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  • Calculating distance from latitude, longitude and height using a geocentric co-ordinate system

    - by Sarge
    I've implemented this method in Javascript and I'm roughly 2.5% out and I'd like to understand why. My input data is an array of points represented as latitude, longitude and the height above the WGS84 ellipsoid. These points are taken from data collected from a wrist-mounted GPS device during a marathon race. My algorithm was to convert each point to cartesian geocentric co-ordinates and then compute the Euclidean distance (c.f Pythagoras). Cartesian geocentric is also known as Earth Centred Earth Fixed. i.e. it's an X, Y, Z co-ordinate system which rotates with the earth. My test data was the data from a marathon and so the distance should be very close to 42.26km. However, the distance comes to about 43.4km. I've tried various approaches and nothing changes the result by more than a metre. e.g. I replaced the height data with data from the NASA SRTM mission, I've set the height to zero, etc. Using Google, I found two points in the literature where lat, lon, height had been transformed and my transformation algorithm is matching. What could explain this? Am I expecting too much from Javascript's double representation? (The X, Y, Z numbers are very big but the differences between two points is very small). My alternative is to move to computing the geodesic across the WGS84 ellipsoid using Vincenty's algorithm (or similar) and then calculating the Euclidean distance with the two heights but this seems inaccurate. Thanks in advance for your help!

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  • Looking for C# framework for plotting scientific data: 2d/3d ...

    - by Ivan
    I need to visualize some scientific calculations. I generally prefer reusing code if there is already a good available instead of inventing wheels each time, that's why I am asking. I need a C# code to draw charts (just outputting a bitmap is ok) of 2d (y=f(x)) and 3d (z=f(x,y)) digital data sets (where any axis can be float, int or datetime), sometimes combined. If I go here and click 3D in the navigation bar on the left, there I can see what I need. But the cheapest version costs $759 there, looks scary for a hobby project of an east-european student :-(

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  • adding up value of array and getting the average

    - by sea_1987
    I have an array that looks similar to this, [4] => Common_Model Object ( [id] => 4 [name] => [date_created] => [last_updated] => [user_id_updated] => [_table] => [_aliases] => Array ( [id] => 4 [name] => [date_created] => [date_updated] => [user_id_updated] => [rating] => 3 [recipe_id] => 5 ) [_nonDBAliases] => Array ( ) [_default] => Array ( ) [_related] => Array ( ) [_enums] => [_alsoDelete] => Array ( ) [_readOnly] => Array ( [0] => date_updated ) [_valArgs] => Array ( ) [_valArgsHash] => Array ( [default] => Array ( ) ) [_valAliases] => Array ( ) [_extraData] => Array ( ) [_inputs] => Array ( ) [_tableName] => jm_ratings [_tablePrefix] => [_niceDateUpdated] => 1st Jan 70 [_niceDateCreated] => 1st Jan 70 [_fetchAdminData] => [_mCache] => [_assets] => Array ( ) ) [3] => Common_Model Object ( [id] => 3 [name] => [date_created] => [last_updated] => [user_id_updated] => [_table] => [_aliases] => Array ( [id] => 3 [name] => [date_created] => [date_updated] => [user_id_updated] => [rating] => 1 [recipe_id] => 5 ) [_nonDBAliases] => Array ( ) [_default] => Array ( ) [_related] => Array ( ) [_enums] => [_alsoDelete] => Array ( ) [_readOnly] => Array ( [0] => date_updated ) [_valArgs] => Array ( ) [_valArgsHash] => Array ( [default] => Array ( ) ) [_valAliases] => Array ( ) [_extraData] => Array ( ) [_inputs] => Array ( ) [_tableName] => jm_ratings [_tablePrefix] => [_niceDateUpdated] => 1st Jan 70 [_niceDateCreated] => 1st Jan 70 [_fetchAdminData] => [_mCache] => [_assets] => Array ( ) ) [2] => Common_Model Object ( [id] => 2 [name] => [date_created] => [last_updated] => [user_id_updated] => [_table] => [_aliases] => Array ( [id] => 2 [name] => [date_created] => [date_updated] => [user_id_updated] => [rating] => 1 [recipe_id] => 5 ) [_nonDBAliases] => Array ( ) [_default] => Array ( ) [_related] => Array ( ) [_enums] => [_alsoDelete] => Array ( ) [_readOnly] => Array ( [0] => date_updated ) [_valArgs] => Array ( ) [_valArgsHash] => Array ( [default] => Array ( ) ) [_valAliases] => Array ( ) [_extraData] => Array ( ) [_inputs] => Array ( ) [_tableName] => jm_ratings [_tablePrefix] => [_niceDateUpdated] => 1st Jan 70 [_niceDateCreated] => 1st Jan 70 [_fetchAdminData] => [_mCache] => [_assets] => Array ( ) ) I wanting to add up the [rating] and get the mean average. But I dont know how do this with PHP, my attempt looks like this, <?php foreach ($rt as $rating) { $total = $rating->rating + $rating->rating } $total / count($rt); ?>

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  • OPTICS Clustering algorithm. How to get the best epsilon

    - by Marco Galassi
    I am implementing a project which needs to cluster geographical points. OPTICS algorithm seems to be a very nice solution. It needs just 2 parameters as input(MinPts and Epsilon), which are, respectively, the minimum number of points needed to consider them as a cluster, and the distance value used to compare if two points are in can be placed in same cluster. My problem is that, due to the extreme variety of the points, I can't set a fixed epsilon. Just look at the image below. The same points structure but in a different scale would result very different. Suppose to set MinPts=2 and epsilon = 1Km. On the left, the algorithm would create 2 clusters(red and blue), but on the right it would create one single cluster containing all of the points(red), but I would like to obtain 2 clusters even on the right. So my question is: is there any kind of way to calculate dynamically the epsilon value to get this result? Thank you very much and excuse my for my poor english. Marco

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  • How to compute the dot product?

    - by WizardOfOdds
    I have the following piece of pseudo-C/Java/C# code: int a[]= { 30, 20 }; int b[] = { 40, 50 }; int c[] = {12, 12}; How do I compute the sign of the dot-product AB . AC? I'm only interested in the sign, so I have: boolean signABxAC = ? Now concretely what do I write to get the sign of the dot-product AB . AC?

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  • Calculating rotation in > 360 deg. situations

    - by danglebrush
    I'm trying to work out a problem I'm having with degrees. I have data that is a list of of angles, in standard degree notation -- e.g. 26 deg. Usually when dealing with angles, if an angle exceeds 360 deg then the angle continues around and effectively "resets" -- i.e. the angle "starts again", e.g. 357 deg, 358 deg, 359 deg, 0 deg, 1 deg, etc. What I want to happen is the degree to continue increasing -- i.e. 357 deg, 358 deg, 359 deg, 360 deg, 361 deg, etc. I want to modify my data so that I have this converted data in it. When numbers approach the 0 deg limit, I want them to become negative -- i.e. 3 deg, 2 deg, 1 deg, 0 deg, -1 deg, -2 deg, etc. With multiples of 360 deg (both positive and negative), I want the degrees to continue, e.g. 720 deg, etc. Any suggestions on what approach to take? There is, no doubt, a frustratingly simple way of doing this, but my current solution is kludgey to say the least .... ! My best attempt to date is to look at the percentage difference between angle n and angle n - 1. If this is a large difference -- e.g. 60% -- then this needs to be modified, by adding or subtracting 360 deg to the current value, depending on the previous angle value. That is, if the previous angle is negative, substract 360, and add 360 if the previous angle is positive. Any suggestions on improving this? Any improvements?

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  • Real life usage of the projective plane theory

    - by Elazar Leibovich
    I'm learning about the theory of the projective plane. Very generally speaking, it is an extension of the plane, which includes additional points which are defined as the intersection points of two parallel lines. In the projective plane, every two lines have an interesection point. Whether they're parallel or not. Every point in the projective plane can be represented by three numbers (you actually need less than that, but nevemind now). Is there any real life application which uses the projective plane? I can think that, for instance, a software which needs to find the intersections of a line, can benefit from always having an intersection point which might lead to simpler code, but is it really used?

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  • The bigger value in a matrix row

    - by marionmaiden
    How can I get the 2 biggers numbers of a matrix row? If the matrix have a bigger number in other row, it can't be shown. For example, let's suppose I have the following matrix int mat[][] ={{1,2,3}{4,5,6}{7,8,9}}; if I search the 2 biggers numbers from the row 0, it should return me 1 and 2.

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  • Need some help understanding this problem

    - by Legend
    I was wondering if someone could help me understand this problem. I prepared a small diagram because it is much easier to explain it visually. Problem I am trying to solve: 1. Constructing the dependency graph Given the connectivity of the graph and a metric that determines how well a node depends on the other, order the dependencies. For instance, I could put in a few rules saying that node 3 depends on node 4 node 2 depends on node 3 node 3 depends on node 5 But because the final rule is not "valuable" (again based on the same metric), I will not add the rule to my system. 2. Execute the request order Once I built a dependency graph, execute the list in an order that maximizes the final connectivity. First and foremost, I am wondering if I constructed the problem correctly and if I should be aware of any corner cases. Secondly, is there a closely related algorithm that I can look at? Currently, I am thinking of something like Feedback Arc Set or the Secretary Problem but I am a little confused at the moment. Any suggestions? PS: I am a little confused about the problem myself so please don't flame on me for that. If any clarifications are needed, I will try to update the question.

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  • How would I find all sets of N single-digit, non-repeating numbers that add up to a given sum in PHP

    - by TerranRich
    Let's say I want to find all sets of 5 single-digit, non-repeating numbers that add up to 30... I'd end up with [9,8,7,5,1], [9,8,7,4,2], [9,8,6,4,3], [9,8,6,5,2], [9,7,6,5,3], and [8,7,6,5,4]. Each of those sets contains 5 non-repeating digits that add up to 30, the given sum. Any help would be greatly appreciated. Even just a starting point for me to use would be awesome. I came up with one method, which seems like a long way of going about it: get all unique 5-digit numbers (12345, 12346, 12347, etc.), add up the digits, and see if it equals the given sum (e.g. 30). If it does, add it to the list of possible matching sets. I'm doing this for a personal project, which will help me in solving Kakuro puzzles without actually solving the whole thing at once. Yeah, it may be cheating, but it's... it's not THAT bad... :P

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  • How do I find the largest factor of an integer in mysql

    - by Bill H
    I am trying to write a select query that will dynamically determine the minimum number of items that can be packaged together. I am having trouble with one part of the query. ... CASE WHEN (pid.product_id) THEN 1 WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 11 = 0)) THEN CEILING(p.inner_pack / 11) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 7 = 0)) THEN CEILING(p.inner_pack / 7) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 6 = 0)) THEN CEILING(p.inner_pack / 6) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 5 = 0)) THEN CEILING(p.inner_pack / 5) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 4 = 0)) THEN CEILING(p.inner_pack / 4) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 3 = 0)) THEN CEILING(p.inner_pack / 3) WHEN ((p.case_pack = p.inner_pack) AND (p.inner_pack % 2 = 0)) THEN CEILING(p.inner_pack / 2) ELSE p.inner_pack END AS min_pack ... What I want to do is find the largest factorial of an integer (p.inner_pack) that is under 12. Is there a better way to do this in mysql?

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  • Ruby BigDecimal sanity check (floating point newb)

    - by Andy
    Hello, Hoping to get some feedback from someone more experienced here. I haven't dealt with the dreaded floating-point calculation before... Is my understanding correct that with Ruby BigDecimal types (even with varying precision and scale lengths) should calculate accurately or should I anticipate floating point shenanigans? All my values within a Rails application are BigDecimal type and I'm seeing some errors (they do have different decimal lengths), hoping it's just my methods and not my object types... Thanks!

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  • Why can't decimal numbers be represented exactly in binary?

    - by Barry Brown
    There have been several questions posted to SO about floating-point representation. For example, the decimal number 0.1 doesn't have an exact binary representation, so it's dangerous to use the == operator to compare it to another floating-point number. I understand the principles behind floating-point representation. What I don't understand is why, from a mathematical perspective, are the numbers to the right of the decimal point any more "special" that the ones to the left? For example, the number 61.0 has an exact binary representation because the integral portion of any number is always exact. But the number 6.10 is not exact. All I did was move the decimal one place and suddenly I've gone from Exactopia to Inexactville. Mathematically, there should be no intrinsic difference between the two numbers -- they're just numbers. By contrast, if I move the decimal one place in the other direction to produce the number 610, I'm still in Exactopia. I can keep going in that direction (6100, 610000000, 610000000000000) and they're still exact, exact, exact. But as soon as the decimal crosses some threshold, the numbers are no longer exact. What's going on? Edit: to clarify, I want to stay away from discussion about industry-standard representations, such as IEEE, and stick with what I believe is the mathematically "pure" way. In base 10, the positional values are: ... 1000 100 10 1 1/10 1/100 ... In binary, they would be: ... 8 4 2 1 1/2 1/4 1/8 ... There are also no arbitrary limits placed on these numbers. The positions increase indefinitely to the left and to the right.

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  • Solving simultaneous equations

    - by Milo
    Here is my problem: Given x, y, z and ratio where z is known and ratio is known and is a float representing a relative value, I need to find x and y. I know that: x / y == ratio y - x == z What I'm trying to do is make my own scroll pane and I'm figuring out the scrollbar parameters. So for example, If the scrollbar must be able to scroll 100 values (z) and the thumb must consume 80% of the bar (ratio = 0.8) then x would be 400 and y would be 500. Thanks

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  • Moving a Ball on iPhone

    - by Chandan Shetty SP
    I am using below formula to move the ball circular, where accelX and accelY are the values from accelerometer, it is working fine. But the problem in this code is mRadius(I fixed its value to 50), i need to change mRadius according to accelerometer values and also i need bouncing effect when it touches other circles please send your answers ASAP... I am waiting. float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); Here is the snap of the game i want to develop. http://iphront.com/wp-content/uploads/2009/12/bdece528ea334033.jpg.jpg

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  • signed angle between two 3d vectors with same origin within the same plane? recipe?

    - by Advanced Customer
    Was looking through the web for an answer but it seems like there is no clear recipe for it. What I need is a signed angle of rotation between two vectors Va and Vb lying within the same 3D plane and having the same origin knowing that: the plane contatining both vectors is an arbitrary and is not parallel to XY or any other of cardinal planes Vn - is a plane normal both vectors along with the normal have the same origin O = { 0, 0, 0 } Va - is a reference for measuring the left handed rotation at Vn The angle should be measured in such a way so if the plane would be XY plane the Va would stand for X axis unit vector of it. I guess I should perform a kind of coordinate space transformation by using the Va as the X-axis and the cross product of Vb and Vn as the Y-axis and then just using some 2d method like with atan2() or something. Any ideas? Formulas?

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  • approximating log10[x^k0 + k1]

    - by Yale Zhang
    Greetings. I'm trying to approximate the function Log10[x^k0 + k1], where .21 < k0 < 21, 0 < k1 < ~2000, and x is integer < 2^14. k0 & k1 are constant. For practical purposes, you can assume k0 = 2.12, k1 = 2660. The desired accuracy is 5*10^-4 relative error. This function is virtually identical to Log[x], except near 0, where it differs a lot. I already have came up with a SIMD implementation that is ~1.15x faster than a simple lookup table, but would like to improve it if possible, which I think is very hard due to lack of efficient instructions. My SIMD implementation uses 16bit fixed point arithmetic to evaluate a 3rd degree polynomial (I use least squares fit). The polynomial uses different coefficients for different input ranges. There are 8 ranges, and range i spans (64)2^i to (64)2^(i + 1). The rational behind this is the derivatives of Log[x] drop rapidly with x, meaning a polynomial will fit it more accurately since polynomials are an exact fit for functions that have a derivative of 0 beyond a certain order. SIMD table lookups are done very efficiently with a single _mm_shuffle_epi8(). I use SSE's float to int conversion to get the exponent and significand used for the fixed point approximation. I also software pipelined the loop to get ~1.25x speedup, so further code optimizations are probably unlikely. What I'm asking is if there's a more efficient approximation at a higher level? For example: Can this function be decomposed into functions with a limited domain like log2((2^x) * significand) = x + log2(significand) hence eliminating the need to deal with different ranges (table lookups). The main problem I think is adding the k1 term kills all those nice log properties that we know and love, making it not possible. Or is it? Iterative method? don't think so because the Newton method for log[x] is already a complicated expression Exploiting locality of neighboring pixels? - if the range of the 8 inputs fall in the same approximation range, then I can look up a single coefficient, instead of looking up separate coefficients for each element. Thus, I can use this as a fast common case, and use a slower, general code path when it isn't. But for my data, the range needs to be ~2000 before this property hold 70% of the time, which doesn't seem to make this method competitive. Please, give me some opinion, especially if you're an applied mathematician, even if you say it can't be done. Thanks.

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  • C# method to scale values?

    - by John S
    Hello, I have a value range from 0 to 255. There is a method that returns an array with a min and max values within this range, i.e: 13, 15, 20, 27, 50 ... 240 where 13 is the min and 240 is the max I need to scale these values so that 13 becomes 0 and 240 becomes 255 and scale all the other values between them proportionally. Is there any C# method that does that? thanks!

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