Class: Matrix

Inherits:
Object show all
Defined in:
lib/cosmos/core_ext/matrix.rb

Overview

COSMOS specific additions to the Ruby Matrix class

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.cfromq(quaternion) ⇒ Object 



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# File 'lib/cosmos/core_ext/matrix.rb', line 88

def self.cfromq(quaternion)
  result = Matrix.zero(3)

  tx = 2.0 * quaternion.x
  ty = 2.0 * quaternion.y
  tz = 2.0 * quaternion.z
  twx = tx * quaternion.w
  twy = ty * quaternion.w
  twz = tz * quaternion.w
  txx = tx * quaternion.x
  txy = ty * quaternion.x
  txz = tz * quaternion.x
  tyy = ty * quaternion.y
  tyz = tz * quaternion.y
  tzz = tz * quaternion.z

  result[0][0] = 1.0 - tyy - tzz;
  result[0][1] = txy + twz;
  result[0][2] = txz - twy;
  result[1][0] = txy - twz;
  result[1][1] = 1.0 - txx - tzz;
  result[1][2] = tyz + twx;
  result[2][0] = txz + twy;
  result[2][1] = tyz - twx;
  result[2][2] = 1.0 - txx - tyy;

  return result
end

.rot(axis, rotation_angle_in_radians) ⇒ Object

Creates a rotation matrix around one axis as defined by: mathworld.wolfram.com/RotationMatrix.html

Parameters:

  • axis (Symbol) —

    Must be :X,:x,1, or :Y,:y,2, or :Z,:z,3

  • rotation_angle_in_radians (Float) —

    The rotation angle in radians to rotate the maxtrix about the given axis



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# File 'lib/cosmos/core_ext/matrix.rb', line 50

def self.rot(axis, rotation_angle_in_radians)
  rotation_matrix = Matrix.identity(3).to_a

  case axis
  when :X, :x, 1
    rotation_matrix[1][1] = cos(rotation_angle_in_radians)
    rotation_matrix[1][2] = sin(rotation_angle_in_radians)
    rotation_matrix[2][2] = rotation_matrix[1][1]
    rotation_matrix[2][1] = -(rotation_matrix[1][2])
  when :Y, :y, 2
    rotation_matrix[0][0] = cos(rotation_angle_in_radians)
    rotation_matrix[2][0] = sin(rotation_angle_in_radians)
    rotation_matrix[2][2] = rotation_matrix[0][0]
    rotation_matrix[0][2] = -(rotation_matrix[2][0])
  when :Z, :z, 3
    rotation_matrix[0][0] = cos(rotation_angle_in_radians)
    rotation_matrix[0][1] = sin(rotation_angle_in_radians)
    rotation_matrix[1][1] = rotation_matrix[0][0]
    rotation_matrix[1][0] = -(rotation_matrix[0][1])
  end

  return Matrix[*rotation_matrix]
end

Instance Method Details

#[](i, j = nil) ⇒ Object

Allow [i] to return an entire row instead of being forced to pass both the row and column (i.e [i,j]) to return an individual element.

Parameters:

  • i (Integer) —

    Row index

  • j (Integer) (defaults to: nil) —

    Optional column index. Pass nil to return the entire row given by i.

Returns:

  • Either the row as an Array or the element



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# File 'lib/cosmos/core_ext/matrix.rb', line 25

def [](i, j = nil)
  if j
    @rows[i][j]
  else
    @rows[i]
  end
end

#[]=(i, j, value) ⇒ Object

Allow [i,j] = x to set the element at row i, column j to value x

Parameters:

  • i (Integer) —

    Row index

  • j (Integer) —

    Column index

  • value (Object) —

    The value to set



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# File 'lib/cosmos/core_ext/matrix.rb', line 39

def []=(i, j, value)
  @rows[i][j] = value
end

#rot4(quaternion) ⇒ Object 



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# File 'lib/cosmos/core_ext/matrix.rb', line 132

def rot4(quaternion)
  # Get rotation matrix
  r = Matrix.cfromq(quaternion)

  4.times do |row|
    x = @rows[0][row]
    y = @rows[1][row]
    z = @rows[2][row]
    3.times do |i|
      @rows[i][row] = x*r[i][0] + y*r[i][1] + z*r[i][2]
    end
  end
  # Ensure the final row is floating point for consistency
  @rows[3].map! {|x| x.to_f }
  return self
end

#scale4(x, y, z) ⇒ Object 



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# File 'lib/cosmos/core_ext/matrix.rb', line 125

def scale4(x, y, z)
  @rows[0][0] *= x; @rows[0][1] *= x; @rows[0][2] *= x; @rows[0][3] *= x;
  @rows[1][0] *= y; @rows[1][1] *= y; @rows[1][2] *= y; @rows[1][3] *= y;
  @rows[2][0] *= z; @rows[2][1] *= z; @rows[2][2] *= z; @rows[2][3] *= z;
  return self
end

#trace ⇒ Object

Sums the diagonal values of the matrix



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# File 'lib/cosmos/core_ext/matrix.rb', line 75

def trace
  sum = 0.0
  @rows.length.times do |index|
    value = @rows[index][index]
    if not value.nil?
      sum += value
    else
      break
    end
  end
  return sum
end

#trans4(x, y, z) ⇒ Object 



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# File 'lib/cosmos/core_ext/matrix.rb', line 117

def trans4(x, y, z)
  @rows[3][0] += x*@rows[0][0] + y*@rows[1][0] + z*@rows[2][0]
  @rows[3][1] += x*@rows[0][1] + y*@rows[1][1] + z*@rows[2][1]
  @rows[3][2] += x*@rows[0][2] + y*@rows[1][2] + z*@rows[2][2]
  @rows[3][3] += x*@rows[0][3] + y*@rows[1][3] + z*@rows[2][3]
  return self
end