Bird feathers developed from the wing fibers (actinofibrils) of pterosaurs.
Also see more details here:
"Bird feathers are analogous to the wing fibers of pterosaurs,"
"Wellnhofer [4, 5] and Padian [6, 7], following von Zittel , described a system of fine structural fibers investing the wing membrane, in a pattern similar to the orientation of the feather shafts of birds and the wing fingers of bats, both principal structural elements supporting the patagium and responsible for the transmission of aerodynamic force.
They are neither embedded within the skin of the wing membrane , nor are they wrinkles . Instead, they are distributed on the ventral surface of the wing, and are not covered by skin."
The spanwise orientation of the fibers in
the distal part of the wing ensures that
the membrane-fiber composite is most
effective in transmitting the aerodynamic
force to the body while at the
same time minimizing the stresses acting
on the distal part of the wing spar. A planar
membrane with integral fibers could
bend readily under these loads. However,
the pterosaur wing was not planar:
in every pterosaur specimen known the
wing spar was markedly bowed downwards,
so that the patagium surface was
also curved into a shallow, dome-like surface.
Because of this curvature the combination
of the wing membrane and the
fibers was much stiffer than either could
be alone: the fibers worked analogously
to the struts of an open umbrella, giving
stiffness to an otherwise fragile, thin
skin. A similar structure is adopted in
many insect wings .
"research has since shown that the wing membranes of pterosaurs were actually highly complex and dynamic structures suited to an active style of flight. First, the outer wings (from the wing to the elbow) were strengthened by closely spaced fibers called actinofibrils. The actinofibrils themselves consisted of three distinct layers in the wing, forming a crisscross pattern when superimposed on one another. The actual function of the actinofibrils is unknown, as is the exact material from which they were made. Depending on their exact composition (keratin, muscle, elastic structures, etc.), they may have been stiffening or strengthening agents in the outer part of the wing. The wing membranes also contained a thin layer of muscle, fibrous tissue, and a unique, complex circulatory system of looping blood vessels."
From David Unwin's book "The Pterosaurs from Deep Time":
"...[T]he wing fibers were embedded within the patagia [wing membranes] and typically measured a little less than one-tenth of a millimetre in diameter- about twice the thickness of a human hair. In some spots unravelled fibers reveal that they were composite structures composed of at least 20 or 30 very fine strands, wound together in a helical fashion. Each strand was only a few hundredth of a millimeter across and probably made of collagen a material that is common in the skin of vertebrates".
"The soft tissue preserved in the holotype (IVPP V12705) of Jeholopterus ningchengensis from the Daohugou Bed (Late Jurassic or Early Cretaceous) of China is described in detail. The plagiopatagium can be divided into the distal, comparatively more rigid actinopagatium and a proximal, more tensile tenopatagium. The actinopatagium extends from the wing finger to the articulation between the humerus and the forearm, and shows the presence of at least three layers containing actinofibrils. In each layer, the actinofibrils are parallel to subparallel, but this direction diverges from layer to layer. When distinct layers of actinofibrils are superimposed (owing to taphonomic compression), a reticular pattern is generated. The presence of layers with differently oriented actinofibrils is widespread in this pterosaur. A well-developed integumental covering formed by fibres (here named pycnofibres) that are thicker than the actinofibrils is present. Ungual sheaths that extend the length of the pedal and manual claws of this taxon are also observed. Although the understanding of the mechanical properties of the wing membrane is hampered by the lack of knowledge regarding the composition of the actinofibrils, the configuration observed in Jeholopterus might have allowed subtle changes in the membrane tension during flight, resulting in more control of flight movements and the organization of the wing membrane when the animal was at rest. "
"The wings of pterosaurs consisted of a narrow wing membrane or patagium primarily supported and controlled by the hyperelongate forelimb, but also attaching to the side of the body and the hindlimb. The patagium consisted of a thin sheet of extensible skin with slender structural fibers (=actinofibrils) arranged in a posterodistally radiating pattern. The function of the actinofibrils has been variously interpreted as 1) to prevent unwanted flapping of the patagium, 2) to camber the patagium, transferring aerodynamic loads anteriorly and proximally to the metacarpus and antebrachium, and 3) to spread the patagium chordwise. Only the last interpretation is consistent with the available data. The actinofibrils resisted longitudinal compression so as to spread the patagium chordwise, to redirect spanwise tension in the proximal patagium as chordwise tension in the distal patagium, and to permit compact folding."
"The actinopatagium extends from the wing finger to the articulation between the humerus and the forearm, and shows the presence of at least three layers containing actinofibrils. In each layer, the actinofibrils are parallel to subparallel, but this direction diverges from layer to layer."
"Italian paleontologist Fabio Dalla Vecchia, one of the world's leading experts on pterosaurs, told Discovery News, "The presence of up to three layers with differently oriented actinofibrils (in the wing membrane) is the most surprising thing in this study."
They are "surprising" only if you think birds descended from dinosaurs.