A apparatus for making a three-dimensional object (glass, glass ceramic or ceramic) that includes: a gripping fixture 102a having a grip surface or a pedestal 102 having a build surface 130, the grip or build surface configured to hold an end of a contiguous, preformed material 106, such as a fiber or a ribbon; a feed system 100 having a feed outlet 118 positioned above the grip or build surface, the feed system configured to feed the contiguous, preformed material into a build zone between the feed outlet and the grip or build surface; and a laser delivery system 134 arranged to direct at least one laser beam through the furnace 132 and into the build zone to form a hot spot 126 in the build zone; and a positioning system 120 arranged to effect relative motion between the grip or build surface and the feed outlet. In some implementations, the apparatus for making a 3D object can also include a furnace 132 enclosing the build zone and the feed outlet.