Pertenece a: RePEc: Research Papers in Economics
Descripción: This Paper develops a methodology to compute transport costs at low infra-country geographical levels. This simultaneously accounts for the real network infrastructure, a distance cost (fuel, repair, tolls), and a time opportunity cost (wages, insurance and general charges, vehicle use). When considering levels, geodesic distance, real distance, and real time are shown to be good substitutes to the measure we develop. By contrast, variations across time are poorly captured by these simpler transport cost measures. Besides, the large decrease in transport costs that occurred in France between 1978 and 1998 - namely 38:2% - is shown to be mainly due to technology improvements and deregulation. New transport infrastructures, which contribute only marginally to this decline, shape the spatial pattern of accessibility improvements, however.Autor(es): Combes, Pierre - Philippe - Lafourcade, Miren -
http://www.alecjacobson.com/weblog/?tag=white-noise&wpmp_switcher=desktop
Posts Tagged ‘white noise’
A very simple method for approximate blue noise sampling on a triangle mesh
Saturday, October 25th, 2014
This morning I was looking over the recent methods for generating blue-noise random samples on an arbitrary surface. Many of them involve dart throwing with complicated rejection schemes to achieve a Poisson-disk sampling (e.g. “Feature-preserving direct blue noise sampling for surface meshes” [Peyrot et al. 2014]), some involve hefty optimization procedures (e.g. “Blue Noise through Optimal Transport” [de Goes et al. 12]). A lot of the effort is spent trying to preserve features. I wasn’t particularly interested in this at the moment, and I just wanted something simple I could quickly code up and play with.
My idea stemmed from the observation that if my surface is a sphere, and I have a enough samples then the distance between samples will approximate their distance in Euclidean space. So an algorithm for Poisson-disk sampling the sphere looks like:
This works quite well:
on the left is the original “white noise” uniform sampling, and on the right I show the iterations of this algorithm converging to a Poisson-disk-like sampling.
Now, for an arbitrary surface my original assumption is no longer true. There may be parts very close to each other in R3 but very far away in terms of the geodesic distance on the surface.
However, there exist a family of methods that lift a surface to an (usually higher dimensional) embedding Rn so that Euclidean distance in Rn approximates geodesic distance (e.g. “Biharmonic Distance” [Lipman et al. 2010]). Using this I can alter my method only slightly to work with arbitrary surfaces:
It’s working quite well:
again, on the left is the original “white noise” uniform sampling, and on the right I show the iterations of this algorithm converging to a Poisson-disk-like sampling.
I’ve put up matlab code for this in the
My idea stemmed from the observation that if my surface is a sphere, and I have a enough samples then the distance between samples will approximate their distance in Euclidean space. So an algorithm for Poisson-disk sampling the sphere looks like:
- Generate n uniformly random samples on the sphere
- For each sample i find distance dij to closest other sample j, in usual R3 sense
- Repeat steps 1 and 2 recursively for all samples i such that i < j and dij > re.
This works quite well:
on the left is the original “white noise” uniform sampling, and on the right I show the iterations of this algorithm converging to a Poisson-disk-like sampling.
Now, for an arbitrary surface my original assumption is no longer true. There may be parts very close to each other in R3 but very far away in terms of the geodesic distance on the surface.
However, there exist a family of methods that lift a surface to an (usually higher dimensional) embedding Rn so that Euclidean distance in Rn approximates geodesic distance (e.g. “Biharmonic Distance” [Lipman et al. 2010]). Using this I can alter my method only slightly to work with arbitrary surfaces:
- Lift surface to Rn using “Biharmonic embedding”
- Generate n uniformly random samples on the original surface (the one still in R3)
- For each sample i find distance dij to closest other sample j, after lifting to Rn
- Repeat steps 2 and 3 recursively for all samples i such that i < j and dij > re,
It’s working quite well:
again, on the left is the original “white noise” uniform sampling, and on the right I show the iterations of this algorithm converging to a Poisson-disk-like sampling.
I’ve put up matlab code for this in the
mesh/random_points_on_mesh.m in my gptoolbox on git. Here’s a use example:[V,F] = load_mesh('/usr/local/igl/libigl/examples/shared/cheburashka.off');
n = 3000;
Pwhite = random_points_on_mesh(V,F,n);
Pblue = random_points_on_mesh(V,F,n,'Color','blue');
t = tsurf([F;size(V,1)+F],[V;V(:,1)+1.1*(max(V(:,1))-min(V(:,1))) V(:,2:3)],'FaceColor','w','EdgeColor','none','FaceAlpha',0.8);
apply_ambient_occlusion(t);
hold on;
scatter3(Pblue(:,1),Pblue(:,2),Pblue(:,3));
scatter3(Pwhite(:,1)+1.1*(max(V(:,1))-min(V(:,1))),Pwhite(:,2),Pwhite(:,3));
hold off;
axis equal;
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