When buffering features in a projected coordinate system with output to a geodatabase feature class, the geometries created may contain circular arc segments (when buffering points, the output will always be circular arcs). When using the Planar method, you can improve the accuracy of buffers created with projected inputs using a projection that minimizes distance distortion, such as an Equidistant Conic or an Azimuthal Equidistant projection, and is geographically appropriate for your input. You can change the coordinate system of a feature class using the Project tool, or you can set the Output Coordinate System geoprocessing environment before executing the Buffer tool, and this coordinate system will be used when creating buffers. In some cases, this may take more time than the geodesic buffer created using the Planar option, but the result is a buffer that more accurately matches the shape of the input feature. If you are concerned about the shape of your buffers and how closely their shape matches the original input features, it is recommended that you investigate using this option, particularly when your input data is in a geographic coordinate system. The shape-preserving geodesic buffer densifies the input features prior to creating the output geodesic buffers to create buffers that more closely represent the input features' shape.
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