Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, include: obtaining one or more design criteria for a modeled object; iteratively modifying a three-dimensional shape of the modeled object in accordance with the one or more design criteria, determining layer boundaries between three or more discrete layers for the three-dimensional shape based on differences among multiple milling depths identified for respective milling lines in a density-based representation of the three-dimensional shape, including adjusting the density-based representation of the three-dimensional shape to reassign milling depths for at least a portion of the milling lines such that the milling depths for the milling lines correspond to the layer boundaries between the three or more discrete layers for the three-dimensional shape, thereby changing the three-dimensional shape of the modeled object; and providing the three-dimensional shape of the modeled object for use in manufacturing a physical structur

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a density-based representation of a modeled object, the density-based representation comprising multiple different subsets of elements, each subset having a starting element at a milling depth, which is one of three or more milling depths for three or more corresponding discrete layers that are each perpendicular to a milling direction for the modeled object; and reassigning milling depths of at least a portion of the multiple different subsets of elements, the reassigning for a current starting element in a current layer for an element subset comprising moving the milling depth for the element subset of the current starting element when an angular difference between other starting elements, which are associated with the current starting element and are located in a different layer, meets or exceeds a threshold value.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the 3D models of the physical structures are produced so as to facilitate manufacturing of the physical structures using 2.5-axis subtractive manufacturing systems and techniques, include: obtaining a design space, design criteria, and in-use case(s); iteratively modifying a generatively designed shape in the design space in accordance with the design criteria and the in-use case(s) using a density-based representation of the generatively designed shape and including adjusting the density-based representation of the generatively designed three dimensional shape in accordance with a milling direction of a 2.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a density-based representation of a modeled object and data specifying a starting element for each of multiple different subsets of elements; processing starting elements having milling depths associated with layers below a top most layer, the processing including, for a current starting element for a current layer, identifying other starting elements that have milling depths associated with a layer above the current layer and are closer to the current starting element than an amount at least equal to a radius of a smallest available milling tool, calculating a maximum angular difference, and moving the milling depth for the element subset of the current starting element to a layer above the current layer, responsive to the maximum angular difference being greater than a threshold, to remove a non-manufacturable corner.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a design space, design criteria, and boundary conditions for numerical simulation; defining an application of the boundary conditions to a voxelized mesh, including specifying a distribution of a load to nodes of voxels in the voxelized mesh that correspond to a surface of preserve geometry; and iteratively modifying a generatively designed three dimensional shape in the design space in accordance with the design criteria and a physical response of the modeled object determined by the numerical simulation performed using the application of the boundary conditions to the voxelized mesh, wherein the distribution of the total loading value during determination of the physical response ensures an equivalence between the total loading value and a sum of loading values distributed to the respective nodes of the voxels that correspond to the surface.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a density-based representation of a modeled object and data specifying a starting element for each of multiple different subsets of elements; processing starting elements having milling depths associated with layers below a top most layer, the processing including, for a current starting element for a current layer, identifying other starting elements that have milling depths associated with a layer above the current layer and are closer to the current starting element than an amount at least equal to a radius of a smallest available milling tool, calculating a maximum angular difference, and moving the milling depth for the element subset of the current starting element to a layer above the current layer, responsive to the maximum angular difference being greater than a threshold, to remove a non-manufacturable corner.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures include: obtaining a density-based representation of a modeled object and data specifying a starting element for each of multiple different subsets of elements; processing starting elements having milling depths associated with layers below a top most layer, the processing including, for a current starting element for a current layer, identifying other starting elements that have milling depths associated with a layer above the current layer and are closer to the current starting element than an amount at least equal to a radius of a smallest available milling tool, calculating a maximum angular difference, and moving the milling depth for the element subset of the current starting element to a layer above the current layer, responsive to the maximum angular difference being greater than a threshold, to remove a non-manufacturable corner.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for computer aided design of physical structures using generative design processes, where the 3D models of the physical structures are produced so as to facilitate manufacturing of the physical structures using 2.5-axis subtractive manufacturing systems and techniques, include: obtaining a design space, design criteria, and in-use case(s); iteratively modifying a generatively designed shape in the design space in accordance with the design criteria and the in-use case(s) using a density-based representation of the generatively designed shape and including adjusting the density-based representation of the generatively designed three dimensional shape in accordance with a milling direction of a 2.