6 results about "Signed distance function" patented technology

The present invention discloses a method for simulating incompressible viscous fluids based on signed distance function representation, and relates to the technical fields of numerical calculation and numerical simulation. The method comprises spatially dividing a calculation area into Cartesian grids; using signed distance functions to represent virtual points in the grid at the solid wall boundary of the calculation area, calculating the perpendicular point from the virtual point to the boundary of the geometric area using a perpendicular calculation algorithm based on signed distance function representation, solving the differential information of the equation at the perpendicular point using an explicit Inverse Lax-Wendroff technique at the perpendicular point, obtaining the grid function value at the virtual point using the differential information, and simultaneously solving the algebraic relationship between the virtual point value and the internal point value, and auxiliary matrix assembly; and using the Crank-Nicolson format to advance the time step forward to realize the numerical simulation of incompressible viscous fluids based on SDF. The present invention realizes complex boundary processing while ensuring the accuracy of the algorithm.

Approaches presented herein provide for the use of implicit functions to simulate differentiable object elasticity. An implicit continuous function, such as a signed distance function (SDF), can be used to approximate the surface of an object by providing scalar values from a set of vertices of a regular grid in which the object representation is to be generated. Interpolation can be applied to determine an approximate surface location and shape within each boundary cell. A trained neural network, such as a multilayer perceptron (MLP), can be used to determine appropriate quadrature points that fall within the volume of the object. A finite element analysis can integrate over these quadrature points, using both continuous and discrete settings, as a basis for performing efficient differentiable elasticity simulations including the deformable object.

This invention discloses a method and apparatus for geometric modeling of complex spacecraft targets based on modular implicit neural representation. By dividing the overall structure into multiple independent functional sub-modules according to the functional attributes and geometric features of the spacecraft, and constructing a signed distance function (SDF) model for each sub-module, high-precision implicit modeling of local geometry is achieved. After independent training of the SDF, by applying pose parameter transformations and coordinate mappings to each module, the complex overall shape of the original spacecraft can be accurately reconstructed. This method not only enables continuous, differentiable, and real-time geometric representation of spacecraft during dynamic structural changes, but also allows for local updates of only the corresponding sub-modules when components are added or replaced, improving modeling efficiency and engineering practicality. This invention is particularly suitable for the geometric description and process modeling needs of complex spacecraft structures with multiple module combinations, multiple deployment mechanisms, and multiple auxiliary modules.

The invention discloses an incompressible viscous fluid simulation method based on symbolic distance function representation, and relates to the technical field of numerical calculation and numerical simulation. The method comprises the following steps: carrying out Cartesian grid division on a calculation area in space; at the solid wall boundary of the calculation area, using a sign distance function to represent a virtual point in the positioning grid, calculating a perpendicular foot point from the virtual point to the geometric area boundary through a perpendicular foot calculation algorithm represented based on the sign distance function, and solving differential information of an equation at the perpendicular foot point through an explicit Inverse Lax-Wendroff technology on the perpendicular foot point, obtaining a lattice point function value at a virtual point through differential information, solving an algebraic relational expression between a virtual point value and an internal point value, and assisting matrix assembly; a Crank-Nicolson format is used for advancing a time step, SDF-based numerical simulation of the incompressible viscous fluid is realized, complex boundary processing is realized, and meanwhile, the precision of an algorithm is ensured.

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.

The invention discloses a complex spacecraft target geometric modeling method and device based on modular implicit neural representation. The overall structure is split into a plurality of mutually independent functional sub-modules according to functional attributes and geometrical characteristics of a spacecraft, and a neural signed distance function SDF model is constructed for each sub-module, so that high-precision implicit modeling of each local geometry is realized. After independent training of the SDF is completed, pose parameter transformation and coordinate mapping are applied to all the modules, and the overall complex shape of an original spacecraft can be accurately reconstructed. According to the method, continuous, differentiable and real-time geometric expression can be carried out on the spacecraft in the dynamic structure change process, local updating can be only carried out on the corresponding sub-modules when the components are added or replaced, and the modeling efficiency and the engineering practicability are improved. The method is particularly suitable for geometric description and process modeling requirements of a complex spacecraft structure with multiple cabin section combinations, multiple unfolding mechanisms and multiple auxiliary modules.