What Are the Four Spatial Dimensions?



A spacial dimension refers to the number of coordinates required to locate a point in space. For example, a point on a Cartesian plane, a two-dimensional construct, requires only two coordinates to describe its location -- x and y values. A point in three-dimensional space requires x, y and z coordinates because space has the added dimension of height. Scientists have proposed additional dimensions, such as the fourth dimension, which requires four coordinates to describe the location of a point. First DimensionThe first dimension is length. One-dimensional objects have neither width nor height and are called lines. Mathematical lines are not the same as the lines you may be familiar with

Related to : What Are the Four Spatial Dimensions?
In C programming: Solving a PDE in two spatial dimensions numerically without using three loops
Hobbies, Games & Toys

I'm trying to write a program in C to solve a PDE in 2 spatial dimentions numerically: W(x,p,t). The acctual equasion involves too many signs that I don't know how to write here, so forgive me for not providing it, but it is fairly irrelevant anyways.


To solve the equation, from what I know - I need three loops:


For (t=0;t<t_max;t+=1)
For (x=0;x<x_max;x+=1)
For (p=0;p<p_max;p+=1)
( The numerical form of the equation, using a 2D array - W[x_max][p_max] )

This works fine for one dimension. - but problem is : in the above case the program simply runs in a million years! - I am serio

How to perform spatial partitioning in n-dimensions?
Hobbies, Games & Toys

I'm trying to design an implementation of Vector Quantization as a c++ template class that can handle different types and dimensions of vectors (e.g. 16 dimension vectors of bytes, or 4d vectors of doubles, etc).


I've been reading up on the algorithms, and I understand most of it:


here and here


I want to implement the Linde-Buzo-Gray (LBG) Algorithm, but I'm having difficulty figuring out the general algorithm for partitioning the clusters. I think I need to define a plane (hyperplane?) that splits the vectors in a cluster so there is an equal number on each side of the plane.


[edit to add more info]
Th

Querying distance on 2 dimensions in a 3 dimension spatial data set
Hobbies, Games & Toys

I have a case requirement where I need to find the nearest N suppliers who supply specific product types. The types in an int range of 0..1048575, which represents an hierarchy. Any supplier could have multiple points since they could supply multiple product types.


I could store the long & lat in PostGIS and the types in an indexed int array column, and query against both with a limit of N. However, I don't believe this will be efficient as I am not sure that PostgreSQL will use both indexes.


Another idea I have is to store the types in a third "vertical" dimension. This would create stacked "vertical" shape segments at the long & lat shape

Formula for determining dimensions of interior divs based on dimensions of exterior div?
Hobbies, Games & Toys

Let's say I have a container div that is 765px wide by 530px high.


I want to dynamically fill as much of that div with 30 smaller divs. Since the container div is a rectangle, the filling divs should be a rectangle as well. Basically, I don't want squares, I want to fill the space.


What is the formula?


Thanks!


Spatial agent models / spatial emergent behaviour [on hold]
Hobbies, Games & Toys
I am trying to use R to model grids of agents that change their decisions based on the decisions of other agents in their direct proximity. Basically - each agent looks to the other agents around him on the grid, and might change its behaviour based on the the actions around him. I have included some sample dinky-toy code per below to show (one iteration) of such dynamic.I am wondering whether a) there is an elegant manner to address the boundaries of the grid (currently the t+1, i+1 code does
Conversion of MySQL spatial query with intermediate tables to PostGre spatial query
Hobbies, Games & Toys
Hi All,
I have the following query which was based on a working query in MySQL:
(dont be afraid of the size of the query you see below, later on I will concentrate on part of this query)
SELECT count(*) FROM ((SELECT * FROM tileinfo where julianDay BETWEEN DATE2JDAY((2003-03-01 00:00:00),0) AND DATE2JDAY((2003-03-01 23:59:59 ),0) AND intersects(tile, geomFromText(POLYGON((-10.84 35.8,18.14 35.8,18.14 59.41,-10.84 59.41,-10.84 35.8)),4326))) tic0 LEFT JOIN (tileinfo_meta__2p left join meta__2p on tileinfo_meta__2p.fk_name = meta__2p.pk_name) on tic0.pk_tileinfo = tileinfo_meta__2p.fk_tileinfo ),
((SELECT * FROM tileinfo where julianDay BETWEEN
R Create a Spatial Bubble Plot That Overlays A basemap of the US and other spatial layers as needed
Hobbies, Games & Toys

I'm trying to produce a nice bubble plot overlaid on top of a basemap of the US (i could import a shapefile if that is preferred but i've been using the R basemaps.

library(ggplot2,sp,raster,maps,mapdata,maptools,ggmap,rgeos)
myData =
data.frame(name=c("Florida","Colorado","california","Harvard","Yellowstone"),
                lat=c(28.1,39,37,42,44.6), 
                long=c(-81.6,-105.5,-120,-71,-110),
                pop=c(280,156,128,118,202))

Using this code below, that i adapted from another stack overflow post (Create bubble plot in R using satellite map), i am able to overlay a bubble plot on a map of the US. However this renders very slowly, the extent is too tight, it is bounded in a box, i'm not able to add other layers to the plot from what i can tell, and the base map is thick and not visually clean.

xy <- myData[,c("long", "lat")]
nl <- getData('GADM', country="USA", level=1) #raster data, format
SpatialPolygonsDataFrame
nl <- gSimiplify(nl, tol=0.01, topologyPreserve=TRUE)
# coercing the polygon outlines to a SpatialLines object
spl <- list("sp.lines", as(nl, "SpatialLines"))
SPDF <- SpatialPointsDataFrame(coords=xy, data=myData)
coordinates(myData) <- c("lat", "long")
projection(SPDF)<- "+proj=longlat +ellps=WGS84 +datum=WGS84
+no_defs +towgs84=0,0,0"
coordinates(SPDF)[1:5,] #retrieves spatial coordinates form the
dataframe
bubble(SPDF, "pop", sp.layout=spl, main="This is It!")

I can draw a nice basemap using this code. I add points to the map but they are not sized by the pop column in my data. And i can add additional layers to this map. But can i control the size of the points and the symbol itself like i can using a bubble plot?

map(database= "world", ylim=c(45,90), 
    xlim=c(-160,-50), col="grey80", 
    fill=TRUE, projection="gilbert", 
    orientation= c(90,0,225))

coord <- mapproject(myData$lon, myData$lat,
proj="gilbert",orientation=c(90, 0, 225))
points(coord, pch=20, cex=1.2, col="red") 

Can anyone please guide me towards the best way to plot a bubble map in R where i can adjust the fill and outline of the symbols in the bubble map, And i can add a clean basemap, that i can a) control the colors of (fill and lines) and b) add additional layers to (for instance another shapefile layer).

Thank you in advance for any advice.



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