  IFS fractals - the attractors of Iterated Function Systems - have motivated
plenty of research to date, partly due to their simplicity and applicability in
various fields, such as the modeling of plants in computer graphics, and the
design of fractal antennas. The statement and resolution of the Fractal-Line
Intersection Problem is imperative for a more efficient treatment of certain
applications. This paper intends to take further steps towards this resolution,
building on the literature. For the broad class of hyperdense fractals, a
verifiable condition guaranteeing intersection with any line passing through
the convex hull of a planar IFS fractal is shown, in general R^d for
hyperplanes. The condition also implies a constructive algorithm for finding
the points of intersection. Under certain conditions, an infinite number of
approximate intersections are guaranteed, if there is at least one.
Quantification of the intersection is done via an explicit formula for the
invariant measure of IFS.
