Method for simulating numerically controlled milling using adaptively sampled distance fields

A method for simulating the milling of an object by moving a shape along a path intersecting the object, the object comprising a set of geometric elements, the method comprising a processor for performing steps of the method, the method further comprising the steps of:

• representing the set of geometric elements with a corresponding set of geometric element distance fields;
• generating a composite adaptively sampled distance field (ADF) to represent the object, the composite ADF comprising a set of cells, each cell comprising:
• a subset of the set of geometric element distance fields;
• and
• a procedural reconstruction method for combining the subset of geometric element distance fields to reconstruct a composite distance field of a portion of the object represented by the cell;
• representing the shape by a shape distance field:
• representing path by a parametric function;
• defining a swept volume distance field to represent a swept volume generated by moving the shape along the path, the swept volume distance field defined in a continuous manner according to a swept volume reconstruction method for reconstructing the swept volume distance field at a sample point, the swept volume reconstruction method further comprising the steps of:
• determining, in a continuous manner, an optimal set of parameters of the parametric function, the optimal set of parameters defining an optimal placement of the shape along the path;
• transforming the shape distance field to the optimal placement to produce a transformed shape distance field;
• and
• determining distance data from the transformed shape distance field at the sample point to reconstruct the swept volume distance field at the sample point;
• and
• editing the composite ADF to incorporate the swept volume distance field into the composite ADF, the editing further comprising the steps of:
• determining a set of edit cells of the composite ADF from the swept volume;
• and
• regenerating the composite ADF within the set of edit cells, the regeneration incorporating the swept volume distance field into the set of edit cells of the composite ADF to simulate the milling of the object by moving the shape along the path.