How to build a complete mesh from an incomplete one?

Question

Mathematics

Hello.
The task is to draw isolines on the map, according to known points. One point stores the data of longitude, latitude and number.
The algorithms I found for C# conrec and contours work well, but they require a completely filled uniform grid (a two-dimensional array of values, where the array indexes are considered to be its coordinates).
The problem is that my data is not evenly distributed, and I need to build a uniform grid on it. I've been struggling with this for a week now and I can't overcome it (knowledge in mathematics fails).
I also looked in the direction of triangulation, but everything is even.
Tell me, how can I draw isolines on an uneven grid, or how to go from an uneven grid to a uniform one?

Answer 1

I think it's better to look again in the direction of triangulation.
After the Delaunay triangulation of the initial points is built, then for any triangle and any height level, the intersection of the isoline with the triangle will be either empty, or a point, or a segment. The coordinates of the ends of the segment are determined by linear interpolation. And it will be possible to continue the isoline simply by walking along the triangles.
The problem arises when the isoline hits the vertex. Theoretically, there can be more than two paths from a vertex - if it turns out to be a saddle point. To avoid this, it is enough to look at all the data at the beginning, and if a "round" number comes across, change it slightly.

Answer 2

I also didn’t quite change what an uneven grid is, can you just take the average of the nearest values ​​\u200b\u200bin the point where there is no value? Well, or somehow interpolate ..