I have both a start and end CATransform3D that I would like to manually animate between. That is, I would like to calculate the intermediate transform for time t = 0 (start) to 1 (end). The transforms are a combination of translate and scale, if that matters.
I realize that Apple provides a number of ways to automatically animate from a start to end state, but in my particular use case I actually need to compute the intermediate transform at a given time.
The general case is a stinker. The specific case is easier. Assuming you start with the identity transform I would suggest simply writing code that interpolates the values of your scale and translation setting, creating a new transform for each frame, and then applying that transform. Changes to scale and translate are both mathematically simple. Rotation would be a more expensive (read slower) calculation since it involves trig.
Related
I'm looking at the freely available Solar potential dataset on Google BigQuery that may be found here: https://bigquery.cloud.google.com/table/bigquery-public-data:sunroof_solar.solar_potential_by_censustract?pli=1&tab=schema
Each record on the table has the following border definitions:
lat_max - maximum latitude for that region
lat_min - minimum latitude for that region
lng_max - maximum longitude for that region
lng_min - minimum longitude for that region
Now I have a coordinate (lat/lng pair) and I would like to query to see whether or not that coordinate is within the above range. How do I do that with BQ Standard SQL?
I've seen the Geo Functions here: https://cloud.google.com/bigquery/docs/reference/standard-sql/geography_functions
But I'm still not sure how to write this query.
Thanks!
Assuming the points are just latitude and longitude as numbers, why can't you just do a standard numerical comparison?
Note: The first link doesn't work without a google account, so I can't see the data.
But if you want to become spatial, I'd suggest you're going to need to take the border coordinates that you have and turn them into a polygon using one of: ST_MAKEPOLYGON, ST_GEOGFROMGEOJSON, or ST_GEOGFROMTEXT. Then create a point using the coords you wish to test ST_MAKEPOINT.
Now you have two geographies you can compare them both using ST_INTERSECTION or ST_DISJOINT depending on what outcome you want.
If you want to get fancy and see how far aware from the border you are (which I guess means more efficient?) you can use ST_DISTANCE.
Agree with Jonathan, just checking if each of the lat/lon value is within the bounds is simplest way to achieve it (unless there are any issues around antimeridian, but most likely you can just ignore them).
If you do want to use Geography objects for that, you can construct Geography objects for these rectangles, using
ST_MakePolygon(ST_MakeLine(
[ST_GeogPoint(lon_min, lat_min), ST_GeogPoint(lon_max, lat_min),
ST_GeogPoint(lon_max, lat_max), ST_GeogPoint(lon_min, lat_max),
ST_GeogPoint(lon_min, lat_min)]))
And then check if the point is within particular rectangle using
ST_Intersects(ST_GeogPoint(lon, lat), <polygon-above>)
But it will likely be slower and would not provide any benefit for this particular case.
Does Maya allow one to compute the output attributes at frame N using the output attributes calculated at Frame (N-1) as inputs? With the proviso that at (e.g.) Frame 0 we don't look at the previous frame but use some sort of initial condition. Negative frames would be calculated by looking forward in time.
e.g. The translate of the ball at Frame N is computed to be the translate of the ball at Frame N-1 + 1cm higher. At frame zero the ball is given an initial translate of zero.
The DataBlock has a setContext function but the docs appear to forbid using that to do 'timed evaluation'. I could hit the attribute plugs directly and get value with a different time but that would be using inputs outside of the data block.
Is the Maya dependency API essentially timeless - only allowing calculation using the state at the current time? With the only solution to use animation curves which are also essentially timeless (their input state of key frames remaining the same regardless of the time)?
A simple node connection is supposed to be updated on demand, ie for the 'current' frame. It's supposed to be ahistorical -- you should be able to jump to a given frame directly and get a complete evaluation of the scene state without history.
If you need offset values you can use a frame cache node to access a different point in the value stream. You connect the attribute you want to lag to the frameCache's 'stream' plug, and then connect either the 'future' or 'past' attribute to the plug on your node. The offset is applied by specifying the index value for the connections, ie, frameCache1.past[5] is 5 frames behind the value that was fed into the frameCache.
You can also do this in a less performant, but more flexible way by using an expression node. The expression can poll an attribute value at a particular time by calling getAttr() with the -t flag to specify the time. This is much slower to evaluate but lets you apply any arbitrary logic to the time offset you might want.
I want to use a python Min-Cost Flow solver to be able to construct new networks. This means that I have an initial complete graph, with the vertices being either suppliers or having a demand. Using the algorithm should tell me, based on their costs, what edges will be used to settle all demands. Different to the existing problems, the cost of an edge when being used are not only described by a unit cost but also have an investment of this edge which is independent of the flow. I have been looking into the source code of networkx and or-tools but cannot figure out how to adapt these to implement the investment cost of the edges. Does someone have a better idea or can help me adapting the code?
Best Regards
Justus
You cannot solve this with a standard graph algorithm (eg: MinCostFlow).
Instead you need to formulate it as a Mixed Integer Program.
You can start with this example:
https://developers.google.com/optimization/assignment/assignment_mip
But you need to tweak it a little bit:
You need two classes of decision variables: invest_var (binary) and flow_var (continuous).
The objective will look like this:
min: sum(flow_cost[i,j]*flow_var[i,j]) + sum(invest_cost[i,j]*invest_var[i,j])
And you need to add an additional constraint for each link:
flow_var[i,j] <= BIG_INT * invest_var[i,j]
The purpose of these to constrain flow_var to 0 if invest_var is 0.
Demand and Supply constraints will be similar as in the example.
BIG_INT is a constant. You can set it as:
BIG_INT=max(flow_upper_bound[i,j])
Where flow_upper_bound is an upper bound on your flow_var variables.
Notice, that the problem now becomes a Mixed Integer Linear Program instead of just being a Linear Program.
Approximate program behavior:
I have a map image with data associated with the map indicated by RGB index. The data has been populated into an MS Access database. I imported the information in the database into my program as an array and sorted them to go in the order I want the program to run.
I want the program to find the nearest pixel that has a different color from the incumbent pixel being compared. (Colors are stored as string attributes of object Pixel)
First question: Should I use integers to represent my colors instead of string? Would this make the comparison function run significantly faster?
In order to find the nearest pixel of different color, the program begins with all 8 adjacent pixels around the incumbent. If a nonMatch is not found, it then continues onto the next "degree", and in this fashion, it spirals out from the incumbent pixel until it hits a nonMatch. When found, the color of the nonMatch is saved as an attribute of incumbent. After I find the nonMatch for each of the Pixels, the data is re-inserted into the database
The program accomplishes what I want in the manner I've written it, but it is very very slow. After 24 hours, I am only about 3% through with execution.
Question Two: Does my program behavior sound about right? Is this algorithm you would use if you had to accomplish this task?
Question Three: Would it be appropriate for me to use threads in order to finish execution of the program faster? How exactly does that work? (I am brand new to threads, but know a little of the syntax)
Question Four: Would it be more "intelligent" for my program to find the nonMatch for each pixel and insert it into the database immediately after finding it? (I'm making a guess that this would be good in multi-threading, because while one record is accessing the database (to insert), another record is accessing the array of pixels (shared global variable in program).
Question Five: If threading is a good idea, I'm guessing I would split the records up into more manageable chunks (i.e. quarters), and have each thread run the same functions for their specified number of records? Am I close at all?
Please let me know if I can clarify or provide code samples, I just figured that this is more of a conceptual topic so do not want to overburden the post.
1.) Yes, integers compare much faster than strings. Additionally the y use much less memory
2.) I would adapt the algorithm in this way:
E.g.: #1: Let's say, for pixel(87,23) you found the nearest nonMatch to be (88,24) at degree=1 - you can immediately invert the relation and record, that the nearest nonMatch to (88,24) is (87,23). On degree=1 you finished 2 pixels with 1 search.
E.g. #2: Let's say, for pixel (17,18) you found the nearest nonMatch to be (17,20) at degree=2. You can immediately record, that all pixels, that border on both (16,19), (17,19) and (18,19) have the nearest noMatch (17,20) at degree=1, and that one of them is the nearest noMatch to (17,20). On degree=2 (or higher), you finished 5 pixels with 1 search.
3.) Using threads is a two-sided sword: You can do searches in parallel, but you need locking if you write to your array. So this depends on how many CPU cores you can throw at the problem. If this is 3 or more, threads will surely speed up the search.
4.) The results from 2.) make it necessary to mark a pixel as "done" in your array, as you might have finished up to 5 pixels with 1 search. I recommend you put those into a queue and use a dedicated thread to write the queue back into the database: MS Access can't handle concurrent updates, so a single database writer thread looks like a good idea.
5.) I recommend you NOT chunk up the array: You will run into problems with pixels on the edges of a chunk having their nearest nonMatch in a different chunk. Instead if you use e.g. 4 Threads, let them run 1.) From NW corner E, then S 2.) From SE Corner W, then N 3.) From NE Corner S, then W 4. From SW Corner N, then E
Yes. Using a integer would make it much faster
You can reuse the work you have done for previous pixel. Eg. If (a,b) is the nearest non-equal pixel of (x,y), it is likely that points around (x,y) might also have (a,b) as the nearest non-equal pixel
You can use different threads to work on different pixels instead of dividing searching for one pixel
IMHO, steps 1&2 should make your program much faster and you might not need multi-threading.
Yes, I'd convert colour strings to Integers for speed, or even Color structures if you intend to display them on the screen.
Don't work directly with the database if you can avoid it. Copy the necessary data out of the database into an array before you start, and copy your results back when you're finished.
Although I'm coding in Objective C, this is more of a general programming question.
What is the best way to convert a constantly changing scalar value to a changing interval or frequency?
Right now every time the scalar value changes I am destroying the NSInterval
ie
[self.myTimer invalidate];
self.myTimer = nil;
and creating a new one, but this seems like a VERY expensive way to achieve my goal, since the changing scalar value in my case represents the horizontal velocity of a swipe.
For a rough analogy, think of the speed of a swipe being reflected in a visual metronome, the faster you swipe, the higher(shorter interval) the frequency of the metronome.
First, understand that this is a "measurement" problem. To solve this problem, isolate the minimum attributes needed to solve the problem and derive the rest.
The distance moved and the time taken to move the distance are derived attributes of each measurement, in this case the measurement is named "swipe". In a racing analogy, the measurement is called a lap.
The "speed" can now be calculated. This will be the "velocity", which is simply distance/time.
The distance can be calculated given the start and end points of the swipe.
To obtain the time value, create an startTime instance of NSDate in touchesBegan:withEvents: and in touchesEnded:withEvents: calculate elapsedTimeInterval using [startTime timeIntervalSinceNow];
Depending on your needs, you may need a Measurement class with properties for startPosition, endPosition, startTime and endTime so you can keep track of "fastest" speed etc.
Take a look at Analysis Patterns by Martin Fowler. I find it very useful when trying to map domain problems to software solutions.