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Using a spherical model of the earth may give adequate accuracy and leads to simple fast calculations. Convert all coordinates into earth-centered (3D) cartesian coordinates. For example, the formula (cos(lon)*cos(lat), sin(lon)*cos(lat), sin(lat)) will do. (It uses a distance measure in which the earth's radius is one unit, which is convenient.) ...


The formula for calculating grid convergence (sometimes called meridian convergence) for spherical UTM projections was given (very incorrectly until just now) at How to Calculate North? In case that is not clear γ = arctan [tan (λ - λ0) × sin φ] where γ is grid convergence, λ0 is longitude of UTM zone's central ...


I have done a fair amount of research into this problem, now, and I believe that the best way to do this is to create a weighted graph with vertices for every point in the line-string and every intersection between steps along the line-string and apply Dijkstra's Algorithm to find the shortest path from the starting vertex to the end-point. Why my ...


Select single route: Planarize segments, i.e. split them, where their intersection point is not the end point. Find shortest route between start and end point of the route: Delete remaining. I've used my own scripts for this example designed to facilitate network tasks, you might consider using Network Analyst


In ArcMap the Cartography tools "Smooth Line" or "Simplify Line" may give the results you want visually and can be scripted to work in model builder if you need to do the process repetitively. The down side is that smoothing the line or simplifying the line may remove some of your data for speed and barrier detection. You could instead ignore the noise in ...


If Java works for you, take a look into http://github.com/Esri/geometry-api-java. It has OperatorSimplify for polygon repair. It also has OperatorSimplifyOGC if you want the polygons to be also OGC compliant.


Building on @Brad Nesom's answer, if you're willing to look at an FME solution, there are some transformers that can help with your problem. But probably the most useful one would be the Geometry Validator. It has many options for identifying and repairing geometry errors. As you can see, the dialog contains many tests including Self-Intersections in 2D: ...


This is commonly referred to as feature detection. There are many software packages that have libraries for feature detection/extraction. To name a few: Python (Scikit-image): Template Matching Blob Detection Matlab: Feature Detection and Extraction


It is an error. Your link and presumably image source is the 10.0 help. The error is still present in the 10.1 help. However in the 10.2 help, it has been corrected to show only a 1. It's also worth noting that if you work through the math matrix as whuber has done at Arcmap 10 restrict Flow Accumulation, that error is apparent as well as the adjacent 35 ...


Take a look at tilebelt https://github.com/mapbox/tilebelt : quadkeyToTile(quadkey)

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