3D Tessellation Gap Filling with Constrained Delaunay Meshes
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Solution Overview
Problem
Existing methods for processing a tessellation forming a surface representation of a real-world 3D object are inefficient and require significant manual interaction, leading to physiological burden and high resource consumption, while failing to accurately represent the object's geometry due to gaps and self-intersections.
Innovation Solution
A computer-implemented method using a constrained tetrahedral Delaunay mesh to add tetrahedra faces to the tessellation, minimizing surface creation and filling gaps while maintaining conformality, thereby improving the tessellation's quality and reducing manual processing time and resource consumption.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If manual methods are used to process tessellation and fill gaps, then the tessellation quality can be improved, but the processing time and resource consumption increase significantly
Solution Approach 1:
The system automatically processes the tessellation by identifying gaps and self-intersections, then performs corrections without requiring manual intervention. The computer-implemented method autonomously classifies tetrahedrons, detects geometric errors, and generates corrected tessellations, allowing the system to serve itself rather than requiring human operators.
Solution Approach 2:
The patent replaces manual mechanical processing with an automated computational system. Instead of human operators manually examining and correcting tessellation data, a computer-implemented algorithm processes the geometric data, identifies issues through automated classification, and applies corrections programmatically, substituting human mechanical work with automated computational mechanics.
2Measurement precision
If existing gap-filling methods are applied to the tessellation, then the geometric accuracy may be improved, but the method complexity and computational resources required increase
Solution Approach 1:
The patent segments the tessellation processing into distinct classification groups (first group and second group of tetrahedrons). By dividing the complex geometric data into manageable segments and applying different processing rules to each segment, the method simplifies the overall complexity while maintaining geometric accuracy in identifying gaps and self-intersections.
Solution Approach 2:
The patent approaches the tessellation correction problem by introducing a classification dimension, categorizing tetrahedrons into different groups based on their geometric properties and relationships. This additional dimensional approach to organizing and processing the data simplifies the identification of gaps and self-intersections without requiring complex direct manipulation of the geometric structures.
3Reliability
If the tessellation is processed to eliminate self-intersections and gaps, then the representation accuracy of the 3D object improves, but the computational resources and processing time increase
Solution Approach 1:
The patent performs preliminary classification of tetrahedrons into different groups before executing the gap-filling and self-intersection correction operations. By pre-organizing the geometric data and identifying problematic regions in advance, the method reduces the computational resources required during the actual correction process, as the system only needs to process identified issues rather than examining the entire tessellation.
Data Source
AI summary
The disclosure relates to a computer-implemented method for tessellation processing. The tessellation forms a surface representation of a real-world 3D object. The method comprises providing a constrained tetrahedral Delaunay mesh comprising the tessellation. The mesh is conformal and comprises one or more sets of tetrahedrons, each set representing a gap between portions of the tessellation, each gap having a size lower than a predefined threshold. The method further comprises determining a set of one or more tetrahedra faces of the mesh to be added to the tessellation, includes minimizing an objective function that includes a term penalizing surface creation by face addition to the tessellation. The minimization is under the constraint that a given set of tetrahedra faces of the Delaunay mesh is to be added to the tessellation. The given set of tetrahedra faces includes, for each gap of one or more gaps, the tetrahedra faces meshing the gap.