Parametric Curve Boolean Operations for IC Layout
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Solution Overview
Problem
Existing integrated circuit (IC) design tools cannot perform Boolean operations directly on curved boundaries defined by parametric curve functions, leading to loss of original mathematical information such as point positions, intersections, tangents, and curvature, and making it difficult to reconstruct the original curved boundaries after approximation to polygons.
Innovation Solution
A method that receives lists of curves defining boundary sets, determines intersections, assigns nodes to intersection points, determines curve sections, and performs desired Boolean operations on these sections to obtain the features in the integrated circuit, maintaining the original information by working directly with parametric curve functions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If curved boundaries are approximated to polygons using existing methods, then Boolean operations can be performed, but mathematical information about point positions, intersections, tangents, curvature, and derivative functions is lost
Solution Approach 1:
The patent transforms the representation parameters of curved boundaries from parametric curve functions to piecewise linear polygonal representations. This parameter transformation enables compatibility with existing Boolean operation algorithms while accepting the trade-off of losing mathematical properties such as curvature, tangents, and derivative information. The method systematically converts continuous parametric representations into discrete vertex-based polygon representations that can be processed by standard computational geometry tools.
2Adaptability or versatility
If curved boundaries are converted to polygons, then existing Boolean operation tools can be used, but it becomes difficult to reconstruct the original mathematically defined curved boundaries
Solution Approach 1:
The patent creates a simplified copy of the original curved boundary in the form of a polygonal approximation. This copy retains the essential topological and geometric characteristics sufficient for Boolean operations, while the original parametric representation is preserved separately for potential reconstruction purposes. The method establishes a mapping between the original curve parameters and the resulting polygon vertices, enabling reverse engineering of the approximate boundary shape.
3Loss of information
If parametric curve functions are used directly, then mathematical information is preserved, but existing Boolean operation methods cannot be applied
Solution Approach 1:
The patent introduces an intermediary transformation process that bridges parametric curve functions and polygonal representations. This intermediary step involves sampling the parametric curves at discrete parameter values to generate control points, which then define the polygonal approximation. The method acts as a mediator that translates between the continuous mathematical representation and the discrete computational geometry format required by existing Boolean operation tools.
Data Source
AI summary
A method includes receiving a first list including a plurality of first curves defining a first boundary set and a second list including a plurality of second curves defining a second boundary set. The first and second curves are indicative of features in an integrated circuit based on parametric values. The method includes determining intersections between pairs of curves from the first and the second lists, assigning a node to each intersection point of a pair of curves, and determining curve sections between the intersection points for each intersected curve. The method includes determining a successor of each curve section, determining boundaries formed by the curve sections, performing the Boolean operation between the boundaries to obtain the one or more features in the integrated circuit from the two or more boundaries, and generating a layout of the integrated circuit including the features for manufacturing a mask for reproducing the features.