A contribution of a geometric element's attribute to a value of the image sample is determined analytically for an analytic dimension of evaluation and using sampling for a discrete dimension of evaluation. Motion blur effects are rendered by analytically determining the proportions of shutter time during which image samples are exposed to objects. Space-time projections are determined by the geometry edges' positions at the beginning and the end of the shutter time, which define surfaces of space-time projections. The times that the sample ray of an image sample enter and leave the space-time projections specify the proportions of the image sample's shutter time during which scene geometry is exposed to image sample points. The attribute value of an image sample point is determined from values of all of the scene geometry visible to the image sample point during the shutter time, each weighted by the time that it is visible.