Class: Geom::Matrix3D

Inherits:
Matrix
  • Object
show all
Defined in:
lib/geom/matrix3d.rb

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.identity ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 3

def self.identity
  Matrix3D[
    [1,0,0,0],
    [0,1,0,0],
    [0,0,1,0],
    [0,0,0,1]
  ]
end

.multiply_vector_3x3(m, v) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 103

def self.multiply_vector_3x3(m,v)
  ma = m.to_a
  vx = v.x
  vy = v.y
  vz = v.z

  v.x = vx * ma[0][0] + vy * ma[0][1] + vz * ma[0][2]
  v.y = vx * ma[1][0] + vy * ma[1][1] + vz * ma[1][2]
  v.z = vx * ma[2][0] + vy * ma[2][1] + vz * ma[2][2]
end

.reflection(plane) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 90

def self.reflection(plane)
  a = plane.normal.x
  b = plane.normal.y
  c = plane.normal.z

  self[
    [1-(2*a*a) , 0-(2*a*b) , 0-(2*a*c) , 0],
    [0-(2*a*b) , 1-(2*b*b) , 0-(2*b*c) , 0],
    [0-(2*a*c) , 0-(2*b*c) , 1-(2*c*c) , 0],
    [0         , 0         , 0         , 1]
  ]
end

.rotation(x, y, z, rad) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 12

def self.rotation(x,y,z,rad)
  n_cos = Math.cos(rad)
  n_sin = Math.sin(rad)
  s_cos = 1 - n_cos

  sxy = x * y * s_cos
  syz = y * z * s_cos
  sxz = x * z * s_cos

  sz  = n_sin * z
  sy  = n_sin * y
  sx  = n_sin * x

  n11  = n_cos + x * x * s_cos
  n12  = -sz + sxy
  n13  = sy + sxz
  n14  = 0

  n21  = sz + sxy
  n22  = n_cos + y * y * s_cos
  n23  = -sx + syz
  n24  = 0

  n31  = -sy + sxz
  n32  = sx + syz
  n33  = n_cos + z * z * s_cos
  n34  = 0

  self[
    [n11,n12,n13,n14],
    [n21,n22,n23,n24],
    [n31,n32,n33,n34],
    [0,0,0,1]
  ]
end

.rotationX(rad) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 48

def self.rotationX(rad)
  c = Math.cos(rad)
  s = Math.sin(rad)

  self[
    [1,0, 0,0],
    [0,c,-s,0],
    [0,s, c,0],
    [0,0, 0,1],
  ]
end

.rotationZ(rad) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 60

def self.rotationZ(rad)
  c  = Math.cos(rad)
  s  = Math.sin(rad)

  self[
    [c,-s,0,0],
    [s, c,0,0],
    [0, 0,1,0],
    [0, 0,0,1]
  ]
end

.scale(x, y, z) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 81

def self.scale(x,y,z)
  self[
    [x,0,0,0],
    [0,y,0,0],
    [0,0,z,0],
    [0,0,0,1]
  ]
end

.translation(x, y, z) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 72

def self.translation(x,y,z)
  self[
    [1,0,0,x],
    [0,1,0,y],
    [0,0,1,z],
    [0,0,0,1]
  ]
end

Instance Method Details

#*(other) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 114

def *(other)
  multiply(other)
end

#multiply(other) ⇒ Object 



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# File 'lib/geom/matrix3d.rb', line 118

def multiply(other)
  # matrix multiplication is m[r][c] = (row[r]).(col[c])
  s = to_a
  o = other.to_a
  rm00 = s[0][0] * o[0][0] + s[0][1] * o[1][0] + s[0][2] * o[2][0]
  rm01 = s[0][0] * o[0][1] + s[0][1] * o[1][1] + s[0][2] * o[2][1]
  rm02 = s[0][0] * o[0][2] + s[0][1] * o[1][2] + s[0][2] * o[2][2]
  rm03 = s[0][0] * o[0][3] + s[0][1] * o[1][3] + s[0][2] * o[2][3] + s[0][3]

  rm10 = s[1][0] * o[0][0] + s[1][1] * o[1][0] + s[1][2] * o[2][0]
  rm11 = s[1][0] * o[0][1] + s[1][1] * o[1][1] + s[1][2] * o[2][1]
  rm12 = s[1][0] * o[0][2] + s[1][1] * o[1][2] + s[1][2] * o[2][2]
  rm13 = s[1][0] * o[0][3] + s[1][1] * o[1][3] + s[1][2] * o[2][3] + s[1][3]

  rm20 = s[2][0] * o[0][0] + s[2][1] * o[1][0] + s[2][2] * o[2][0]
  rm21 = s[2][0] * o[0][1] + s[2][1] * o[1][1] + s[2][2] * o[2][1]
  rm22 = s[2][0] * o[0][2] + s[2][1] * o[1][2] + s[2][2] * o[2][2]
  rm23 = s[2][0] * o[0][3] + s[2][1] * o[1][3] + s[2][2] * o[2][3] + s[2][3]

  Matrix3D[
    [rm00, rm01, rm02, rm03],
    [rm10, rm11, rm12, rm13],
    [rm20, rm21, rm22, rm23],
    [   0,    0,    0,    1]
  ]
end