B-spline to Bezier Coordinate Conversion for Intersection Detection
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Solution Overview
Problem
Existing drawing data examination methods for charged particle beam drawing apparatuses, particularly those using B-spline curves, face inefficiencies and inaccuracies in detecting intersections, leading to false failures even when curves do not intersect, due to stringent shape constraints.
Innovation Solution
A method that converts B-spline curve coordinates into Bezier curve coordinates, allowing for intersection determination based on a threshold value, thereby relaxing shape constraints and improving examination accuracy by using a Bezier curve for intersection analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If B-spline curve is used for mask data amount reduction, then data compression efficiency is improved, but false intersection detection occurs leading to examination accuracy deterioration
Solution Approach 1:
The patent introduces a Bezier curve as an intermediary representation to resolve the contradiction between B-spline compression efficiency and intersection detection accuracy. The Bezier curve serves as a mediator that preserves geometric fidelity for accurate intersection analysis while allowing the original B-spline to maintain data compression benefits. This intermediary approach enables independent optimization of both compression and detection functions.
Solution Approach 2:
The patent creates a copy of the curve geometry in Bezier representation to perform intersection examination. By maintaining both B-spline (for compression) and Bezier (for accurate intersection detection) representations, the system can examine the copied Bezier version without compromising the compressed B-spline data structure, thus eliminating false failures while preserving compression efficiency.
2Reliability
If stringent shape constraints are applied for intersection examination, then false failures are reduced, but examination process complexity increases
Solution Approach 1:
The patent changes the mathematical representation parameters from B-spline to Bezier curves. This parameter change enables the use of standard, well-established intersection examination algorithms that work reliably with Bezier curves, thereby improving examination accuracy without requiring complex custom algorithms. The parameter transformation simplifies the examination process by leveraging existing geometric computation methods.
Data Source
AI summary
A drawing data examination method acquires coordinates representing the positions of a first control point group forming a B-spline curve; calculates a B-spline curve intersection ratio; converts the coordinates of the first control point group into the coordinates of a second control point group of a Bezier curve when the B-spline curve intersection ratio exceeds a threshold value, and determines whether the figure after the coordinate conversion has an intersection; and determines whether the figure of the drawing data has an intersection based on the first control point group when the B-spline curve intersection ratio is equal to or smaller than the threshold value, and converts the coordinates of the first control point group into the coordinates of the second control point group when the figure of the drawing data has an intersection, and determines whether the figure after the coordinate conversion has an intersection.