Abstract: Fundamental principles of perspective transformation are discussed in the paper. Based on the fact that parallel-lines in some angle with view plane intersect at a vanishing-point, two methods are presented to produce a perspective view: one is to keep the view plane vertical while rotating objects to some angle, to achieve perspective transformation effect, and the other is by means of inclining the projective view to achieve the effect. To the first method, three best perspective transformation matrices are presented, and with regard to the second method, homogeneous perspective transformation matrix is presented, for generating 3-vanishing-point drawing through the inclining view. Both methods are vanishing-point pre-controllable. It means that the vanishing-point could be pre-determined, then the transformation matrix is generated afterwards, As a result, the generation theory of perspective transformation is relatively well solved. We prove that for each 3D object there must be a corresponding 3D object, with its parallel projection the same as the perspective projection of the former counter object, and at the same time, the corresponding depth relationship is well preserved. With this useful property, a complicated perspective projection can be converted to a simple parallel projection, so that the complexity of 3D graphics processing could be greatly reduced.