Earth Model Vertex Mapping to 2D Array
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Solution Overview
Problem
Existing methods for mapping vertices from one coordinate system in an earth model to another in a 2D array are time-consuming and produce less than desirable results, especially with large data sets, as they disrupt the topology of the vertices.
Innovation Solution
A method that aligns the earth model and 2D array by processing vertices on vertical and horizontal curves, marking points on reference lines, forming current curves, and optimizing vertex spacing to reduce memory requirements, allowing for efficient mapping without disrupting topology.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If conventional mapping techniques are used to transform vertices from earth model coordinate system to 2D array coordinate system, then mapping can be achieved, but processing time is excessive and topology of vertices is disrupted
Solution Approach 1:
The patent segments the 2D mapping problem into multiple 1D projection problems along orthogonal curves. By dividing the complex 2D topology preservation task into simpler 1D mappings along coordinate curves, the processing time is reduced while maintaining vertex topology through systematic segmentation of the transformation space.
Solution Approach 2:
The patent transforms the 2D mapping problem into a series of 1D problems by projecting vertices along orthogonal curves. This dimensionality reduction approach simplifies the computational complexity from O(n²) to O(n), significantly reducing processing time while preserving topology through the structured 1D projection methodology.
2Area of stationary object
If region expansion and area preservation technique is used, then area coverage is maintained, but implementation becomes challenging and processing time increases
Solution Approach 1:
The patent changes the approach from area-based transformation to parameter-based vertex mapping. By transforming vertices along orthogonal curves using parameterized equations rather than area-preserving transformations, the implementation complexity is reduced while maintaining accurate spatial representation through parameterized curve projections.
3Manufacturing precision
If large equation system approach is used to expand small cells and shrink large cells, then cell distribution is optimized, but the equation system becomes huge and challenging to implement
Solution Approach 1:
The patent segments the cell distribution optimization problem into independent 1D optimization problems along orthogonal curves. Instead of solving one huge system of equations for the entire 2D domain, the method divides it into manageable 1D segments that can be processed independently, reducing computational complexity while achieving optimal cell distribution through cumulative 1D transformations.
Solution Approach 2:
The patent reduces the 2D cell distribution optimization problem to a series of 1D problems by projecting along orthogonal curves. This dimensionality reduction transforms an intractable large-scale equation system into a series of small, manageable 1D optimization problems that are computationally efficient while preserving the overall cell distribution optimization goal.
Data Source
AI summary
Systems and methods for mapping vertices from one coordinate system in an earth model to another coordinate system in a two-dimensional (2D) array without disrupting the topology of the vertices.