1. A projection system comprising: a projector assembly; a storage that stores parameters for projective transformation; and a controller that generates a pre-projective transformation image based on an extracted image obtained from a source image by the controller, applies projective transformation to the pre-projective transformation image using the parameters to produce an output image, and causes the projector assembly to output the output image and project a projected image on a surface for projection; wherein in a case where the extracted image has been obtained in a predetermined range of the source image by the controller, the projected image is projected onto the surface for projection so that the pre-projective transformation image is located at a predetermined position in the surface for projection; and when, a change, from the predetermined range, of a range to extract in the source image to obtain the extracted image leads to a change of a coordinate of pixels of the pre-projective transformation image by a V pixel unit from a coordinate obtained in the case where the extracted image has been obtained in the predetermined range, the controller translates the pre-projective transformation image by a V pixel and applies projective transformation to the pre-projective transformation image using the parameters to produce the output image.