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  • Derivative Calculator

    - by burki
    Hi! I'm interested in building a derivative calculator. I've racked my brains over solving the problem, but I haven't found a right solution at all. May you have a hint how to start? Thanks

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  • WPF Coordinates of intersection from two Line objects

    - by Becky Franklin
    I have two Line objects in C# WPF, and I'm trying to construct a method to work out the coordinates at which the lines intersect (if at all). After giving myself a headache reminding myself of high school maths to do this, I can't work out how to map it into programming format - anyone know how to do this? Thanks very much, Becky

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  • PHP Calculating future date by adding days to a variable date

    - by OneNerd
    I was looking at this post, and it is close to what I need: http://stackoverflow.com/questions/1669165/php-how-to-count-60-days-from-the-add-date However, in that post, the calculation is performed by adding 60 days to the current date. What I need to do is calculate the date based on a variable date (and not the current date). Something like this: $my_date = $some_row_from_a_database; $date_plus_10_days = ???; Anyone know how to do that? Thanks

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  • Draw Lines Over a Circle

    - by VOX
    There's a line A-B and C at the center between A and B. It forms a circle as in the figure. If we assume A-B line as a diameter of the circle and then C is it's center. My problem is I have no idea how to draw another three lines (in blue) each 45 degree away from AC or AB. No, this is not a homework, it's part of my complex geometry in a rendering. http://www.freeimagehosting.net/image.php?befcd84d8c.png

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  • correcting fisheye distortion programmatically

    - by Will
    I have some points that describe positions in a picture taken with a fisheye lens. I've found this description of how to generate a fisheye effect, but not how to reverse it. How do you calculate the radial distance from the centre to go from fisheye to rectilinear? My function stub looks like this: Point correct_fisheye(const Point& p,const Size& img) { // to polar const Point centre = {img.width/2,img.height/2}; const Point rel = {p.x-centre.x,p.y-centre.y}; const double theta = atan2(rel.y,rel.x); double R = sqrt((rel.x*rel.x)+(rel.y*rel.y)); // fisheye undistortion in here please //... change R ... // back to rectangular const Point ret = Point(centre.x+R*cos(theta),centre.y+R*sin(theta)); fprintf(stderr,"(%d,%d) in (%d,%d) = %f,%f = (%d,%d)\n",p.x,p.y,img.width,img.height,theta,R,ret.x,ret.y); return ret; } Alternatively, I could somehow convert the image from fisheye to rectilinear before finding the points, but I'm completely befuddled by the OpenCV documentation. Is there a straightforward way to do it in OpenCV, and does it perform well enough to do it to a live video feed?

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  • Histogram matching - image processing - c/c++

    - by Raj
    Hello I have two histograms. int Hist1[10] = {1,4,3,5,2,5,4,6,3,2}; int Hist1[10] = {1,4,3,15,12,15,4,6,3,2}; Hist1's distribution is of type multi-modal; Hist2's distribution is of type uni-modal with single prominent peak. My questions are Is there any way that i could determine the type of distribution programmatically? How to quantify whether these two histograms are similar/dissimilar? Thanks

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  • efficiently determining if a polynomial has a root in the interval [0,T]

    - by user168715
    I have polynomials of nontrivial degree (4+) and need to robustly and efficiently determine whether or not they have a root in the interval [0,T]. The precise location or number of roots don't concern me, I just need to know if there is at least one. Right now I'm using interval arithmetic as a quick check to see if I can prove that no roots can exist. If I can't, I'm using Jenkins-Traub to solve for all of the polynomial roots. This is obviously inefficient since it's checking for all real roots and finding their exact positions, information I don't end up needing. Is there a standard algorithm I should be using? If not, are there any other efficient checks I could do before doing a full Jenkins-Traub solve for all roots? For example, one optimization I could do is to check if my polynomial f(t) has the same sign at 0 and T. If not, there is obviously a root in the interval. If so, I can solve for the roots of f'(t) and evaluate f at all roots of f' in the interval [0,T]. f(t) has no root in that interval if and only if all of these evaluations have the same sign as f(0) and f(T). This reduces the degree of the polynomial I have to root-find by one. Not a huge optimization, but perhaps better than nothing.

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  • How to perform spatial partitioning in n-dimensions?

    - by kevin42
    I'm trying to design an implementation of Vector Quantization as a c++ template class that can handle different types and dimensions of vectors (e.g. 16 dimension vectors of bytes, or 4d vectors of doubles, etc). I've been reading up on the algorithms, and I understand most of it: here and here I want to implement the Linde-Buzo-Gray (LBG) Algorithm, but I'm having difficulty figuring out the general algorithm for partitioning the clusters. I think I need to define a plane (hyperplane?) that splits the vectors in a cluster so there is an equal number on each side of the plane. [edit to add more info] This is an iterative process, but I think I start by finding the centroid of all the vectors, then use that centroid to define the splitting plane, get the centroid of each of the sides of the plane, continuing until I have the number of clusters needed for the VQ algorithm (iterating to optimize for less distortion along the way). The animation in the first link above shows it nicely. My questions are: What is an algorithm to find the plane once I have the centroid? How can I test a vector to see if it is on either side of that plane?

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  • Power Law distribution for a given exponent in C# using MathNet

    - by Eric Tobias
    Hello! I am currently working on a project where I need to generate multiple values (floats or doubles preferably) that follow a power law distribution with a given exponent! I was advised to use the MathNet.Iridium library to help me. The problem I have is that the documentation is not as explicit as it should be if there is any! I see multiple distributions that fit the general idea of the power law distribution but I cannot pinpoint a good distribution to use with a certain exponent as a parameter. Does anybody have more experience in that matter and could give me some hints or advice?

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  • make a 3D spotlight cone matrix

    - by Soubok
    How to create the transformation matrix (4x4) that transforms a cylinder (of height 1 and diameter 1) into a cone that represents my spotlight (position, direction and cutoff angle) ? --edit-- In other words: how to draw the cone that represents my spotlight by drawing a cylinder through a suitable transformation matrix.

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  • Finding coordinates of a point between two points?

    - by Nicros
    Doing some 3D stuff in wpf- want to use a simpler test to see if everything is working (before moving to curves). The basic question is given two points x1,y1,z1 and x2,y2,z2 I have calculated the distance between the points. But how to find the coordinates of another point (x3,y3,z3) that lies on that line at some distance? I.e. if my line is 100 long between -50,0,0 and 50,0,0 what are the coordinates of the point at 100 * 0.1 along the line? I think this is a simple formula but I haven't found it yet....

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  • Power function fit to data set

    - by czerasz
    I have a set of data (in ArrayCollection) and I need to fit a power function { f(x)= B + x^alpha } to it, before display in LineChart. As result I need the alpha and B paremeter. How to do this with Flex?

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  • Is there a Java library with 3D spline functions?

    - by Liam
    In particular, I need a way to represent a curve/spline that passes through a set of known 3D points, and a way of finding other points on the curve/spline, by subdivision/interpolation. For example, if I have a set of points P0 to PN, I want to find 100 points between P0 and P1 that are on a spline that passes through P0 and P1. I see that Java3D's KBRotPosScaleSplinePathInterpolator performs such a calculation, but it is tied to that API's scenegraph model and I do not see how to return the values I need.

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  • Calculating bounding box a certain distance away from a lat/long coordinate in Java

    - by Bryce Thomas
    Given a coordinate (lat, long), I am trying to calculate a square bounding box that is a given distance (e.g. 50km) away from the coordinate. So as input I have lat, long and distance and as output I would like two coordinates; one being the south-west (bottom-left) corner and one being the north-east (top-right) corner. I have seen a couple of answers on here that try to address this question in Python, but I am looking for a Java implementation in particular. Just to be clear, I intend on using the algorithm on Earth only and so I don't need to accommodate a variable radius. It doesn't have to be hugely accurate (+/-20% is fine) and it'll only be used to calculate bounding boxes over small distances (no more than 150km). So I'm happy to sacrifice some accuracy for an efficient algorithm. Any help is much appreciated. Edit: I should have been clearer, I really am after a square, not a circle. I understand that the distance between the center of a square and various points along the square's perimeter is not a constant value like it is with a circle. I guess what I mean is a square where if you draw a line from the center to any one of the four points on the perimeter that results in a line perpendicular to a side of the perimeter, then those 4 lines have the same length.

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  • How to generate a lower frequency version of a signal in Matlab?

    - by estourodepilha.com
    With a sine input, I tried to modify it's frequency cutting some lower frequencies in the spectrum, shifting the main frequency towards zero. As the signal is not fftshifted I tried to do that by eliminating some samples at the begin and at the end of the fft vector: interval = 1; samplingFrequency = 44100; signalFrequency = 440; sampleDuration = 1 / samplingFrequency; timespan = 1 : sampleDuration : (1 + interval); original = sin(2 * pi * signalFrequency * timespan); fourierTransform = fft(original); frequencyCut = 10; %% Hertz frequencyCut = floor(frequencyCut * (length(pattern) / samplingFrequency) / 4); %% Samples maxFrequency = length(fourierTransform) - (2 * frequencyCut); signal = ifft(fourierTransform(frequencyCut + 1:maxFrequency), 'symmetric'); But it didn't work as expected. I also tried to remove the center part of the spectrum, but it wielded a higher frequency sine wave too. How to make it right?

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  • Scrolling a canvas as a shape you're moving approaches its edges

    - by Steven Sproat
    Hi, I develop a Python-based drawing program, Whyteboard. I have tools that the user can create new shapes on the canvas, such as text/images/rectangles/circles/polygons. I also have a Select tool that allows the users to modify these shapes - for example, moving a shape's position, resizing, or editing polygon's points' positions. I'm adding in a new feature where moving or resizing a point near the canvas edge will automatically scroll the canvas. I think it's a good idea in terms of program usability, and annoys me when other program's don't have this feature. I've made some good progress on coding this; below is some Python code to demonstrate what I'm doing. These functions demonstrate how some shapes calculate their "edges": def find_edges(self): """A line.""" self.edges = {EDGE_TOP: min(self.y, self.y2), EDGE_RIGHT: max(self.x, self.x2), EDGE_BOTTOM: max(self.y, self.y2), EDGE_LEFT: min(self. x, self.x2)} def find_edges(self): """An image""" self.edges = {EDGE_TOP: self.y, EDGE_RIGHT: self.x + self.image.GetWidth(), EDGE_BOTTOM: self.y + self.image.GetWidth(), EDGE_LEFT: self.x} def find_edges(self): """Get the bounding rectangle for the polygon""" xmin = min(x for x, y in self.points) ymin = min(y for x, y in self.points) xmax = max(x for x, y in self.points) ymax = max(y for x, y in self.points) self.edges = {EDGE_TOP: ymin, EDGE_RIGHT: xmax, EDGE_BOTTOM: ymax, EDGE_LEFT: xmin} And here's the code I have so far to implement the scrolling when a shape nears the edge: def check_canvas_scroll(self, x, y, moving=False): """ We check that the x/y coords are within 50px from the edge of the canvas and scroll the canvas accordingly. If the shape is being moved, we need to check specific edges of the shape (e.g. left/right side of rectangle) """ size = self.board.GetClientSizeTuple() # visible area of the canvas if not self.board.area > size: # canvas is too small to need to scroll return start = self.board.GetViewStart() # user's starting "viewport" scroll = (-1, -1) # -1 means no change if moving: if self.shape.edges[EDGE_RIGHT] > start[0] + size[0] - 50: scroll = (start[0] + 5, -1) if self.shape.edges[EDGE_BOTTOM] > start[1] + size[1] - 50: scroll = (-1, start[1] + 5) # snip others else: if x > start[0] + size[0] - 50: scroll = (start[0] + 5, -1) if y > start[1] + size[1] - 50: scroll = (-1, start[1] + 5) # snip others self.board.Scroll(*scroll) This code actually works pretty well. If we're moving a shape, then we need to know its edges to calculate when they're coming close to the canvas edge. If we're resizing just a single point, then we just use the x/y coords of that point to see if it's close to the edge. The problem I'm having is a little tricky to describe - basically, if you move a shape to the left, and stop moving it, if you positioned the shape within the 50px from the canvas, then the next time you go to move the shape, the code that says "ok, is this shape close to the end?" gets triggered, and the canvas scrolls to the left, even if you're moving the shape to the right. Can anyone think on how to stop this? I created a youtube video to demonstrate the issue. At about 0:54, I move a polygon to the left of the canvas and position it there. The next time I move it, the canvas scrolls to the left even though I'm moving it right Another thing I'd like to add, but I'm stuck on is the scroll gaining momentum the longer a shape is scrolling? So, with a large canvas, you're not moving a shape for ages, moving 5px at a time, when you need to cover a 2000px distance. Any suggestions there? Thanks all - sorry for the super long question!

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  • What statistics can be maintained for a set of numerical data without iterating?

    - by Dan Tao
    Update Just for future reference, I'm going to list all of the statistics that I'm aware of that can be maintained in a rolling collection, recalculated as an O(1) operation on every addition/removal (this is really how I should've worded the question from the beginning): Obvious Count Sum Mean Max* Min* Median** Less Obvious Variance Standard Deviation Skewness Kurtosis Mode*** Weighted Average Weighted Moving Average**** OK, so to put it more accurately: these are not "all" of the statistics I'm aware of. They're just the ones that I can remember off the top of my head right now. *Can be recalculated in O(1) for additions only, or for additions and removals if the collection is sorted (but in this case, insertion is not O(1)). Removals potentially incur an O(n) recalculation for non-sorted collections. **Recalculated in O(1) for a sorted, indexed collection only. ***Requires a fairly complex data structure to recalculate in O(1). ****This can certainly be achieved in O(1) for additions and removals when the weights are assigned in a linearly descending fashion. In other scenarios, I'm not sure. Original Question Say I maintain a collection of numerical data -- let's say, just a bunch of numbers. For this data, there are loads of calculated values that might be of interest; one example would be the sum. To get the sum of all this data, I could... Option 1: Iterate through the collection, adding all the values: double sum = 0.0; for (int i = 0; i < values.Count; i++) sum += values[i]; Option 2: Maintain the sum, eliminating the need to ever iterate over the collection just to find the sum: void Add(double value) { values.Add(value); sum += value; } void Remove(double value) { values.Remove(value); sum -= value; } EDIT: To put this question in more relatable terms, let's compare the two options above to a (sort of) real-world situation: Suppose I start listing numbers out loud and ask you to keep them in your head. I start by saying, "11, 16, 13, 12." If you've just been remembering the numbers themselves and nothing more, and then I say, "What's the sum?", you'd have to think to yourself, "OK, what's 11 + 16 + 13 + 12?" before responding, "52." If, on the other hand, you had been keeping track of the sum yourself while I was listing the numbers (i.e., when I said, "11" you thought "11", when I said "16", you thought, "27," and so on), you could answer "52" right away. Then if I say, "OK, now forget the number 16," if you've been keeping track of the sum inside your head you can simply take 16 away from 52 and know that the new sum is 36, rather than taking 16 off the list and them summing up 11 + 13 + 12. So my question is, what other calculations, other than the obvious ones like sum and average, are like this? SECOND EDIT: As an arbitrary example of a statistic that (I'm almost certain) does require iteration -- and therefore cannot be maintained as simply as a sum or average -- consider if I asked you, "how many numbers in this collection are divisible by the min?" Let's say the numbers are 5, 15, 19, 20, 21, 25, and 30. The min of this set is 5, which divides into 5, 15, 20, 25, and 30 (but not 19 or 21), so the answer is 5. Now if I remove 5 from the collection and ask the same question, the answer is now 2, since only 15 and 30 are divisible by the new min of 15; but, as far as I can tell, you cannot know this without going through the collection again. So I think this gets to the heart of my question: if we can divide kinds of statistics into these categories, those that are maintainable (my own term, maybe there's a more official one somewhere) versus those that require iteration to compute any time a collection is changed, what are all the maintainable ones? What I am asking about is not strictly the same as an online algorithm (though I sincerely thank those of you who introduced me to that concept). An online algorithm can begin its work without having even seen all of the input data; the maintainable statistics I am seeking will certainly have seen all the data, they just don't need to reiterate through it over and over again whenever it changes.

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