Coordinate Transformation for Real-World Mapping With Polynomial Rays
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Solution Overview
Problem
Existing measurement devices for real-world environments suffer from inherent errors due to environmental factors such as temperature variations, pressure, and Earth's curvature, leading to inaccurate distance and direction measurements, particularly in photogrammetry and laser scanning.
Innovation Solution
A method involving transforming rays from a first coordinate system to a second system, sampling the transformed rays into synthetic points, determining discrepancies, adding new points if necessary, and performing polynomial regression to establish a correlation between the systems, thereby accounting for refraction, map projection, and geoid height.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional measurement devices are used in real-world environments, then measurements can be obtained, but inherent errors from environmental factors (temperature, pressure, Earth's curvature) cause inaccuracy in distance and direction measurements
Solution Approach 1:
The patent introduces a polynomial transformation function as an intermediary between the local tangent plane coordinate system and the projected coordinate system. This transformation function acts as a mediator that accounts for environmental factors such as Earth's curvature, refraction, and geoid variations, thereby eliminating systematic errors in coordinate transformation while preserving measurement accuracy.
2Measurement precision
If complex calibration and transformation procedures are performed to account for environmental factors, then measurement accuracy improves, but computational time and complexity increase
Solution Approach 1:
The patent transforms the complex coordinate transformation problem into a polynomial parameter fitting problem. By sampling transformed ray coordinates and fitting polynomial parameters through regression, the method achieves accurate coordinate transformation with reduced computational complexity compared to traditional iterative optimization methods, thereby reducing computation time while maintaining measurement precision.
3Measurement precision
If polynomial regression with many synthetic points is performed to increase accuracy, then transformation precision improves, but computational complexity increases
Solution Approach 1:
The patent employs adaptive sampling of synthetic points along transformed rays, using more points only where necessary to achieve the desired precision threshold. This partial action approach avoids uniformly using excessive points across all rays, thereby achieving the required transformation precision with reduced overall computational complexity compared to using a fixed large number of points for all transformations.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach provides a computationally efficient and accurate representation of the real-world environment, reducing systematic errors in mapping projections and enabling faster, more precise rendering on a computer screen.
Implementation Method 1
performing a polynomial regression based on at least a subset of the synthetic points to determine a polynomial function representing the synthetic points, and thereby providing a correlation between the first coordinate system and the second coordinate system
Data Source
AI summary
Provided is a computer implemented method for representing at least part of a real-world environment based on measurements performed by a measurement device. The method comprises transforming a ray from the first coordinate system to a second coordinate system used for representation of said measurements, sampling the transformed ray to be represented by a plurality of synthetic points, determining a discrepancy between the transformed ray and a straight line connecting the synthetic points, if the discrepancy is larger than a specific threshold value, reducing the specific distance between the synthetic points, and/or adding a new synthetic point between the synthetic points, performing a polynomial regression based on at least a subset of the synthetic points to determine a polynomial function representing the synthetic points, and thereby providing a correlation between the first coordinate system and the second coordinate system. An apparatus on which the method is implemented is also provided.