ABSTRACT
ABSTRACT: There is a great interest implementing decorative patterns to complex forms in contemporary architecture. This paper provide mathematical solutions to colonize any type of complex surface with Islamic star patterns by means of drawing it previously on a Euclidian plane and translating it to a complex surface. This translation is achieved through mathematical association between a plane interval and its surface in the space. By means of parametric equations we translate any original tessellation built in the plane to the target surface, eluding so uncontrolled troubles as result of a simple perspective projection. Mathematical procedures to develop this procedure are implemented scripts Rhinoceros© minimizing distortions by choosing appropriate parametric equations. The system can be generalizing to any layout drawn in the original orthogonal plane and for any target complex form we would want to colonize. The condition is the layout must be reduced a simple tile-seed. 1 INTRODUCTION Throughout history Islamic star pattern designers have tried to colonize with their layouts different geometric surfaces families beginning with the more simples in the plane and evolving to more complex double curvature surfaces such a sphere. This evolution has been only developed by means of Euclidian geometric knowledge without using of not geometrical operations. We believe current Islamic star pattern designers must know mathematical and computational tools that recent scientific knowledge offer us trying to colonize new complex surfaces until recently would have been unimaginable and inaccessible by means of draw tools very commons in contemporary architecture designers.
