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I have a mosaic whose rasters are using a custom coordinate system:

US_IFR
Authority: Custom

Projection: Lambert_Conformal_Conic
false_easting: 0.0
false_northing: 0.0
central_meridian: -95.0
standard_parallel_1: 33.0
standard_parallel_2: 45.0
latitude_of_origin: 39.0
Linear Unit: Meter (1.0)

Geographic Coordinate System: GCS_North_American_1983
Angular Unit: Degree (0.0174532925199433)
Prime Meridian: Greenwich (0.0)
Datum: D_North_American_1983
  Spheroid: GRS_1980
    Semimajor Axis: 6378137.0
    Semiminor Axis: 6356752.314140356
    Inverse Flattening: 298.257222101

After adding the rasters, I modify their footprints to trim off unnecessary parts using a feature class to replace the original footprints. The feature class was created in the same custom coordinate system. At this point, the mosaic looks great, all the images are properly stitched together and all the extraneous information is removed.

However, once I project to web mercator:

WGS_1984_Web_Mercator_Auxiliary_Sphere
WKID: 3857 Authority: EPSG

Projection: Mercator_Auxiliary_Sphere
False_Easting: 0.0
False_Northing: 0.0
Central_Meridian: 0.0
Standard_Parallel_1: 0.0
Auxiliary_Sphere_Type: 0.0
Linear Unit: Meter (1.0)

Geographic Coordinate System: GCS_WGS_1984
Angular Unit: Degree (0.0174532925199433)
Prime Meridian: Greenwich (0.0)
Datum: D_WGS_1984
  Spheroid: WGS_1984
    Semimajor Axis: 6378137.0
    Semiminor Axis: 6356752.314245179
    Inverse Flattening: 298.257223563

in preparation to publish as a map service, the rasters get bent, but the footprints remain straight lines. This means that some of the desired content is stripped off and some of the undesired content is let in.

Any idea why the footprint did not bend in the same way the raster did?

US IFR: US IFR

Web Mercator: Web Mercator

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This is not something that I have tested but I suspect that it would be worth trying the Build Footprints tool which:

Computes the extent of every raster in a mosaic dataset.

...

The Approximate Number of Vertices parameter is used to define the complexity of the footprints. The higher the number of vertices will mean the footprint is more accurate and more irregular. Valid values range from 4 to 10,000. You can set your value to be -1 so that no generalization will take place, but this may mean your footprint will have a very large number of vertices.

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