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I see that there is an option that allows for one to set the view if you provide the coordinates for these bounds, but nowhere in the documentation do I see anything pertaining to retrieving these values as defined by the canvas container / rectangle.

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The current view bounds can be calculated by Camera.computeViewRectangle. Note that the results here can be approximate, due to the complexity of a perspective 3D view of the globe.

For details on that, see Cesium 3D - Determining the Map Scale of the viewed Globe.

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