Bevel Curves on Splines: Handling Self-Intersections
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Solution Overview
Problem
Computer-aided design (CAD) programs face challenges in applying bevel curves to splines, leading to unwanted deformations and difficulties with self-intersecting splines, such as bumps forming on extruded geometries, which are hard to remove and fill.
Innovation Solution
A method is implemented to detect self-intersections in splines, divide them into sections, remove sections with inward-pointing normals, and link corresponding vertices with neighbor splines to create a geometry, allowing for the automatic removal of deformations and filling of holes formed by bevel curve application.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a bevel curve is applied to a spline to create custom geometries, then the geometry can be shaped and modified, but unwanted deformations such as bumps protruding from the geometry occur
Solution Approach 1:
The spline is divided into multiple segments at detected self-intersection points. This segmentation allows the system to identify and remove only the problematic inward-pointing segments that cause bumps, while preserving the valid portions of the spline geometry.
Solution Approach 2:
Segments with inward-pointing normals are extracted and removed from the spline. This extraction eliminates the source of unwanted deformations (bumps) while maintaining the integrity of the remaining geometry.
2Adaptability or versatility
If a bevel curve is applied to a self-intersecting spline, then custom geometries can be created, but the process cannot be easily performed with traditional methods
Solution Approach 1:
The system automatically detects self-intersection points and performs the necessary segmentation and segment removal operations without requiring manual intervention. This self-service approach makes the process easy to use while supporting complex self-intersecting spline geometries.
Solution Approach 2:
The system changes the parameter evaluation by computing normals at each segment and identifying those with inward-pointing directions. This parameter-based approach enables automatic handling of self-intersecting splines through mathematical criteria rather than manual processing.
3Manufacturing precision
If sections are removed from the spline to eliminate deformations, then unwanted bumps are removed, but holes are left in the geometry
Solution Approach 1:
Neighbor splines are merged with the processed spline by linking corresponding vertices to create a closed geometry. This merging process automatically fills the holes left by segment removal, resulting in a complete solid geometry without gaps.
4Reliability
If corresponding vertices are linked to create geometry with polygons, then a complete solid can be formed, but the process becomes complex
Solution Approach 1:
The system automatically links corresponding vertices between neighbor splines and fills openings with polygons without requiring manual intervention. This automated process creates complete solid geometries reliably while keeping the user interface simple.
Data Source
AI summary
The present disclosure includes, among other things, systems, methods and program products for application of bevel curves to splines.