I have a file that contains many identical surfaces overlapped. How could I check if two surfaces are identical and overlapped and delete one of them using VBA functions?
As gdir said there is no direct way.
However you can compare some properties which you can measure such as surface area, length of boundary, number of verticies on the boundary, various extremum points, center of gravity, moments of inertia, etc.
Although these properties don't mathematically prove or disprove that two surfaces are the identical/different in most cases some combination of them will suffice.
Related
I am trying to create an algorithm that can take a set of objects and organize them in a given area such that a box bounding all of the shapes is optimized (either by area used, or by maximizing the span along one of the dimensions, etc.). All of the shapes are closed and bounded.
The purpose of this is to try and minimize material waste from using a laser cutter. The shapes are generated in CAD and can read into this algorithm. The algorithm will then take arguments for the working area (effective laser cutting area) as well as the minimum separation between any two objects, then attempt to organize the objects within the specified dimensions while trying to minimize the area usage. Alternatively, the algorithm can also try to maximize the object locations along one axis while minimizing the span along the other dimension. This would be akin to cutting off a smaller workpiece to cut from.
Ideally, the algorithm would be able to make translations AND rotations, but rotations aren't necessary.
For example, this Picture depicts the required transformation.
It should work with an arbitrary, but small (<25) number of objects.
Lastly, I don't expect anyone to solve this for me, but I would appreciate help toward either finding an algorithm that can do this, or developing my own. Thank you.
I dont know to what extent you want to create said algorithm or how you want to implement it, But i know of a program called OptiNest that can do what you ask. It organizes geometric shapes to optimize the layout and minimize waste on a plane, i think in an autocad format.
I have SVG abirtrary paths which i need to pack as efficiently as possible within a given rectangle(as less waste of space as possible). After some research i found the bin packing algorithms which seems to be dealing with boxes and not curved random shapes(my SVG shapes are quite complex and include beziers etc.).
AFAIK, there is no deterministic algorithm for actually packing abstract shapes.
I wish to be proven wrong here which would be ideal(having a mathematical deterministic method for packing them). In case I am right however and there is not, what would be the best approach to this problem
The subject name is Shape Nesting, Nesting Problem or Nesting Process.
In Shape Nesting there is no single/uniform algorithm or mathematical method for nesting shapes and getting the least space waste possible.
The 1st method is the packing algorithm(creates an imaginary bounding
box for each shape and uses a rectangular 2D algorithm to pack the
bounding boxes).
This method is fast but the least efficient in regards to space
waste.
The 2nd method is some kind of incremental rotation. The algorithm
rotates the shape at incremental steps and checks if it fits in the
space. This is better than the packing method in regards to space
waste but it is painstakingly slow,
What are some other classroom examples for achieving a solution to this problem?
[Edit1] new answer
as mentioned before bin-packing is NP complete (hard) so forget about algebraic solution
known approaches are:
generate and test
either you test all possibility of the problem and remember the best solution or incrementally add items (not all at once) one by one with the same way. It is basically what you are doing now without proper heuristic is unusably slow. But has the best space efficiency (the first one is much better but much slower) O(N!)
take advantage of sorting items by size
something like this it is much faster almost O(N.log(N)) (according to used sorting algorithm). Space efficiency strongly depends on the items size range and count. For rectangular shapes is this the best approach (fastest and usable even for N>1000). For complex shapes is this not a good way but look at it anyway maybe you get some idea ...
use of Neural network
This is extremly vague approach without any warrant of solution but possible best space efficiency/runtime ratio
I think there could be some field approach out there
I sow a few for generating graph layouts. All items create fields (booth attractive and repulsive) so they are moving to semi-stable state.
At first all items are at random locations
When the movement stop remember best solution and shake all items a little or randomize their position again.
Cycle this few times
This approach is much faster then genere and test and can provide very close solution to it but it can hang in local min/max or oscillate if the fields are not optimally choosed. For example all items can have constant attractive force to each other and repulsive force getting stronger only when the items are very close. You have to prevent overlapping of items (either by stronger repulsion or by collision tests). You have also to create some rotation moment for example with that repulsive force. It differs on any vertex so it creates a rotation moment (that can automatically align similar sides closer together). Also you can have semi-stable state with big distances between items and after finding best solution just turn off repulsion fields so they stick together. Sometimes it can have better results some times not ... here is nice example for graph layout computation
Logic to strategically place items in a container with minimum overlapping connections
Demo from the same QA
And here solver for placing sliders in 2D:
How to implement a constraint solver for 2-D geometry?
[Edit0] old answer before reformulating the question
I am not clear what you want to achieve.
have SVG picture and want to separate its parts to rectangular regions
as filled as can be
least empty space in them
no shape change in picture
have svg picture and want to change its shapes according to some purpose
if this is the case some additional info is needed
[solution for 1]
create a list of points for whole SVG in global SVG space (all points are transformed)
for line you need add 2 points
for rectangles 4 points
circle/elipse/bezier/eliptic arc 8 points
find local centres of mass
use classical approach
or can speed things up by computing the average density of points per x,y axis separately and after that just check all combinations of found positions of local max of densities if they really are sub cluster center or not.
all sub cluster center is the center of your region
now find the most far points which are still part of your cluster (the are close enough to neighbour points)
create rectangular area that cover all points from sub cluster.
you also can remove all used points from list
repeat fro all valid sub clusters
until all points are used
another not precise but simpler approach is:
find SVG size
create planar map of svg with some precision for example int map[256][256].
size of map can be constant or with the same aspect as SVG
clear map with 0
for any point of SVG set related map point to 1 (or inc or whatever)
now just segmentate map and you will have find your objects
after segmentation you have position and size of all objects
so finding of bounding boxes should be easy
You can start with a variant of the rectangle bin-packing algorithm and add rotation. There is a method "Guillotine bin packer" and you can download a paper and a library at github.
Sort of a programming question, sort of a general logic question. Imagine a circular base with a pattern of circles:
And another circle, mounted above and able to rotate, with holes that expose the colored circles below:
There must be an optimal pattern of either the colored circles or the openings (or both) that will allow for all N possible combinations of colors... but I have no idea how to attack the problem! At this point, combinations of 2 seem probably the easiest and would be fine as a starting point (red/blue, red/green, red/white, etc).
I would imagine there will need to be gaps in the colors, unlike the example above. Any suggestions welcome!
Edit: clarified the question (hopefully!) thanks to feedback from Robert Harvey
For two holes, you could look for a perfect matching in a bipartite graph, each permutation described by two nodes, one in each partition. Nodes would be connected if they share one element, i.e. the (blue,red) node from the first partition connected to the (red,green) node of the second. The circles arranged in the same distance would allow for both of these patterns. A perfect matching in that graph would correspond to chains or cycles of permutations where two of them always share a single color. A bit like dominoes. If you had a set of cycles of the same length, you could interleave them to form the pattern on the lower disk. I'm not sure how easy it will be to obtain these same length cycles, though, and I also don't know how to generalize this to more than two elements in each permutation.
I have a set of points which form some curve, see picture. This curve consists of straight and curved sections and I do not know exactly where they start or end. In the presented picture I know at least five pieces: two straight sections, one section with a constant radius, two other types of curves. I want to be able to recognise those sections, to separate them from each other and to work with them as with separate curves.
Update.
In my opinion splines would not work in the way I want, and not surely Besier. I was thinking about Non-linear Least Squares but was not sure if it suits this case. If I am able to separate the parts, then I can use Linear Least Squares for straights and some non-linear for other parts. Otherwise, I need some universal method which will work for all types of curves: 1, 2 and 3 power.
Please share your thoughts.
Thank you.
For a bent tube I would suggest multidimensional spline fitting. Your tube does not look like a composition of of straight and curved sections, but curves smoothly all the way.
http://en.wikipedia.org/wiki/Spline_interpolation
This is the starting point if you want to read further.
Taking a guess I suppose you are not experienced with splines, so if you could put out the dataset in table form me or some other reader could interpolate the given data with a 3D spline curve.
How can i detect if two or more objects collide?
I would like to use only default frameworks, such Core Graphics. Or i have to use Box2d or Cocos2d?
EDIT
You're right, the question isn't really clear.
So this is the situation :
i have multiple UIImageView which move with the accelerometer, but i want that when two or more images collides these isn't overlap each others. Is it clear?
Probably you want a multi-step process.
First, define a "center" and "radius" for each object, such that a line drawn around the center at the selected radius will entirely encompass the object without "too much extra". (You define how hard you work to define center and radius to prevent "too much".)
An optional next step is to divide the screen into quadrants/sections somehow, and compute which objects (based on their centers and radii) lie entirely within one quadrant, which straddle a quadrant boundary, which straddle 4 quadrants, etc. This allows you to subset the next step and only consider object pairs that are in the same quadrant or where one of the two is a straddler of one sort or another.
Then, between every pair of objects, calculate the center-to-center distance using the Pythagorean theorem. If that distance is less than the sum of the two objects' radii then you have a potential collision.
Finally, you have to get down and dirty with calculating actual collisions. There are several different approaches, depending on the shape of your objects. Obviously, circles are covered by the prior step, squares/rectangles (aligned to the X/Y axes) can be computed fairly well, but odd shapes are harder. One scheme is to, on a pair of "blank" canvases, draw the two objects, then AND together the two, pixel by pixel, to see if you come up with a 1 anywhere. There are several variations of this scheme.
As mentioned, your question is pretty vague, and therefore difficult to answer succinctly. But to give you some ideas to go by, you can do this with core animation, though some 3rd party gaming engines/frameworks may be more efficient.
Essentially, you create a timer that fires quite often (how often would depend on the size of the objects you're colliding and their speed - too slow and the objects can collide and pass each other before the timer fires - math is your friend here).
Every time the timer fires you check each object on screen for collisions with the others. For efficiencies sake you should ensure that you only check each pair once - ie. if you have A,B,C,D objects, check A & D but not D & A.
If you have a collision handle it however you want (animation/points/notification/whatever you want to do).
There's way too much to cover here in a post. I'd suggest checking out the excellent writeup on the Asteroids game at cocoawithlove, especially part 3 (though not iOS the principles are the same):
http://cocoawithlove.com/2009/03/asteroids-style-game-in-coreanimation.html