Video projectors have advanced from being tools for only delivering presentations on flat or planar surfaces to tools for delivering media content in such applications as augmented reality, simulated sports practice and invisible displays. With the use of non-planar surfaces for projection comes geometric and radiometric distortions. This work dwells on correcting geometric distortions occurring when images or video frames are projected onto static and deformable non-planar display surfaces. The distortion-correction process involves (i) detecting feature points from the camera images and creating a desired shape of the undistorted view through a 2D homography, (ii) transforming the feature points on the camera images to control points on the projected images, (iii) calculating Radial Basis Function (RBF) warping coefficients from the control points, and warping the projected image to obtain an undistorted image of the projection on the projection surface. Several novel aspects of this work have emerged and include (i) developing a theoretical framework that explains the cause of distortion and provides a general warping pattern to be applied to the projection, (ii) carrying out the distortion-correction process without the use of a distortion-measuring calibration image or structured light pattern, (iii) carrying out the distortioncorrection process on a projection display that deforms with time with a single uncalibrated projector and uncalibrated camera, and (iv) performing an optimisation of the distortioncorrection processes to operate in real-time. The geometric distortion correction process designed in this work has been tested for both static projection systems in which the components remain fixed in position, and dynamic projection systems in which the positions of components or shape of the display change with time. The results of these tests show that the geometric distortion-correction technique developed in this work improves the observed image geometry by as much as 31% based on normalised correlation measure. The optimisation of the distortion-correction process resulted in a 98% improvement of its speed of operation thereby demonstrating the applicability of the proposed approach to real projection systems with deformable projection displays.