Provided is a method performed on a processor for simulating the milling of an object by moving a shape along a path intersecting the object. A composite adaptively sampled distance field (ADF) is generated to represent the object, where the composite ADF includes a set of cells. Each cell in the composite ADF includes a set of distance fields and a procedural reconstruction method for reconstructing the object within the cell. The shape is represented by a shape distance field. The path is represented by a parametric function. A swept volume distance field is defined in a continuous manner to represent a swept volume generated by moving the shape along the path according to a swept volume reconstruction method which reconstructs the swept volume distance field at a sample point. The composite ADF is edited to incorporate the swept volume distance field into the composite ADF to simulate the milling.