I need to find the nearest intersection of a given line with the objects (or physical bodies) on the scene.
Is there an easy way in Phaser 3 to do it? Or do I need to find intersection points with individual objects?
Related
What is the most efficient way to check, whether a line segment is (partly or totaly) outside of a polygon?
In the picture, the green line segements are allowed, whereas the red ones are forbidden.
Background information: This is for creating a Delaunay mesh.
One possible solution might be, to check, whether the line segment intersects any edge of the polygon or the middle point is outside the polygon. But is it really the most efficient way?
Given two 2D polygons, how do I calculate the shortest translation that brings the first inside the second?
Assume there is a solution (i.e. the first does in fact fit inside the second)
Prefer a simple algorithm over completeness of solution. For example if the algorithm is simplified by making assumptions about the shapes having a certain number of sides, being concave, etc. then make those assumptions.
I can imagine a brute force solution, where I first calculate which are the offending vertices that lie outside the initial polygon. I'd then iterate through these external vertices and find the closest edge to each. Then I'm stuck. Each distance from an external vertex to an edge creates a constraint (a "need to move"). I then need to solve this system of constraints to find the movement that fulfills them all without creating any new violations.
I'm not sure if this can be a general solution, but here is at least a point to start with:
We want to move the green polygon into the red polygon. We use several translations. Each translation is defined by a start point and an end point.
Step 1: Start point is the mid-point between the left-most vertex and the right-most vertex in green polygon. End point, same criterion with the red polygon:
Step 2: Start point is the mid-point between the top-most vertex and the low-most vertex. End point, same criterion with the red polygon:
Notice that setps 1 & 2 are kind of centering. This method with mid points is similar to use the bounding boxes. Other way would be using circumcircles, but they are hard to get.
Step 3: Find the vertex in red polygon closest to an edge in the green polygon. You will need to iterate over all of them. Find the line perpendicular to that edge:
Well, this is not perfect. Depending on the given polygons it's better to proceed the other way: closest vertex in green to edges in red. Choose the smallest distance.
Finally, move the green polygon along that line:
If this method doesn't work (I'm sure there are cases where it fails), then you can also move the inner polygon along a line (a red edge or a perpendicular) that solves the issue. And continue moving until no issues are found.
I am trying to offset a polygon using clipper, and I need all the vertices from the original polygon to be mirrored in the offset polygon. The trouble is that when you pass a polygon with vertices on a straight line, you get back a polygon without any vertices on straight lines, as I have attempted to illustrate in this diagram:
Polygon Offsetting vertices
Does anybody know of a way to modify the behaviour of clipper, or a different library that can do this for me?
Thanks
Internal routine FixupOutPolygon() removes such (usually redundant) vertices (in version 4.8). I see no option to disable it.
Read the license. If it permits to modify sources for yourself, then you could comment out it's call in the sources.
I am working on a 3d application and am currently looking for a way to project a line segment defined by two points in screen-space onto a three-dimensional polygonal mesh (in my case a triangle mesh). The goal is to find the intersection points in world-space of the line segment with the edges of the mesh.
I can only think of two ways to do this, but neither is ideal. The first is to sample the line segment (in screen-space) at small intervals and ray trace at those intervals to find the world-space coordinates where the ray hits the mesh, but this does not easily give me the intersection points of the line segment with the mesh edges.
The other way I can think of is to somehow back-project the mesh into screen-space, find the intersections there (in 2d) and then project those intersection points back to 3d. The problem with this is that the screen-space coordinate system may change between the selection of the first and second endpoints of the line segment (due to moving the camera).
If any of that was confusing, then here is an image that approximately shows what I'm trying to do (the white dots indicate the points that I want to find). However, in my case the yellow curve is simply a line segment.
[Yunjin Lee, et al. "Mesh scissoring with minima rule and part salience." 2005]
Any help is very much appreciated.
Here's my suggestion:
Project the screen line into world space (getting a plane in world space).
Intersect the plane with the triangles in the mesh, getting a set of edges.
Add the edges to a data structure that keeps only the parts of the edges that are closest to the camera plane (see the diagram below, in which the red line segments and their endpoints are the ones we want to keep). This is like building up an image via a Z-buffer, except that because we know that this set is piecewise linear, we don't have to rasterize it, we can just maintain a sorted list of endpoints.
I have a relational database where each entry is marked as a dot with latitude/longitude coordinates. I give the user the ability to mark an arbitrary polygon on a map, and want to return all entries that are within the polygonal shape.
What would be the best way to achieve this?
Also, it might be worth to point out that small errors are ok (ie. if there is an effective way to turn the polygon into a set of rectangles, then that is fine).
Use spatial extensions, most databases have this.
In MySql you can only use them with MyISAM tables which are not transactional.
http://dev.mysql.com/doc/refman/5.0/en/spatial-extensions.html
One way to quickly cut down on the number of points to consider is to compute the bounding rectangle for the polygon (i.e. just min-x, min-y, max-x, max-y of the points in the polygon), and then select for points within the bounding rectangle (i.e. where x is between min-x and max-x and same for y).
Of course not all these points are necessarily inside the polygon, but now you can hone it with code.
An old hack:
Count the number of times a line connecting <point far away> to <point in question> crosses any of the bounding segments of the polygon.
Even numbers mean the point is outside the polygon
Odd numbers mean it is inside the polygon