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What matrix gluLookAt generates? (3)

gluLookAt implementation in python

Here is my gluLookAt matrix computation code by python (numpy) and its test code. This code cares rather comprehensiveness than efficiency, therefore, there are matrix multiplication and matrix transpose. You can remove this if you want to have more efficient code. The test compares the result of this implementation and the OpenGL's computation result with less than 1.0e-6 error. As far as I tested, the result is in the error threshold in Ubuntu 10.04, python 2.6, glx version 1.4

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# Copyright (C) 2010-2011 H. Yamauchi
# under New (3-clause) BSD license

#
# get lookat matrix (gluLookAt compatible matrix) python, numpy
#
# \param[in]  _eye    eye point
# \param[in]  _lookat lookat point
# \param[in]  _up     up vector
# \return 4x4 gluLookAt matrix
def getLookAtMatrix(_eye, _lookat, _up):
  ez = _eye - _lookat
  ez = ez / numpy.linalg.norm(ez)

  ex = numpy.cross(_up, ez)
  ex = ex / numpy.linalg.norm(ex)

  ey = numpy.cross(ez, ex)
  ey = ey / numpy.linalg.norm(ey)

  rmat = numpy.eye(4)
  rmat[0][0] = ex[0]
  rmat[0][1] = ex[1]
  rmat[0][2] = ex[2]

  rmat[1][0] = ey[0]
  rmat[1][1] = ey[1]
  rmat[1][2] = ey[2]

  rmat[2][0] = ez[0]
  rmat[2][1] = ez[1]
  rmat[2][2] = ez[2]

  tmat = numpy.eye(4)
  tmat[0][3] = -_eye[0]
  tmat[1][3] = -_eye[1]
  tmat[2][3] = -_eye[2]

  # numpy.array * is element-wise multiplication, use dot()
  lookatmat = numpy.dot(rmat, tmat).transpose()

  return lookatmat


#
# test getLookAtMatrix routine
#
# generate two matrices, glmat by gluLookAt, mat by getLookAtMatrix.
# Then compare them. (To run this test, You need OpenGL bindings and
# also your Camera implementation that provides eye, lookat, up.)
#
def test_gluLookAt_matrix():

    GL.glLoadIdentity()

    # This is your camera. It tells eye, lookat, up.
    [ep, at, up] = gl_camera.get_lookat()
    GLU.gluLookAt(ep[0], ep[1], ep[2],
                  at[0], at[1], at[2],
                  up[0], up[1], up[2])

    # OpenGL gluLookAt matrix
    glmat = None
    glmat = GL.glGetDoublev(GL.GL_MODELVIEW_MATRIX)

    # my matrix
    mat   = getLookAtMatrix(ep, at, up)

    # debug output
    print 'glmat'
    print glmat
    print 'mat'
    print mat

    # compare glmat and mat
    for i in range(4):
        for j in range(4):
            if(math.fabs(glmat[i][j] - mat[i][j]) > 1.0e-6):
                raise StandardError ('matrix does not match.')
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