a b c

Relief carving is modelled with the “offsetting along the normal” operation where the offset value is defined by two-dimensional depth data. To generate depth data we use a polygon-to-function conversion algorithm. In the example shown above we illustrate the following steps:

• a concave polygon (reptile's contour) was taken from the image (a) (“Reptiles” by M.Escher);
• the polygon was represented by a real function F(X,Y) with zero value at polygon edges;
• positive values of the function were used as depth data (b);
• offsetting along the normal was applied to a stone model to carve the reptile ©.

Details on polygon-to-function conversion and other examples can be found in the technical report:

Pasko A.A., Savchenko A.V., Savchenko V.V. “Implicit curved polygons”, Technical Report 96-1-004, University of Aizu, Japan, 1996.
Electronic version: PostScript + gzip (523K)