Principle of Four-Circle Format (4CF) Imaging of 3-D objects

  • A novel method of representing the surface data of objects is described here.   
    (Indian Patent No. - 346245)
  • The shape and colour detail of a 3-D object could be captured among four circular zones, as illustrated below.
Card image cap

  • The two grey colored circles in the upper region contains the coded data of cube shape.
  • The two color circles in the lower region stores the surface color detail of Rubik's cube.
  • The left and right circles of the image pertain to the front and back portions of the object.
  • A geometrical method of mapping the object's surface to the circular zone is outlined below:

  • Card image cap

  • A suitable center point O within the 3-D object model is first chosen.
  • An imaginary sphere centered at O and radius (say, 125 units) is superposed on the model.
  • Let F and B denote front and back direction pole points on the sphere surface.
  • By stereographic projection from B/F poles, the front/back hemispheres can be mapped as circles.
  • As depicted in the figure, ray from O to a surface point P intersects the sphere surface at r .
  • Extension of line segment B-r intersects the tangential plane of F at p .
  • The distance OP (after scaling) is coded as a grey scale pixel value at p, to trace the shape.
  • While the (Red,Green,Blue) color value of P is assigned to the p point in the bottom circle.
  • The obtained (1000x1000 pixel) raster image contains the full solid angle view of the object.
  • A decoder program can interpret the 4CF image and render interactive views on user screen.