An image processing apparatus comprising: a corresponding region identifying section configured to: determine, based on positional relations between a surface to which to map a texture image in a target space for rendering and a screen plane on which to define a display image, a region on the plane of the texture image in such a manner that the region corresponds to one of the pixels representing the surface for mapping in the display image, calculate partial differential values of functions for transforming position coordinates on the screen plane to corresponding position coordinates on the texture image plane, determine the corresponding region based on the partial differential values, determine as the corresponding region a parallelogram having sides positioned in the same directions as vectors having the partial differential values as components of the vectors; and a pixel value calculating section configured to sample texel values in the corresponding region so as to determine and output the value of the pixel representing the surface for mapping, wherein the pixel value calculating section is configured to change the number of sampling points in accordance with a size of the corresponding region, and to change the number of the sampling points in accordance with the lengths of the sides of a rectangle circumscribing the parallelogram. a corresponding region identifying section configured to: determine, based on positional relations between a surface to which to map a texture image in a target space for rendering and a screen plane on which to define a display image, a region on the plane of the texture image in such a manner that the region corresponds to one of the pixels representing the surface for mapping in the display image, calculate partial differential values of functions for transforming position coordinates on the screen plane to corresponding position coordinates on the texture image plane, determine the corresponding region based on the partial differential values, determine as the corresponding region a parallelogram having sides positioned in the same directions as vectors having the partial differential values as components of the vectors; and determine, based on positional relations between a surface to which to map a texture image in a target space for rendering and a screen plane on which to define a display image, a region on the plane of the texture image in such a manner that the region corresponds to one of the pixels representing the surface for mapping in the display image, calculate partial differential values of functions for transforming position coordinates on the screen plane to corresponding position coordinates on the texture image plane, determine the corresponding region based on the partial differential values, determine as the corresponding region a parallelogram having sides positioned in the same directions as vectors having the partial differential values as components of the vectors; and a pixel value calculating section configured to sample texel values in the corresponding region so as to determine and output the value of the pixel representing the surface for mapping, wherein the pixel value calculating section is configured to change the number of sampling points in accordance with a size of the corresponding region, and to change the number of the sampling points in accordance with the lengths of the sides of a rectangle circumscribing the parallelogram.