion and another, the result represents the this rotation followed by the given quaternion's rotation.

Parameters:

• other (Quaternion) —

  The rotation to add in the series.

Returns:

• (self)

See Also:

• #concatenate

# File 'lib/numerix/quaternion.rb', line 137

def concatenate!(other)
end

#conjugate ⇒ Quaternion

Creates the conjugate of this quaternion.

Returns:

• (Quaternion) —

  the conjugate of the os instance.

See Also:

• #conjugate!

# File 'lib/numerix/quaternion.rb', line 86

def conjugate
end

#conjugate! ⇒ self

Alters this instance to be its conjugate.

Returns:

• (self)

See Also:

• #conjugate

# File 'lib/numerix/quaternion.rb', line 95

def conjugate!
end

#dot(other) ⇒ Float

Calculates the dot product of two quaternions.

Parameters:

• other (Quaternion) —

  The source quaternion to compute product from.

Returns:

• (Float) —

  the dot product of the quaternions.

# File 'lib/numerix/quaternion.rb', line 109

def dot(other)
end

#identity? ⇒ Boolean

Returns true if the quaternion is the identity quaternion, otherwise false.

Returns:

• (Boolean) —

  true if the quaternion is the identity quaternion, otherwise false.

# File 'lib/numerix/quaternion.rb', line 49

def identity?
end

#inverse ⇒ Quaternion

Returns the inverse of this quaternion.

Returns:

• (Quaternion) —

  the inverse of this quaternion.

# File 'lib/numerix/quaternion.rb', line 100

def inverse
end

#length ⇒ Float Also known as: magnitude

Returns the length of the quaternion.

Returns:

• (Float) —

  the length of the quaternion.

# File 'lib/numerix/quaternion.rb', line 54

def length
end

#length_squared ⇒ Float

Returns the length of the quaternion squared.

Returns:

• (Float) —

  the length of the quaternion squared.

# File 'lib/numerix/quaternion.rb', line 61

def length_squared
end

#lerp(quaternion, amount) ⇒ Quaternion

Linearly interpolates between this quaternion and another based on the given weighting.

Parameters:

• quaternion (Quaternion) —

  The source quaternion to interpolate between.

• amount (Float) —

  Value between 0.0 and 1.0 indicating the weight of the given quaternion.

Returns:

• (Quaternion) —

  the interpolated quaternion.

See Also:

• #lerp!

# File 'lib/numerix/quaternion.rb', line 152

def lerp(quaternion, amount)
end

#lerp!(quaternion, amount) ⇒ self

Linearly interpolates between this quaternion and another based on the given weighting, altering the values of this quaternion.

Parameters:

• quaternion (Quaternion) —

  The source quaternion to interpolate between.

• amount (Float) —

  Value between 0.0 and 1.0 indicating the weight of the given quaternion.

Returns:

• (self)

See Also:

• lerp

# File 'lib/numerix/quaternion.rb', line 166

def lerp!(quaternion, amount)
end

#normalize ⇒ Quaternion

Returns a new quaternion with the same direction as the given quaternion, but with a length of 1.0.

Returns:

• (Quaternion) —

  a normalized quaternion.

# File 'lib/numerix/quaternion.rb', line 69

def normalize
end

#normalize! ⇒ self

Alters this quaternion instance to maintain same direction, but adjust values so that quaternion has a length of 1.0.

Returns:

• (self)

# File 'lib/numerix/quaternion.rb', line 77

def normalize!
end

#slerp(quaternion, amount) ⇒ Quaternion

Interpolates between this quaternion and another using spherical linear interpolation.

Parameters:

• quaternion (Quaternion) —

  The source quaternion to interpolate between.

• amount (Float) —

  Value between 0.0 and 1.0 indicating the weight of the given quaternion.

Returns:

• (Quaternion) —

  the interpolated quaternion.

See Also:

• #slerp!

# File 'lib/numerix/quaternion.rb', line 180

def slerp(quaternion, amount)
end

#slerp!(quaternion, amount) ⇒ self

Note:

This function is identical to #slerp, but alters the values of this instance without creating a new object.

Interpolates between this quaternion and another using spherical linear interpolation.

Parameters:

• quaternion (Quaternion) —

  The source quaternion to interpolate between.

• amount (Float) —

  Value between 0.0 and 1.0 indicating the weight of the given quaternion.

Returns:

• (self)

See Also:

• slerp

# File 'lib/numerix/quaternion.rb', line 197

def slerp!(quaternion, amount)
end

#to_a ⇒ Array<Float> Also known as: elements

Returns an Array representation of this instance.

Returns:

• (Array<Float>) —

  an Array representation of this instance.

# File 'lib/numerix/quaternion.rb', line 207

def to_a
end

#to_h ⇒ Hash{Symbol => Float}

Returns a Hash representation of this instance.

Returns:

• (Hash{Symbol => Float}) —

  a Hash representation of this instance.

# File 'lib/numerix/quaternion.rb', line 214

def to_h
end

#to_s ⇒ String

Returns a String representation of this instance.

Returns:

• (String) —

  a String representation of this instance.

# File 'lib/numerix/quaternion.rb', line 202

def to_s
end

#to_vec4 ⇒ Vector4

Returns a Vector4 representation of this instance.

Returns:

• (Vector4) —

  a Vector4 representation of this instance.

# File 'lib/numerix/quaternion.rb', line 219

def to_vec4
end