# What is the name for n dimensional data sampled at regular intervals in n-1 dimensions?

I'm looking for a word to describe n-dimensional data sampled at regular intervals in n-1 dimensions. For example, a 3d dataset would have data sampled at regular intervals on a 2d grid. A 4d dataset would have points sampled at regular intervals on a 3d grid.

I would like to use a word like "volumetric data" since it "fills" a space (though I don't believe "dense" would be the correct word to use here, and I believe "volumetric" implies just 3 dimensional data).

Is there a word for this type of data?

Thanks

• Can you clarify what do you mean by "sampled at regular intervals on a 2d grid"? Like, a 2d dataset would be sampled at points a a single line? – Itamar Mushkin Nov 3 '19 at 14:31
• Sorry, yes. What I mean by "sampled at regular intervals" is that for a data set of dimension n, we have n-1 intervals. Then each sample is taken at each "step" along these intervals. That is, (provided the point is within the bounds of our sampling space), each data point is of the form (S1 * I1, S2 * I2, ... , Sn-1 * In-1, value at that point) for Sn an integer, In the interval along that axis. – QuestionAsker Nov 3 '19 at 14:50
• @QuestionAskercould To me, this still sounds unclear (you suddenly speak about n-1 intervals instead of dimensions). Could you give a real-life example? – Sextus Empiricus Nov 3 '19 at 14:57
• I'll try using a concrete dimensions rather than "n". Let's imagine we're building a 3d data set in which we "sample at regular intervals" on the 2d plane. We choose i1 and i2 to be the intervals we sample at. Then each data point in our 3d dataset is of the form (a * i1, b * i2, (value of data sampled at (a * i1, b * i2)) ) for a and b integers. So the interval i1 tells us the size of the jumps we take along the x axis and i2 tells us the size of the jumps we take along the y axis. Is that any clearer? – QuestionAsker Nov 3 '19 at 15:16
• Most people would characterize this as a regularly sampled $n-1$-dimensional dataset. Google "lattice data" geostatistics for more. Do those hits match what you have in mind? – whuber Nov 3 '19 at 18:30

What this question appears to be asking is the name for lattice data for $$Y=f(x_1,x_2,x_3,...,x_{n-1})$$, where $$Y$$ is the $$n^{\text{th}}$$ dimension. As @whuber says, this is just "lattice data" for 2D it would be just equal interval data, for 3D it would be a 2D lattice, for 4D a 3D lattice etc.