Date post: | 30-Dec-2015 |
Category: |
Documents |
Upload: | winfred-sutton |
View: | 228 times |
Download: | 2 times |
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
4
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
5
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
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 randomly distributed 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 Fij between points i and j is given according to the equation :
10
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
11
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].
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%
16
Control of the design the closer the point is to the edge, stronger
is the force
Without edge force Without edge force