Can a point view another point around an obstructing point?

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In summary, triangulating fixed points in space with weighted pressure values is necessary in order to create a contour map. However, existing methods such as the AngleBetween function or Delaunay Triangulation may not be suitable for this purpose due to issues with openGL rendering and the need for a more specific method for contour mapping. Suggestions for researching surveying software and utilizing manual methods for contour mapping may be more effective in solving this problem.
  • #1
wiyosaya
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I am not sure that this is the correct forum for this question.

I have multiple sets of 3, 3D (x, y, z) points in space. They are fixed points in space, and I cannot move them. Each point is weighted with a pressure value. I need to be able to determine if point 1 can view point 3 given that point 2 might prevent point 1 from viewing point 3.

What I am attempting to do is write a triangulation algorithm, only I have to create the triangles between points that are fixed. I cannot move them. The result should look as close as possible to a contour map.

If I look at the system of points as if it were flattened, point 3 might be either too far left or right of point 2 such that drawing a triangle edge either too far left or too far right of point 2 will overlap an edge from an existing triangle, and that causes an incorrect triangulation.

For example, I am using C#, and the Vector3D class, and I figured that I might be able to use the "AngleBetween" function to calculate the angles between point 1 and point 3, and point 1 and point 2 and then determine if the angles are such that point if the angle between point 3 is greater than the angle between point 2, then point 1 will not be able to triangulate with point 3 properly. However, the angle calculated by the AngleBetween function does not give angles that consistently indicate the viewability of point 3 from point 1 given that point 2 might be obstructing. I assume that the AngleBetween function is not calculating the angle that would allow me to solve this problem.

I have had a course in linear algebra, however, I do not use it regularly, so I am having difficulty in determining what to do to make the program work as I would like it to.

Does anyone have an idea how this might be solved? I am really looking for suggestions as to how to set up this problem mathematically as opposed to how to program it in C#, or any language, for that matter. The mathematics is what I need help with, not the programming language.

Thanks in advance.
 
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  • #2
Maybe you want to calculate the angle between the vectors (point2 - point1) and (point3 - point1) and check if it is close to 0, instead of calculating two different angles.

Or instead of trying to invent your own method, see http://en.wikipedia.org/wiki/Delaunay_triangulation
 
  • #3
Thanks for the suggestion. I'll have to give that a try to see if it works.

I looked at Delaunay Triangulation, however, there are complications that are a result of the default way that openGL renders its triangles. If I were interested only in the distance between points, Delaunay would work great; however, what I am really interested in is producing a contour map of the pressures at each point. If I triangulate simply based on distance, the default openGL rendering generates artifacts. The best openGL rendering follows a path of the least differential pressure between points. In essence, it ends up more of a routing problem, like Dykstra - http://en.wikipedia.org/wiki/Dijkstra's_algorithm
 
  • #4
If you are trying to make a contour map, I suggest you research algorithms used by software for surveyors. Surveyors often need to draw contour maps from irregularly spaced measurements.

I haven't researched surveying software recently. I've had experience drawing contour maps by hand. In writing some contour drawing software for a grid years ago, I do recall that not all contour drawing programs are based on finding the "even" elevations on the sides of a triangle. Some use a method closed to the manual method, which involves picking a given contour and "following" it across the map.
 
  • #5
...and something to keep in mind is that drawing contours is a problem that need not have a unique answer. For example if you have found a point where the elevation (or pressure) is 96 and you want to see how the 96 contour continues, you look for a point in the vicinity that has an elevation of 96 or greater and another point that has an elevation of 96 or less. If you have fairly smooth terrain there will be only one such pair of points. However, in very rough terrain there may be several pairs of points. The contour you are drawing may not go directly from where you are to any point you could interpolate. It might even turn around. For example if you are interpolating to find the 96 contour near the top of a ridge whose top is, say, 96.3 and your measurements are not finely spaced enough then you won't be able to determine when the 96 contour should cross a little valley in the ridge and proceed on the other side.
 

1. Can a point located behind an obstructing point be seen by another point?

Yes, it is possible for a point to view another point located behind an obstructing point. However, the obstructing point may partially block the view and distort the perspective.

2. How does the distance between the points affect their ability to view each other?

The distance between the points does not necessarily affect their ability to view each other. However, the closer the points are to each other, the more likely they are to have an unobstructed view.

3. What factors determine if a point can view another point around an obstructing point?

The main factors that determine if a point can view another point around an obstructing point are the distance between the points, the height of the obstructing point, and the angle of the view from both points.

4. Can the shape or size of the obstructing point impact the view between two points?

Yes, the shape and size of the obstructing point can have an impact on the view between two points. For example, a tall and wide object may completely block the view, while a smaller and thinner object may only partially obstruct the view.

5. Is it possible for two points to have a clear view of each other even if there are multiple obstructing points?

Yes, it is possible for two points to have a clear view of each other even if there are multiple obstructing points. This can occur if the obstructing points are spaced out in a way that allows for an unobstructed line of sight between the two points.

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