If you have a 2d display lets say a (100×100) pixels and you wanted to graph a 3d point(10, 10, 10). Where would it go? How would the 2d (x,y) be formed from the (x,y,z) value?

Question

If you have a 2d display lets say a (100×100) pixels and you wanted to graph a 3d point(10, 10, 10). Where would it go? How would the 2d (x,y) be formed from the (x,y,z) value?

In: Mathematics

Answer 1

Rule 2.

Better to r/asksciencediscussion about this.

Answer 2

You use something to indicate the position on Z-axis, just like relief is represented on maps: high mountain peaks are white, deep water is dark blue etc.

Answer 3

The simplest answer is to truncate; you ignore the z value completely and draw it as if everything is on a flat plane.

This loses information – you cannot definitely say the position of the object, as that information has been lost. There is no lossless way to map 3 dimensions onto 2*dimensions. Solutions like adding color actually add a dimension in the process.

Answer 4

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Answer 5

The term you want to search for is called “orthographic projection”, and because 3D objects cannot be perfectly captured in 2D, there are many different ways of making an orthographic projection, many of them using matrix mathematics to correlate the parts from the dimension that isn’t there into combinations of the other two dimensions.