Simulating Decorative Mosaics14 CVD uses Nature: –honeycombs –giraffe spots Sampling –approximates Poisson-disk (low discrepancy) –can bias for filter function
Simulating Decorative Mosaics15 Hardware-assisted VDs SG99: Hoff et al –uses graphics hardware –draw cone at each site –orthogonal view from above –each region is single-coloured –can extend to non-point sites (curves) project
Simulating Decorative Mosaics16 Key idea Cone is distance function –radius = height Non-euclidean distance: –different kind of cone –eg square pyramid –can be non-isotropic (rotate pyramid around Z) r h h=|x-a|+|y-b| (a,b) (x,y) h
Simulating Decorative Mosaics17 Basic Tiling Algorithm Compute orientation field (details later) scatter points on image –use pyramids to get oriented tiles apply Lloyds method to spread sites evenly draw oriented tile at each site
Simulating Decorative Mosaics18 Details Lloyds method: –To compute centroid of each Voronoi region: 1: read back pixels, 2: get average (row,col) per colour 3: convert back to object coords.
Simulating Decorative Mosaics19 Lloyd Near Convergence
Simulating Decorative Mosaics20 Orientation Field Choose edges that need emphasis compute generalized VD for edges (Hoff99) get gradient vector of distance field –distance = z-buffer distance gradient orientation = tile orientation –points away from edges
Simulating Decorative Mosaics21 Orientation Field
Simulating Decorative Mosaics22 Edge Discrimination Must line up tiles on edges But both sides of edge oriented same –square tiles ==> 180 o rotational symmetry Use hardware –draw edge thick, different colour –voronoi regions move away from edges –leaves gap where edge is.
Simulating Decorative Mosaics35 Summary New method for packing squares on curvilinear grid Minimizes sum of particle distances
Simulating Decorative Mosaics36 Further Work Reduce grout –final pass: adjust tile shapes currently dont use adjacency info –use divergence of orientation field · Improve colour –real tiles have fixed colour set: Dither? How?