Generation of Random Digital Simple Curves with Artistic Emulation

Abstract

This paper presents two novel interdependent techniques for random digital simple curve generation. The first one is about generating a curve of finite length, producing a sequence of points defining a digital path ρ ‘on the fly’. The second is for the creation of artistic sketches from line drawings and edge maps, using multiple instances of such random digital paths. A generated digital path ρ never intersects or touches itself, and hence becomes simple and irreducible. This is ensured by detecting every possible trap formed by the previously generated part of ρ, which, if entered into, cannot be exited without touching or intersecting ρ. The algorithm is completely free of any backtracking and its time complexity is linear in the length of ρ. For artistic emulation, a curve-constrained domain is defined by the Minkowski sum of the input drawing with a structuring element whose size varies with the pencil diameter. An artist’s usual trait of making irregular strokes and sub-strokes, with varying shades while sketching, is thus captured in a realistic manner. Algorithmic solutions of non-photorealism are perceived as an enrichment of contemporary digital art. Simulation results for the presented algorithms have been furnished to demonstrate their efficiency and elegance.