(3) gluLookAt はどんな matrix を生成するのか?

gluLookAt implementation in python

gluLookAt matrix の私の python (numpy) での実装と，その test を以下に示す．この実装はわかりやすさを主にしているので matrix 乗算とtranspose が入っているが，もちろんこれらを省略するような実装も可能である．Test の結果，2つの matrix は私が試した限りでは，1.0e-6 以下の誤差で一致する．(Ubuntu 10.04, python 2.6, glx version 1.4)

# Copyright (C) 2010 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.')