1. An apparatus for computed tomography wherein a three-dimensional (3D) volume image data set is rendered into a two-dimensional (2D) displayed image, comprising a graphics processing unit (GPU) comprising a plurality of programmable vertex shaders that are coupled to a plurality of programmable pixel shaders, one or more of the vertex shaders and the pixel shaders being adapted to determine a color of each pixel in the 2D image as an iterative function of intensities and gradients at a plurality of sample points in the 3D image through which a ray associated with a particular pixel is passed, where the calculation of the iterative function for a given sample point along a ray associated with that particular pixel is based on a result of calculations of the iterative function for other sample points on that ray, wherein at least one of the pixel shaders computes a gradient at a sample point along a ray based on differences in intensities at a plurality of points in the 3D image data neighboring that sample point; said at least one of the pixel shaders computes the gradient at the sample point along the ray in a second coordinate system rotated relative to a first coordinate system in which the 3D image data is represented, wherein at least one axis of the second coordinate system aligned along the ray; and said at least one of the pixel shaders subsequently rotates the gradient computed in the second coordinate system back to the first coordinate system.