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3D virtual mosaics: Opus Palladium and mixed stylesVisual Comput 2009

報告者 :丁琨桓

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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

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Opus Palladium

opus palladium 3D mosaic

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Distribution of square tiles of variable sizes [ 3D mosaics with variable-sized tiles, Visual Co

mput 2008 ] Step1 : Random tile distribution on the surface o

f a polyhedral model Step2 : Point relaxation on the surface

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Random tile distribution on the surface of a polyhedral model distributed randomly over the surface polygon capacity

Ai : the area of polygon i

rci : the polygon radius of curvature

f : the mapping function

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Mapping curvatures into tile size

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

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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 randomly distributed with capacity function

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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.

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Point relaxation on the surface

The repulsive force Fij between points i and j is given according to the equation :

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Point relaxation on the surface

ri and rj 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

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Point relaxation on the surface

Kf is a parameter that controls the strength of repulsion. In simulations used kf in the interval [0.04, 0.1].

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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

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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

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Rendering variable-shaped tiles using Voronoi diagrams

Grout generated after tile reduction. From left to right: 10%,20%, and 30%

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

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Control of the design the closer the point is to the edge, stronger

is the force

Without edge force Without edge force

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Result

A 3D mosaic lion sculpture

# of tiles : 20000tsmin : 0.1tstsmax : 3ts

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Result

Opus Palladium style# of tiles : 15000tsmin : 0.5tstsmax : 2ts

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Conclusion Although Voronoi polygons capture most of the s

hape variation present in real irregular mosaic tiles, they still look too regular for some designs.

opus palladium 3D mosaic