Abstract: Certain aspects and features of this disclosure relate to modeling shapes using SDF approximation. For example, a method involves partitioning a surface-bounding volume configured to contain the surface of a shape using a volumetric grid. The method also involves approximating, using a basis function, a value of a signed distance function (SDF) for samples taken inside, and on a boundary of, each surface-containing cell of the grid, and storing, based on the sign changes, coordinates for each of the cells. The method further involves constructing a surface-bounding volume hierarchy for the shape by assigning bounding volumes to each of the cells based on the coordinates. The method additionally involves determining an intersection of a ray with each surface-bounding volume in the surface-bounding volume hierarchy and rendering or storing a representation of the shape based on each intersection.

Abstract: Certain aspects and features of this disclosure relate to modeling shapes using SDF approximation. For example, a method involves partitioning a surface-bounding volume configured to contain the surface of a shape using a volumetric grid. The method also involves approximating, using a basis function, a value of a signed distance function (SDF) for samples taken inside, and on a boundary of, each surface-containing cell of the grid, and storing, based on the sign changes, coordinates for each of the cells. The method further involves constructing a surface-bounding volume hierarchy for the shape by assigning bounding volumes to each of the cells based on the coordinates. The method additionally involves determining an intersection of a ray with each surface-bounding volume in the surface-bounding volume hierarchy and rendering or storing a representation of the shape based on each intersection.

Abstract: Certain aspects and features of this disclosure relate to modeling shapes using differentiable, signed distance functions. 3D modeling software can edit a 3D model represented using the differentiable, signed distance functions while displaying the model in a manner that is computing resource efficient and fast. Further, such 3D modeling software can automatically create such an editable 3D model from a reference representation that can be obtained in various ways and stored in a variety of formats. For example, a real-world object can be scanned using LiDAR and a reference representation can be produced from the LiDAR data. Candidate procedural models from a library of curated procedural models are optimized to obtain the best procedural model for editing. A selected procedural model provides an editable, reconstructed shape based on the reference representation of the object.

Abstract: A multi-characteristic remeshing system that generates remeshed 3D graphical surfaces can include a compact geometric descriptive language (“CGDL”) conversion module, one or more geometric characteristic parsing modules, and a geometric computation module. The CGDL conversion module receives an input mesh for a 3D graphical object and CGDL source text that describes target characteristics of an output mesh of the 3D graphical object. Each geometric characteristic parsing module identifies inherent geometric characteristics of the input mesh, and generates a geometric characteristic map. The geometric characteristic map includes instructions to generate the output mesh with respective target characteristics. The instruction describes a relationship of the one or more inherent geometric characteristics with the respective target characteristic.