1. A projector that projects inputted original images on a projection surface, said projector comprising; an image capturing unit configured to capture an image of a projection target image projected by said projector on the projection surface, the projection target image being an original image to be projected or a corrected image generated by correcting an original image; a shape model hold unit configured to hold shape models each expressing a corresponding predetermined type of a shape; a model selection unit configured to select, as a projection surface shape model, a shape model expressing a type of a shape of the projection surface from among the shape models held in said is shape model hold unit based on correspondence relationships between first feature points on the projection target image and second feature points on the image captured by said image capturing unit; a parameter calculation unit configured to calculate a model parameter using the projection surface shape model based on correspondence relationships between the first feature points on the projection target image and the second feature points on the image captured by said image capturing unit in order to approximate the image captured by said image capturing unit to the original image, the model parameter being used to approximate a shape of the projection surface shape model to the shape of the projection surface and indicating a positional relationship between the projection surface and said projector, and the calculation being performed for each of projection target images including the projection target image; a correction unit configured to, when the model parameter is calculated, correct another original image to be projected using the projection surface shape model and the model parameter; and a projection unit configured to project, as another projection target image, the corrected image corrected by said correction unit on the projection surface.