A method is disclosed for displaying endoscopic images that includes three-dimensional surfaces, variable viewing points, directions, and orientations. A computer receives a captured endoscopic image. A virtual surface is defined in the computer with the captured image textured onto the virtual surface. A virtual viewing point, virtual viewing direction, and virtual viewing orientation are defined relative to the virtual surface. A rendered image of the virtual surface is then created. The rendered image is displayed to the user. Video is displayed on the virtual surface by updating the image texture with each new frame.