1 3D virtual mosaics: Opus Palladium and mixed styles Visual Comput 2009 報告者 : 丁琨桓

2 Introduction Previous works on such surface mosaics have used only square-shaped tiles, with fixed or variable size. In this paper present a method to simulate mosaic sculptures using tiles with irregular shapes, a method known by mosaicists as Opus Palladium

3 Opus Palladium opus palladium 3D mosaic

4 Distribution of square tiles of variable sizes [ 3D mosaics with variable-sized tiles, Visual Comput 2008 ] Step1 : Random tile distribution on the surface of a polyhedral model Step2 : Point relaxation on the surface

5 Random tile distribution on the surface of a polyhedral model distributed randomly over the surface polygon capacity Ai : the area of polygon i rc i : the polygon radius of curvature f : the mapping function

6 Mapping curvatures into tile size Function for mapping curvatures into tile sizes Radius of curvature (Rc) in the plane

7 Random tile distribution on the surface of a polyhedral model Polygons with higher curvature, i.e., smaller radius of curvatures, will receive more tiles. distributed randomlydistributed with capacity function

8 Point relaxation on the surface In order to achieve an even distribution over the surface by use a relaxation process. The algorithm considers each point as an interacting particle that produces a force field around it.

9 Point relaxation on the surface The repulsive force F ij between points i and j is given according to the equation :

10 Point relaxation on the surface r i and r j are the radii of the ideal circles around the tile. d is the distance between points i and j r : the radius of the circle

11 Point relaxation on the surface K f is a parameter that controls the strength of repulsion. In simulations used k f in the interval [0.04, 0.1].

12 Point relaxation on the surface the only neighboring points considered are the ones located in either primary (share an edge) or secondary faces (share a vertex) with the supporting polygon. For the red triangle, the primary (cyan) and secondary (green) neighbors

13 Rendering variable-shaped tiles using Voronoi diagrams Voronoi polygons have enough shape variation and are a good candidate for tiles with variable shape. Voronoi diagram

14 Rendering variable-shaped tiles using Voronoi diagrams Grout generated after tile reduction. From left to right: 10%, 20%, and 30%

15 Control of the design [Artificial mosaics, Visual Comput 2005]

16 Control of the design the closer the point is to the edge, stronger is the force Without edge force

17 Result A 3D mosaic lion sculpture # of tiles : ts min : 0.1ts ts max : 3ts

18 Result Opus Palladium style # of tiles : ts min : 0.5ts ts max : 2ts

19 Conclusion Although Voronoi polygons capture most of the shape variation present in real irregular mosaic tiles, they still look too regular for some designs. opus palladium 3D mosaic