A method performed on a processor reconstructs a distance field of an object at a sample point, where the object is a swept volume generated by moving a shape along a path. The shape is represented by a shape distance field. The path is represented by a parametric function. Distance data at the sample points is determined, where the distance data characterizes the distance field of the object at the sample point. An optimal set of parameters defining an optimal placement of the shape along the path is determined in a continuous manner. The shape distance field is transformed to the optimal placement to produce a transformed shape distance field. The distance data is determined at the sample point from the transformed shape distance field to reconstruct the distance field at the sample point.