Two geometrical models (an affine transformation and a projective transformation) were applied as the mapping function between physical space and visual space (or cognitive space). In visual and cognitive spaces, one of geometrical properties is an anisotropic property. Both geometrical models have an advantage to be able to explain the anisotropic property. Based on the four experiments, in all cases, the projective transformation fitted the data better than the affine transformation . As the projective transformation includes the affine transformation as the special case, it is proposed to use projective transformation as the geometrical model of visual space and cognitive space. If the coefficients of x and y of the denominator of the projective transformation are close to 0, the affine transformation will be enough to explain the data. Otherwise，the projective transformation will be recommended.