Abstract: A method of modeling a solid shape in a volume of space may include segmenting the volume into a plurality of equal portions of a given first size, determining, with respect to each portion, a first fill status based on whether each respective portion includes material of the shape, segmenting selected portions of the volume, based on the first fill status, into equal portions of a given second size that is smaller than the first size, determining, with respect to each selected portion, a second fill status, segmenting second selected portions of the volume, based on the second fill status, into equal portions of a given third size that is smaller than the second size, determining, with respect to each second selected portion, a third fill status, and generating a hybrid dynamic tree data structure based on the based on the first, second and third fill statuses.

Abstract: A method associates a cell in the composite adaptive distance field (cADF) with a machining instruction that changes a type of the cell or a type of a distance field in the cell in forming a composite surface of the workpiece to produce at least part of an association, and associates the distance field in the cell with the machining instruction changing the type of the distance field in forming the composite surface of the workpiece to produce at least part of the association. In response to receiving a command to undo a simulation of the machining to the intermediate machining instruction, a subset of cells and a subset of distance fields forming the composite surface of the workpiece at a time of the simulation by the intermediate machining instruction are identified using the association and the intermediate representation of the workpiece is determined using the subset of cells and the subset of distance fields.

Abstract: A method of modeling a solid shape in a volume of space may include segmenting the volume into a plurality of equal portions of a given first size, determining, with respect to each portion, a first fill status based on whether each respective portion includes material of the shape, segmenting selected portions of the volume, based on the first fill status, into equal portions of a given second size that is smaller than the first size, determining, with respect to each selected portion, a second fill status, segmenting second selected portions of the volume, based on the second fill status, into equal portions of a given third size that is smaller than the second size, determining, with respect to each second selected portion, a third fill status, and generating a hybrid dynamic tree data structure based on the based on the first, second and third fill statuses.

Abstract: A method associates a cell in the cADF with a machining instruction that changes a type of the cell or a type of a distance field in the cell in forming a composite surface of the workpiece to produce at least part of an association, and associates the distance field in the cell with the machining instruction changing the type of the distance field in forming the composite surface of the workpiece to produce at least part of the association. In response to receiving a command to undo a simulation of the machining to the intermediate machining instruction, a subset of cells and a subset of distance fields forming the composite surface of the workpiece at time of the simulation by the intermediate machining instruction are identified using the associate and the intermediate representation of the workpiece is determined using the subset of cells and the subset of distance fields.