Fig. A.1.

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Approach for handling both filament and prominence boundary conditions within Lightweaver. Top panel; the cone-averaging approach employed to ensure proper sampling of the limb-darkening function with height. Bottom panels; the tracing of the base quadrature across the solar surface for both the filament (left) and prominence (right) cases. These panels consider a view top-down onto the solar surface from, for example, Solar Z = 1.3 R⊙. This base quadrature sampling is augmented with the additional cones as shown in the top panel.
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