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

2. 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. 3 Opus Palladium opus palladium 3D mosaic

4. 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. 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. 6 Mapping curvatures into tile size Function for mapping curvatures into tile sizes Radius of curvature (Rc) in the plane

7. 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. 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. 9 Point relaxation on the surface The repulsive force F ij between points i and j is given according to the equation :

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

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

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

17. 17 Result A 3D mosaic lion sculpture # of tiles : 20000 ts min : 0.1ts ts max : 3ts

18. 18 Result Opus Palladium style # of tiles : 15000 ts min : 0.5ts ts max : 2ts

19. 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