I read some about quadtrees, and I am trying to take advantage of them for pathfinding. To this end, I am trying to use a quadtree to create a connected graph, where each "minimum rectangle" (a childless node) is directly connected to its adjacent minimum rectangles. To illustrate... if you take a look at the bottom-right rectangle in http://en.wikipedia.org/wiki/File:Point_quadtree.svg, that rectangle is a childless node in the tree, and it should be directly connected to the three rectangles surrounding it, which are also childless nodes.
Creating the quadtree is pretty easy, but I'm not sure how to detect connections with it. Can anyone offer me some insight?
Thanks in advance!
The bottom right rectangle is just a child of the adjacent 3 rectangle. Look from above at it like a pyramid when you are standing at the top and look how the quadtree divide the space recursivley into 4 directions. here is a better explanation http://blog.notdot.net/2009/11/Damn-Cool-Algorithms-Spatial-indexing-with-Quadtrees-and-Hilbert-Curves
Related
I'm trying to work out which tiles a rectangle overlaps.
Right now I'm just taking the mix/max bounds of the rect, and iterating through the grid tiles that are within those bounds. And for each tile I check whether the tile rectangle intersects with the other rectangle. This isn't very performant as I still have to iterate a lot of tiles and do a lot of intersection checks.
I'm wondering if theres a more performant or mathematical way to achieve this.
Sort rectangle vertices by Y-coordinate and treat horizontal bands between vertice Y-positions separately (it is possible to get 1, 2 or 3 bands).
For every Y-interval you have left and right sides, walk through them using Bresenham algorithm (for pixels) or Amanatides-Woo algorithm (for cells/voxels).
For every horizontal you have the leftmost and the rightmost cell, fill also all cells between them.
Also look for triangle rasterization algorithms for more ideas.
What options should I use for making my graph looking like an Elipse ? I was messing with the hierarchical option under the layout module, but I've not gotten nowhere near my desired shape.
My graph is left to right, left node group connects to middle one, and middle one connects to the right one. It can be perceived as this image below.
Can someone point me in the right direction ? Thanks for your expertise
As for the elliptic shape around the nodes and edges, you can either set a background image to your graph area or create a node of large size (but this way you may have troubles with node repulsion, though). Unfortunately, there's no way to make sure that all the nodes will always be inside the ellipse (unless you access the vis' canvas and deal with it on low level or do some other hackery).
Also AFAIK it is impossible to create those wavy edges, but for those rounded ones you may want to use repulsion physics instead of barnesHut. See also physicsConfiguration example.
This seems to be a rather asked question - (hear me out first! :)
I've created a polygon with perlin noise, and it looks like this:
I need to generate a texture from this array of points. (I'm using Monogame/XNA, but I assume this question is somewhat agnostic).
Anyway, researching this problem tells me that many people use raycasting to determine how many times a line crosses over the polygon shape (If once, it's inside. twice or zero times, it's outside). This makes sense, but I wonder if there is a better way, given that I have all of the points.
Doing a small raycast for every pixel I want to fill in seems excessive - is this the only/best way?
If I have a small 500px square image I need to fill in, I'll need to do a raycast for 250,000 individual pixels, which seems like an awful lot.
If you want to do this for every pixel, you can use a sweeping line:
Start from the topmost coordinate and examine a horizontal ray from left to right. Calculate all intersections with the polygon and sort them by their x-coordinate. Then iterate all pixels on the line and remember if you are in or out. Whenever you encounter an intersection, switch to the other side. If some pixel is in, set the texture. If not, ignore it. Do this from top to bottom for every possible horizontal line.
The intersection calculation could be enhanced in several ways. E.g. by using an acceleration data structure like a grid, quadtree, etc. or by examining the intersecting or touching edges of the polygon before. Then, when you sweep the line, you will already know, which edges will cause an intersection.
I am trying to write an application to draw schematic diagrams which contain rectangles, lines and circles. Now I want to add another functionality to drag a rectangle to different position. The problem I am facing is to detect whether I have clicked within a rectangle or not. I know there is a function like Rectangle.Contains(Point). To use such method I need to use a for loop to check against each rectangle. If I have a large number of rectangles present, then its not wise to use this method. Is there any other way to do this task.
You need a computer graphics textbook, this and similar problems are often discussed.
If memory serves me, make sure the point is below the top edge of the rectangle, above the bottom edge, left of the right edge and right of the left edge.
Regarding testing a bunch of rectangles in a loop. Consider having a circle that each rectangle fits in, a bounding circle. First test to see if the point is farther from the origin of the circle than the radius of the circle. If so there is no need to test the rectangle, its a miss. OK, that was a very theoretical answer. In reality calculating the distance from the point to the origin can be a very expensive calculation, it involves a square root, it may be faster to do the four comparisons of the point in rectangle check. Again if memory servers me, we don't really care what the distance from the origin is only if it is greater than the radius. So only partially perform the distance calculation, omitting the final square root, and compare against the square of the radius. Of course you still need to experiment and profile to make sure this bounding circle check is faster than just doing the regular point in rectangle check and you need to make sure you will have sufficient misses to offset the hits where you will end up doing both the bounding circle and rectangle checks.
You need to use a spatial index to find quickly in which rectangle the mouse is. I suggest a R-tree, here is the theorical part:
http://en.wikipedia.org/wiki/R-tree
And the c#,implementation:
http://sourceforge.net/projects/cspatialindexrt/
Create an rtee, add your rectangles then call the rtree.nearest method with the mouse coordinate to know the rectangles containing the mouse cursor. You can play with the distance parameter.
Hope it helps,
Anben Panglose.
I would go about dividing the display region into a quadrant.
Then place the rectangles into top-left, top-right, bottom-left, bottom-right grids.
Placing them means, creating a list for every quadrant and placing the rectangles in it.
Once the point is clicked, determine which quarter it belongs to and search in those rectangles only. This approach reduces your linear search by 4 times.
Remember that you need to also take care of overlapping where the point can belong to many rectangles. Here the z-order of your rectangles matter. So while the list is maintained for a quadrant, it should be sorted with it's z-order as a key.
Hope this helps.
May be something like this?
public bool isRectangelContainPoint(RectangleF rec, PointF pt)
{
if (pt.X >= rec.Left && pt.X <= rec.Right && pt.Y <= rec.Bottom && pt.Y >= rec.Top)
return true;
else
return false;
}
I'm trying to create a graph using Graphviz (complied with neato), and I would like to place nodes in specific locations. For this, I'm specifying exact edge lengths for all edges. However, I don't want all edges to be visible in the final image.
Do you know of any way to hide edges? I should mention that I tried coloring the edges white, but what happens is that I get white lines painted over the graph nodes - it's not very aesthetic...
It can be done using
nodeA -> nodeB [style=invis]
I found out that another way to go is to define:
outputorder="edgesfirst"
for the graph.