Abstract: This paper presents a method for texturing any surface using texture samples while avoiding distortion, discontinuity and repetitiveness. The principle consists in replacing global parameterization of the surface by a serie of local parameterization, and reporting the continuity constraints to the content. For doing this, we make a set of triangular samples whose borders are compatible, we build a mesh of quasi-equilateral triangles on the surface, we project these triangles on the surface using geodesics, and we parameterize each triangular texture patch. We propose solutions to synthesize textures samples having the continuity property in the case of Perlin and Worley procedural textures, and to draw or edit images.