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

- A novel method of representing the surface data of objects is described here. (patent applied - 201741026182)

- The shape and colour detail of a 3-D object could be captured among four circular zones, as illustrated below.

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:

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 to render interactive views on user screen.