Abstract: An arrangement for machining surfaces with a numerically controlled tool in which the tool is provided with a parabolic profile to obtain a substantially smooth surface finish. The workpiece to be machined is moved relative to the cutting tool in substantially a plane of the workpiece. After milling a contour along that plane, the workpiece or the tool is incremented to an adjacent parallel plane for the purpose of milling another contour on the workpiece. The slope of the surface element on the workpiece between the adjacent planes is computed, and the cutting tool is oriented so that the portion of the tool in contact with the workpiece along that surface element, possesses the computed slope. The cutting tool may be formed with cutting edges having straight-line segments interconnected and directed substantially along a parabolic surface. The slopes on the cutting edges of the tool vary in magnitude from substantially zero to infinity.

Abstract: A plurality of projectors are positioned in spaced relationship about an object with a surface to be geometrically analyzed. The projectors have cooperating masks which project onto the object illuminated patterns that subdivide the object into predetermined sections. Each mask has a predetermined pattern of sections, and is applied in sequence. The masks are cooperatively advanced in the projectors, with a separate illuminating pattern prevailing on the object each time that the masks are advanced. The combinations of the patterns on the masks define closely-spaced sections subdividing the object. The patterns are coded so that each section is uniquely defined in coded form. Cameras having the entire object within their field of view, photograph the object each time a separate mask is applied.

Abstract: An arrangement for locating points on a surface, in which the surface is irradiated selectively and subdivided into a number of sections. The subdivided sections are made to overlap so that a region of one section overlaps the region of a neighboring section. Images of the irradiated sections are recorded, and then scanned for purposes of defining the location of predetermined points within overlapping regions of the subdivided sections. The location of the points within overlapping regions is dependent on a predetermined relationship of irradiated intensities of the points obtained during the scanning procedure.

Abstract: A navigational plotter in which a geographical map or chart has marked thereon lines of position corresponding to the Omega or Loran navigation system aids, for example. The intersections of the lines of position with a base line on the chart are recorded in coded form on a separate strip of the chart. The coded signals on the chart strip are read out by the plotter, so that the position of the marker or indicator of the plotter may be read out directly in terms of lines of position corresponding to Omega or Loran systems. The marker or indicator of the plotter may also be positioned directly from information obtained in terms of Omega or Loran lines of position.

Abstract: The spatial locations of points defining a specular surface are determined by disposing the specular surface in the field of view of a lens and by using the specular surface to view by reflection an irradiated reference surface disposed successively in different positions. Reference surface indicia viewed in common line of sight relation to each specular surface point in such different positions of the reference surface are identified. Radiant energy reflected by a specular surface point through the lens node and the location of the lens node defines a further line in space. The intersection of this further line and such line of sight defines the spatial location of such specular surface point. Photographic records made with the reference surface in such different positions contain representations of reflected radiant energy for all specular surface points in the field of view of the lens and in line of sight relation to the reference surface.