computational-geometry

What is the fastest way to find closest point to the given point in data array? For example, suppose I have an array A of 3D points (with coordinates x, y and z, as usual) and point (x_p, y_p, z_p). How do I find the closest point in A to (x_p, y_p, z_p)? As far as I know, slowest way to do it is to use linear search. Are there any better solutions? Addition of any an auxiliary data structure is possible. dkamins You may organize your points in an Octree . Then you only need to search a small subset. A Octree is a fairly simple data structure you can implement yourself (which would be a

I would like to determine a polygon and implement an algorithm which would check if a point is inside or outside the polygon. Does anyone know if there is any example available of any similar algorithm? Just have a look at the point-in-polygon (PIP) problem . Ian Boyd If i remember correctly, the algorithm is to draw a horizontal line through your test point. Count how many lines of of the polygon you intersect to reach your point. If the answer is odd, you're inside. If the answer is even, you're outside. Edit: Yeah, what he said ( Wikipedia ): kober C# code bool IsPointInPolygon(List<Loc>

I have some lines that are connected at various points. I want to draw the outline of these lines and I also want to deal with the extra lines at the connection points. I have seen two similar questions in this website: Here and here I have handled the normal cases by offsetting the Centerlines and then changing the start and end points of the lines. but I haven't been able to deal with special cases when the points are near each other. Unfortunately, my reputation is low I couldn't post images to explain this better. I'm coding in Visual Basic .net and I'm writing for Autocad, but any advice

I'm looking for an algorithm to detect if a circle intersects with any other circle in the same plane (given that there can be more than one circle in a plane). One method I have found is to do the separating axis test. It says: Two objects don't intersect if you can find a line that separates the two objects, i.e. a line such that all objects or points of an object are on different sides of the line. However, I don't know how to apply this method to my case. Can anybody help me? dasblinkenlight Two circles intersect if, and only if, the distance between their centers is between the sum and

How can I find the largest circle that can fit inside a concave polygon? A brute force algorithm is OK as long as it can handle polygons with ~50 vertices in real-time. cletus The key to solving this problem is first making an observation: the center of the largest circle that will fit inside an arbitrary polygon is the point that is: Inside the polygon; and Furthest from any point on the edges of the polygon. Why? Because every point on the edge of a circle is equidistant from that center. By definition, the largest circle will have the largest radius and will touch the polygon on at least