Ellipsoid Buffer Representation Using Geodetic Circular Arcs
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Solution Overview
Problem
Existing computing systems cannot accurately represent buffers around geometric objects on an ellipsoid earth model, as they lack support for circular arcs, leading to inaccurate polygonal approximations that require a large number of vertices for higher accuracy.
Innovation Solution
A method is introduced to define and render buffers using circular arcs on an ellipsoid or round-object model, where each arc is defined by three data points, including geodetic coordinates, allowing for more accurate and compact representations by using the SqlGeography.BufferWithCurves method in database applications like SQL Server.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If polygonal approximations are used to represent buffers on an ellipsoid model, then the representation can be implemented with existing computational methods, but the accuracy is insufficient and requires a large number of vertices
Solution Approach 1:
The patent applies spherical geometry principles by representing buffers on an ellipsoid model using great circle arcs and spherical trigonometry. Instead of planar polygonal approximations, the solution uses curved arcs that follow the Earth's surface geometry, defined by three geodetic coordinates (latitude, longitude, and height) to create accurate buffer zones that respect the planet's curvature.
2Measurement precision
If circular arcs are used to represent buffers accurately, then the representation precision is improved, but existing products do not support circular arcs on ellipsoid earth models
Solution Approach 1:
The patent transforms the buffer representation from planar Cartesian coordinates to geodetic coordinates (latitude, longitude, height) on an ellipsoid model. By changing the coordinate system parameters and using spherical trigonometry calculations, the solution enables circular arc representations that are compatible with geographic information systems while maintaining mathematical accuracy on the Earth's curved surface.
3Measurement precision
If polygonal approximations with many vertices are used, then higher accuracy is achieved, but computational efficiency decreases
Solution Approach 1:
The patent uses great circle arcs that follow the Earth's curvature instead of straight line segments. This curved representation naturally achieves higher accuracy with fewer segments because the arcs conform to the spherical geometry, reducing the computational burden of processing numerous vertices while maintaining or improving buffer representation precision.
Data Source
AI summary
A method with acts for representing a buffer about a feature represented on an ellipsoid or round-object model. The method includes accessing a definition of a buffer stored on one or more computer readable medium in a format readable by a computer application. The definition of the buffer includes a number of arcs around a feature on an ellipsoid or round-object model. Each of the arcs is defined using three points defined using geodetic coordinates. The three points includes two endpoints of a given arc and a point on the arc between the two endpoints. The method further includes rendering the buffer by rendering the plurality of arcs. The method further includes displaying the rendered buffer to a user at a computing system display.