Abstract: A splined radial panel solar collector structure approximates compound curvature surfaces by a three-dimensional arrangement of compactly stowable flat reflective panel segments mounted on a collapsible, space-deployable support structure of linear components. The support framework is formed of an umbrella-like framework of radially-extending ribs, struts and cords which deploy away from a central hub to form a system of radial trusses. A semirigid reflective surface structure is divided into sections of radial panels which are supported and shaped by an arrangement of radially tensioned flexible tape members aligned with the ribs. Connecting ties between the tapes and the ribs cause the tapes to assume a catenary curve. The ribs and flexible tape members are bridged circumferentially by sets of cords and ties to which the panels are joined. These cord and tie pairs place the panels in bending to effect a "splined" approximation of a parabola in the radial direction.