CylinderSurface.jl

################################################################################
#                  Specialized Methods for CylinderSurface
#
# Why Specialized?
#   The parametric function that Meshes.jl currently implements for CylinderSurface
#   only parametrizes the rounded walls, but this Geometry surface is defined as
#   including the top and bottom circular base surfaces as well. These methods
#   simply integrate the base and walls and return the sum of the three integrals.
################################################################################

function integral(
        f,
        cyl::Meshes.CylinderSurface,
        rule::I;
        kwargs...
) where {I <: IntegrationRule}
    # The generic method only parametrizes the sides
    sides = _integral(f, cyl, rule; kwargs...)

    # Integrate the Disk at the top
    disk_top = Meshes.Disk(cyl.top, cyl.radius)
    top = _integral(f, disk_top, rule; kwargs...)

    # Integrate the Disk at the bottom
    disk_bottom = Meshes.Disk(cyl.bot, cyl.radius)
    bottom = _integral(f, disk_bottom, rule; kwargs...)

    return sides + top + bottom
end