So basically what I'm trying to do is generate a circle completely out of square tiles in Unity and I am trying to think about the best way mathematically to generate it.
In the end, I want it to look something like:
https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcTHh7I_BURo5qMI73YLZVG6PO4WeFtbT--QL_9qOJovpNaWemar
In this image, the tiles are more rectangular and not all sides are equal, but it gets the point across.
Does anyone know of any mathematical formulas or anything that could be helpful in doing this? I don't necessarily need straight answers (unless you have them :D), but anything to help me along would be appreciated!
Thanks!
Take the starting point (center) and start drawing your first square in the starting direction. Now turn the direction with the Golden ratio: 1.618...
Keep turning this much for every consecutive square you are drawing, every time increasing the distance from the center a little bit.
Apparently sunflowers also grow following this pattern according to this video!
Related
I have actually the following map (isometric projection), and I can move/zoom/rotate without problem with matrix transformations (SpriteBatch): picture.
And I wanted to know if it was possible (if so, how), to get the following result, without referring to 3D: picture.
All suggestions are welcome. Thank you in advance. :)
Its going to be a huge pain in the ass, especially but I think it is at least possible if you don't change the viewing angle.
Some ideas:
Make each tile its own little image unit.
The more far back the tile is from the camera, lower its layer priority when you draw it so that it gets blocked by tiles in front of it. Also you will have to figure out an algorithm that correctly sizes the tiles based on their distance. This algorithm will have to be more and more precise the closer you want to get the tiles, but there should be some mathematical/geometric formula that can do it automatically.
You quite literally CANNOT rotate the camera at all, unless you want to have separate sprites for every single angle for every single tile.
So I am working on a Risk type game in XNA/C#. I have a map, similar this one, and I need to be able to detect mouseovers on each territory (number). If these areas were squares, it would be easy, as they could each be represented by a rectangle. However, they are different size polygons. Is there a polygon shape that behaves similar to a square? If there isn't, how would I go about doing this?
I sugest this:attach color to each number, recreate your picture in these colors: every shape will be in its particular color. Dont draw it onscreen, use it only as reference map. And when the user clicks or moves mouse over your original map, you just simply project mouse coordinates into the color map, check the color of pixel laying under the mouse and because you have each color associated to number of territory...
This is not c# specific (as I've never written anything in the language, so no idea of what apis there are), though there are 2 algorithms that come to mind for detecting if a point is inside a polygon (which can be used to detect if a mouse point is over another polygon/map shape).
One is based on raycasting, where you cast a ray in 1 direction from the (mouse) point to "infinity" (edge of the board in this case) and count the number of times it crosses the polygon's edges. If it is odd, then the point is inside the polygon, if it is even, then the point is outside of the polygon.
A wiki link to it: http://en.wikipedia.org/wiki/Point_in_polygon#Ray_casting_algorithm
The other algorithm that comes to mind works only for triangles I think but it can be more simple to implement I think (taking a quick glance at your shapes, I think they can easily be broken down into triangles and some are already triangles). It is to do with checking if the point is on the same (internal) "side" of all the edges in the triangle. To find out what "side" a point is on vs an edge, you'd take create 2 vectors, the first vector would be the edge itself (made up of 2 points) and the other vector would be the first point of that edge to the input point, then calculate the cross product of those 2 vectors. The result will be negative or positive, which can be used to determine the "direction".
A link to it: http://www.blackpawn.com/texts/pointinpoly/default.html
(On that page is another algorithm that can also work for triangles)
Hit testing on a polygon is not so difficult to do in real time. You could use a KD-Tree for optimisation if the map is huge. Otherwise find a simple Contains method for a polygon and use that. I have one on another computer. Let me know if you'd like it.
As everyone knows, satellites around the earth don't go in a perfect circle. They are more an elliptical orbit.
I'm trying to represent this using OpenGL to draw an orbit around the earth. Currently, I draw a dashed-line composed of 360 markers which makes a series of dashes around the globe in a nice perfect circle.
If I have the Orbital inclination, Perigee and Apogee what would be the way to calculate this circle? I'm trying to find a formula or white paper or something to get me in the right direction....
What this is crazy, of course they are perfect orbits. No but seriously sounds more like a need Physics formua. Try..
http://scienceworld.wolfram.com/physics/Orbit.html
or
http://physics.info/orbital-mechanics-1/
Don't have really any experience here, but if you plan to actually track satellites you will want to use the Keplerian elements ( http://en.wikipedia.org/wiki/Orbital_elements#Keplerian_elements , http://en.wikipedia.org/wiki/Orbital_elements#Orbit_prediction) which get published for satellites. Note that real satellites have perturbation in their orbits so the Keplerian elements for a satellite are regularly updated. If you just need something that "looks" like satellite orbits then the idealized ellipses form the other answer will be fine.
I have a following problem. A large rectangle contains smaller non-intersecting rectangles (The black rectangles in the picture below) and I need to find an algorithm to fill remaining free area with non-intersecting rectangles(red ones in the picture below). Speed is not an issue for the algorithm. Also if someone would have an example source code of the algorithm I would really appreciate that.
Edit. Small clarification I need to get the coordinates of the red rectangles not to draw them. I am also working with point data not images.
http://koti.mbnet.fi/niempi2/Squares.gif
Like most bin-packing problems this one looks like an NP-hard problem to me. With 2 rectangles, there are 8! (= 40320) possible arrangements you need to consider. Three rectangles produces 12! possibilities, a cool 480 million.
You'll need an heuristic to make this computable. Beyond favoring the outer edges of the rectangles closest to the bounding rectangle, I don't see a good one. You'd need tighter requirements on the resulting rectangles you accept, the number of them isn't going to help. Glad this is not my problem :)
Although there are multiple possible solutions, I think you can get to one fairly easily.
I would work in increasing values along one axis. By scanning all rectangles and ordering their edge's appearances along that axis, you could walk through them and create rectangles as you go. Each time you hit a new pair of corners, you can compare with the rectangles you currently have 'open' and determine what to do (close them, start new, divide, etc).
That statement isn't a complete solution, but I think it gets you from a complex solution to a simple one. It also doesn't seem to be NP complete in terms of performance. You might even be able to get O(n) perf.
An interesting problem. Let us know how you get on.
Look at the Region class.
We want a c# solution to correct the scanned image because it is rotated. To solve this problem we must detect the rotation angle first and then rotate the image. This was our first thought for our problem. But then we thought image warping would be more accurate as I think it would make the scanned image like our template. Then we can process it as we know all the coordinates of our template... I searched for a free SDK or a free solution in c#. Helping me in this will be great as it is the last task in our work. Really, thanks for all.
We used the PrimeOCR product to do this. It's not free, but we couldn't find a free program that was comparable.
So, the hard part is to detect the angle of the page.
If you have full control over the template, the simplest way to do this is probably to come up with an easily-detectable symbol (e.g. a solid black circle) and stick 3 of them on the template. Then, detect them (just look for big blocks of pixels with high saturation, in the case of a solid black circle).
So, you'll then have 3 sets of coordinates. If you have a top circle, a left circle, and a right circle with all 3 circles at difference distances from one another, detecting which circle is the top circle should be pretty easy.
Then just call a rotation function. This part is easy and has been done before (e.g. http://www.switchonthecode.com/tutorials/csharp-tutorial-image-editing-rotate ).
Edit:
I suggested a circle because it's easier to find the center, but a rectangle should work, too.
To be more explicit about how to actually locate the rectangles/circles, take the average Brightness value of every a × a group of pixels. If that value is greater than b, then that a × a group of pixels is part of a rectangle. a and b are varables you'll want to come up with yourself.
Use flood-fill (or, more precisely, Connected Component Labeling) group the resulting pixels together. The end result should give you your rectangles.