Self-Intersecting Lattice Mesh Generation Through Geometric Sampling
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Solution Overview
Problem
Existing methods for incarnating self-intersecting lattice structures in three-dimensional models, particularly those with rod-ball and rod-rod clashes, are inefficient and inaccurate due to the use of marching cubes algorithms that do not consider underlying geometry, leading to coarse mesh results and high computing costs.
Innovation Solution
A computer-implemented method that selects intersecting bodies in a self-intersecting lattice, calculates parameter curves, and iteratively determines sample points to generate polylines, using a sampling algorithm combined with lattice geometry-based algorithms to achieve accurate and efficient mesh incarnation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If marching cubes algorithm is used for mesh incarnation, then the algorithm can be applied to entire lattice without considering geometry complexity, but the mesh accuracy deteriorates and computing time increases
Solution Approach 1:
The patent divides the lattice structure into discrete rod and ball elements, treating each intersection as a separate entity. This segmentation allows the algorithm to process each rod-ball or rod-rod intersection individually using analytic geometry, rather than applying marching cubes to the entire lattice as a monolithic volume. The segmentation enables precise calculation of intersection curves while maintaining computational efficiency.
Solution Approach 2:
The patent replaces the marching cubes algorithm (which treats the lattice as a scalar field requiring volumetric sampling) with an analytic geometry-based approach. Instead of mechanically sampling the entire volume and constructing isosurfaces, the new method uses mathematical formulas to directly calculate intersection curves between rods and balls, substituting a geometric calculation system for a volumetric sampling system.
2Adaptability or versatility
If marching cubes algorithm is used for mesh incarnation, then the algorithm can handle self-intersecting lattices, but the computing cost increases proportionally to the cube of required tolerance
Solution Approach 1:
The patent performs preliminary identification and classification of all rod-ball and rod-rod intersections before generating the mesh. By pre-calculating which rods intersect with which balls or rods, and determining the parameter ranges for these intersections, the algorithm avoids the need to sample the entire lattice volume. This preliminary action reduces the computational problem from O(1/tolerance³) to a much more efficient calculation based only on intersection points.
Solution Approach 2:
The patent applies different processing strategies to different parts of the lattice based on their local geometry. At rod-ball intersections, it uses spherical cap geometry calculations; at rod-rod intersections, it uses cylindrical intersection calculations. This local quality approach allows the algorithm to handle self-intersecting lattices efficiently by treating each intersection type with its appropriate geometric model, rather than applying a uniform volumetric sampling approach.
3Productivity
If analytic trimming curves are used for mesh generation, then the mesh generation is efficient and accurate, but the method cannot be applied to self-intersecting lattices where rods clash with balls or other rods
Solution Approach 1:
The patent introduces dynamic adaptability into the mesh generation process by detecting the type of intersection (rod-ball or rod-rod) and dynamically selecting the appropriate analytic curve calculation method. The algorithm determines parameter ranges and intersection characteristics based on the specific geometric configuration, allowing it to adapt to self-intersecting lattices while maintaining the efficiency of analytic curve methods. This dynamic selection enables the system to handle both regular and self-intersecting lattices with the same efficient approach.
Solution Approach 2:
The patent changes the parameters used for curve calculation based on the intersection type. For rod-ball intersections, it uses spherical coordinate parameters and radial distances; for rod-rod intersections, it uses cylindrical parameters and angular positions. By changing the parameterization strategy according to the local geometry, the algorithm maintains analytic tractability while accommodating self-intersecting configurations that would invalidate standard trimming curve approaches.
Data Source
AI summary
A computer-implemented method of incarnating a self-intersecting lattice structure as a mesh in a three-dimensional model is described. A pair of bodies in the lattice is chosen. An initial set of sample points is created by intersecting a set of constant parameter curves within the parameter range lying on the surface of one of the bodies of the pair with the surface of the other body of the pair. Chords between adjacent sample points in the initial set of samples that lie within a pre-determined tolerance of the surfaces of both bodies in the pair are calculated and iterated over until all the sample points are within the pre-determined tolerance. Once this is done for all bodies in the lattice, a mesh is incarnated.