Surface Creation from 3D Curves via Base Graph
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Solution Overview
Problem
Existing CAD systems lack flexibility in shape definition, restricting creative freedom and interactive modification when generating surfaces from 3D curves, as they require precise intersections and organized inputs, limiting their usability for artistic and general product design applications.
Innovation Solution
A computer-implemented method that determines crossings between 3D curves, constructs a base graph, and fits a mesh with a surface, allowing for the creation of surfaces from non-intersecting curves by projecting curves onto a support, discretizing them, and using bi-perpendiculars to identify crossings, ultimately subdividing the graph to create a smooth surface.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing CAD systems require precise intersections and organized inputs for surface creation, then manufacturing precision is improved, but ease of operation deteriorates
Solution Approach 1:
The system performs preliminary actions by automatically determining crossings between curves and constructing the base graph structure before the user needs to create the surface. This pre-processing of geometric relationships eliminates the need for users to manually organize inputs or ensure precise intersections, while the underlying precision is maintained through algorithmic crossing determination.
Solution Approach 2:
The system serves itself by automatically analyzing the spatial relationships between curves, determining crossings, and constructing the base graph without requiring user intervention for organization or precision adjustment. The algorithm independently handles the complex geometric analysis that would otherwise require skilled manual setup.
2Manufacturing precision
If existing systems require curves to be perfectly intersecting or sequenced, then manufacturing precision is improved, but adaptability deteriorates
Solution Approach 1:
The system changes the fundamental parameter from requiring exact intersection points to using crossing determination between curves. Instead of demanding that curves meet at precise locations, the system determines crossings algorithmically, allowing curves to be in any position or sequence while still maintaining precision in the resulting surface creation.
Solution Approach 2:
The base graph construction method serves multiple functions: it handles intersecting curves, non-intersecting curves, and curves in any sequence. This universal approach allows the same algorithm to process diverse curve configurations without requiring separate methods or manual reorganization, thereby increasing adaptability while maintaining precision.
3Manufacturing precision
If existing CAD systems provide rigid constraints for surface generation, then manufacturing precision is improved, but ease of manufacture deteriorates
Solution Approach 1:
The system extracts the complex constraint management from the user's task and transfers it to the algorithm. By taking out the requirement for users to enforce precise intersections and proper sequencing, and replacing it with automatic crossing determination and base graph construction, the system maintains manufacturing precision while dramatically simplifying the design process.
4Manufacturing precision
If existing systems limit surface creation to product design artists, then manufacturing precision is improved, but ease of operation deteriorates
Solution Approach 1:
The system performs all the complex geometric analysis and base graph construction automatically without requiring user expertise. Users simply provide curves in any configuration, and the system self-services by determining crossings, constructing the graph, and generating the surface with high precision. This eliminates the need for specialized knowledge while maintaining quality results.
Data Source
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AI summary
It is provided a computer-implemented method for creating a surface from a plurality of 3D curves. The method comprises providing (S10) a plurality of 3D curves, determining (S20) crossings between pairs of the curves, defining (S30) a base graph comprising nodes representing the crossings and arcs connecting pairs of nodes representing crossings that are neighbors, determining (S40), from the graph, a mesh comprising vertices defined by a 3D position and edges connecting pairs of the vertices, and fitting (S50) the mesh with a surface. A crossing between a given pair of the curves is an indication of a zone where the given pair of the curves are particularly close to each other. By "close to each other", it is meant that the distance between the two curves of the given pair is below a predetermined threshold. By "particularly" close to each other, it is meant that the distance between the two curves at the crossing is smaller than for other zones of the curves. A crossing between two curves may be an intersection between the two curves. However, as the curves may be provided by the user, there is a high probability that the curves usually do not exactly intersect each other, although the user meant to make them intersect. Such a method makes the creation of a surface from a plurality of 3D curves easier.