What Are the Four Spatial Dimensions?


Mark Tran
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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?
What Are the Four Spatial Dimensions?
Hobbies, Games & Toys

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
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

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

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



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