  We extend the recent approach from reference [1] to obtain complete and
analytic solutions (both brane and bulk) of a Simpson-Vaser (SV) geometry
within a braneworld framework. The embedded geometry can represent a
traversable wormhole (TWH), a one-way wormhole (OOWH), or a regular black hole
(RBH). The resulting geometry is regular everywhere, eliminating any
singularity or local de-Sitter core at the origin and on the brane location,
where the regular geometry is given by the SV geometry. The throat of TWHs or
OOWHs can extend into the extra dimension. The event horizon of RBH extends
along the extra dimension, prompting speculation on the extension of entropy
into this dimension. Although the induced geometry is characterized by tension,
acting akin to a positive cosmological constant (thus potentially representing
empty space), the induced four-dimensional geometry remains regular. There is
no need to introduce additional energy sources on the brane to achieve this
regularity. Hence, the brane's geometry, which may depict an RBH, TWH, or OWWH,
is influenced by the geometric properties of the bulk
