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  • How to draw a global day night curve

    - by Lumis
    I see many applications which have world-clock map, and I would like to make my own to enhance some of my mobile apps. I wonder if anybody has any knowledge where to start, how to draw a curved shadow representing the dawn and the sunset on the globe. See the example: http://aa.usno.navy.mil/imagery/earth/map?year=2012&month=6&day=19&hour=14&minute=47 I think that this curve goes up and down and creates an artic day/night etc Perhaps there is some acceptable approximation formula without a need to load data for each our and each global parallel and meridian...

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  • Tessellating to a curve?

    - by Avi
    I'm creating a game engine, and I'm trying to define a 3D model format I want to use. I haven't come across a format that quite does what I want. My game engine assumes a shader model 5+ environment. By the time I'm finished with it, that won't be a very unreasonable requirement. Because it assumes such a modern environment, I'm going to try and exploit tessellation. The most popular way, it seems, to procedurally increase geometry through tessellation is to tessellate to a height map. This works for a lot of things, but has limitations in that height maps still use up VRAM and also only have finite scalability. So I want to be able to use curves to define what a mesh should tessellate to. The thing is, I have no idea what definition of curves I should use, how I should store it, and how I should tessellate to it. Do I use NURBS curves? Bezier? Hermite? And once I figure that out, is there an algorithm to determine how the tessellation shader should produce and move vertices to match the curve as closely as possible? Is the infinite scalability and lower memory usage when compared to height maps worth the added computational complexity? I'm sorry I'm kind if ignorant as to these matters. I just don't know where to start.

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  • OpenGL: How to draw Bezier curve of degree higher then 8?

    - by maciekp
    I am trying to draw high order Bezier Curve using OpenGL evaluators: glMap1f(GL_MAP1_VERTEX_3, 0.0, 1.0, 3, 30, &points[0][0]); glMapGrid1f(30, 0, 1); glEvalMesh1(GL_LINE, 0, 30); or glBegin(GL_LINE_STRIP); for (int i = 0; i <= 30; i++) glEvalCoord1f((GLfloat) i/30.0); glEnd(); When number of points exceeds 8, curve disappears. How to draw higher order Bezier curve using evaluators?

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  • Learning curve webdevelopment

    - by refro
    At the moment our team has a huge challenge, we're being asked to deliver a new GUI for an embedded controller. De deadline is very tight and is set on april 2013. Our team is very diverse some people are on the level of functional programming (mostly C), others (including myself) also master object oriented programming (C++, C#). We build a prototype with android, although it has its quirks it is mostly just OO. For the future there is a wish to support multiple platforms (Windows, Android, iOS). In my opinion a HTML5 app with a native app shell is the way to go. When gathering more information on the frameworks to use etc it becomes obvious to me a paradigm shift is needed. None of us have a web background so we need to learn from the ground up. The shift from functional to oo took us about 6 months to become productive (and some of the early subsystems were rewritten because they were a total mess) . Can we expect the learning curve to be similar? Can this be pulled off with a webapp? (My feeling says it will already be hard to pull off as a native app which is at the edge of our comfort zone)

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  • Moving an object using its velocity on a closed curve

    - by Futaro
    I want that an object follows a path, in Peggle game there are some pegs that have movement in a closed path. How can i get the same result? I guess that I can use parametric curve but I need use the velocity and not the position (x, y). I use NAPE and I have this in my gameloop: //circunference angle = angle + 1*(Math.PI / 180); movableBall.position.x = radius * Math.cos(angle)+ h; movableBall.position.y = radius * Math.sin(angle)+ k; it's works but I can not control the velocity, each movableBall must have its own velocity. Besides, from docs of NAPE:"Setting the position of a body is equivalent to simply teleporting the body; for instance moving a kinematic body by position is not the way to go about things.." I want to use: movableBall.velocity.x =?? movableBall.velocity.y = ?? The final idea is to follow others paths like the Lemniscate of Bernoulli. Thanks!

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  • Learning curve for web development

    - by refro
    At the moment our team has a huge challenge, we're being asked to deliver a new GUI for an embedded controller. The deadline is very tight and is set on April 2013. Our team is very diverse, some people are on the level of functional programming (mostly C), others (including myself) have mastered object oriented programming (C++, C#). We built a prototype for Android, although it has its quirks, it is mostly just OO. For the future there is a wish to support multiple platforms (Windows, Android, iOS). In my opinion a HTML5 app with a native app shell is the way to go. When gathering more information on the frameworks to use etc., it became obvious to me a paradigm shift is needed. None of us have a web background so we need to learn from the ground up. The shift from functional to OO took us about 6 months to become productive (and some of the early subsystems were rewritten because they were a total mess). Can we expect the learning curve to be similar? Can this be pulled off with a web app? (My feeling says it will already be hard to pull off as a native app which is at the edge of our comfort zone).

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  • How can I find the right UV coordinates for interpolating a bezier curve?

    - by ssb
    I'll let this picture do the talking. I'm trying to create a mesh from a bezier curve and then add a texture to it. The problem here is that the interpolation points along the curve do not increase linearly, so points farther from the control point (near the endpoints) stretch and those in the bend contract, causing the texture to be uneven across the curve, which can be problematic when using a pattern like stripes on a road. How can I determine how far along the curve the vertices actually are so I can give a proper UV coordinate? EDIT: Allow me to clarify that I'm not talking about the trapezoidal distortion of the roads. That I know is normal and I'm not concerned about. I've updated the image to show more clearly where my concerns are. Interpolating over the curve I get 10 segments, but each of these 10 segments is not spaced at an equal point along the curve, so I have to account for this in assigning UV data to vertices or else the road texture will stretch/shrink depending on how far apart vertices are at that particular part of the curve.

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  • introducing automated testing without steep learning curve

    - by esther h
    We're a group of 4 developers on a ajax/mysql/php web application. 2 of us end up focusing most of our efforts on testing the application, as it is time-consuming, instead of actually coding. When I say testing, I mean opening screens and testing links, making sure nothing is broken and the data is correct. I understand there are test frameworks out there which can automate this kind of testing for you, but I am not familiar with any of them (neither is anyone on the team), or the fancy jargon (is it test-driven? behavior-driven? acceptance testing?) So, we're looking to slowly incorporate automated testing. We're all programmers, so it doesn't have to be super-simple. But we don't want something that will take a week to learn... And it has to match our php/ajax platform... What do you recommend?

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  • Curve fitting: Find a CDF (or any function) that satisfies a list of constraints.

    - by dreeves
    I have some constraints on a CDF in the form of a list of x-values and for each x-value, a pair of y-values that the CDF must lie between. We can represent that as a list of {x,y1,y2} triples such as constraints = {{0, 0, 0}, {1, 0.00311936, 0.00416369}, {2, 0.0847077, 0.109064}, {3, 0.272142, 0.354692}, {4, 0.53198, 0.646113}, {5, 0.623413, 0.743102}, {6, 0.744714, 0.905966}} Graphically that looks like this: And since this is a CDF there's an additional implicit constraint of {Infinity, 1, 1} Ie, the function must never exceed 1. Also, it must be monotone. Now, without making any assumptions about its functional form, we want to find a curve that respects those constraints. For example: (I cheated to get that one: I actually started with a nice log-normal distribution and then generated fake constraints based on it.) One possibility is a straight interpolation through the midpoints of the constraints: mids = ({#1, Mean[{#2,#3}]}&) @@@ constraints f = Interpolation[mids, InterpolationOrder->0] Plotted, f looks like this: That sort of technically satisfies the constraints but it needs smoothing. We can increase the interpolation order but now it violates the implicit constraints (always less than one, and monotone): How can I get a curve that looks as much like the first one above as possible? Note that NonLinearModelFit with a LogNormalDistribution will do the trick in this example but is insufficiently general as sometimes there will sometimes not exist a log-normal distribution satisfying the constraints.

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  • Parallel curve like algorithm for graphs

    - by skrat
    Is there a well know algorithm for calculating "parallel graph"? where by parallel graph I mean the same as parallel curve, vaguely called "offset curve", but with a graph instead of a curve. Given this picture how can I calculate points of black outlined polygons?

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  • How does the elliptic-curve version of Diffie-Hellman cryptography work?

    - by cmaduro
    Does the Elliptic curve diffie hellman calculation look any different from the standard one defined here: /* * The basic Diffie-Hellman Key Agreement Equation * * The client initiates * A = g^a mod p * * Sends (g p A) to the server * * The server calculates B * B = g^b mod p * * Sends B back to client * * The client calculates K * K = B^a mod p * * The server calucaltes K * K = A^b mod p * */ Or is it just a specific way of selecting g, a, p and b? How are g,a,p and b selected anyway?

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  • Curve fitting: Find the smoothest function that satisfies a list of constraints.

    - by dreeves
    Consider the set of non-decreasing surjective (onto) functions from (-inf,inf) to [0,1]. (Typical CDFs satisfy this property.) In other words, for any real number x, 0 <= f(x) <= 1. The logistic function is perhaps the most well-known example. We are now given some constraints in the form of a list of x-values and for each x-value, a pair of y-values that the function must lie between. We can represent that as a list of {x,ymin,ymax} triples such as constraints = {{0, 0, 0}, {1, 0.00311936, 0.00416369}, {2, 0.0847077, 0.109064}, {3, 0.272142, 0.354692}, {4, 0.53198, 0.646113}, {5, 0.623413, 0.743102}, {6, 0.744714, 0.905966}} Graphically that looks like this: We now seek a curve that respects those constraints. For example: Let's first try a simple interpolation through the midpoints of the constraints: mids = ({#1, Mean[{#2,#3}]}&) @@@ constraints f = Interpolation[mids, InterpolationOrder->0] Plotted, f looks like this: That function is not surjective. Also, we'd like it to be smoother. We can increase the interpolation order but now it violates the constraint that its range is [0,1]: The goal, then, is to find the smoothest function that satisfies the constraints: Non-decreasing. Tends to 0 as x approaches negative infinity and tends to 1 as x approaches infinity. Passes through a given list of y-error-bars. The first example I plotted above seems to be a good candidate but I did that with Mathematica's FindFit function assuming a lognormal CDF. That works well in this specific example but in general there need not be a lognormal CDF that satisfies the constraints.

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  • Extreme Optimization – Curves (Function Mapping) Part 1

    - by JoshReuben
    Overview ·        a curve is a functional map relationship between two factors (i.e. a function - However, the word function is a reserved word). ·        You can use the EO API to create common types of functions, find zeroes and calculate derivatives - currently supports constants, lines, quadratic curves, polynomials and Chebyshev approximations. ·        A function basis is a set of functions that can be combined to form a particular class of functions.   The Curve class ·        the abstract base class from which all other curve classes are derived – it provides the following methods: ·        ValueAt(Double) - evaluates the curve at a specific point. ·        SlopeAt(Double) - evaluates the derivative ·        Integral(Double, Double) - evaluates the definite integral over a specified interval. ·        TangentAt(Double) - returns a Line curve that is the tangent to the curve at a specific point. ·        FindRoots() - attempts to find all the roots or zeroes of the curve. ·        A particular type of curve is defined by a Parameters property, of type ParameterCollection   The GeneralCurve class ·        defines a curve whose value and, optionally, derivative and integrals, are calculated using arbitrary methods. A general curve has no parameters. ·        Constructor params:  RealFunction delegates – 1 for the function, and optionally another 2 for the derivative and integral ·        If no derivative  or integral function is supplied, they are calculated via the NumericalDifferentiation  and AdaptiveIntegrator classes in the Extreme.Mathematics.Calculus namespace. // the function is 1/(1+x^2) private double f(double x) {     return 1 / (1 + x*x); }   // Its derivative is -2x/(1+x^2)^2 private double df(double x) {     double y = 1 + x*x;     return -2*x* / (y*y); }   // The integral of f is Arctan(x), which is available from the Math class. var c1 = new GeneralCurve (new RealFunction(f), new RealFunction(df), new RealFunction(System.Math.Atan)); // Find the tangent to this curve at x=1 (the Line class is derived from Curve) Line l1 = c1.TangentAt(1);

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  • Smoothing Small Data Set With Second Order Quadratic Curve

    - by Rev316
    I'm doing some specific signal analysis, and I am in need of a method that would smooth out a given bell-shaped distribution curve. A running average approach isn't producing the results I desire. I want to keep the min/max, and general shape of my fitted curve intact, but resolve the inconsistencies in sampling. In short: if given a set of data that models a simple quadratic curve, what statistical smoothing method would you recommend? If possible, please reference an implementation, library, or framework. Thanks SO!

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  • Drawing bezier curve with limited subdivisions in OpenGL

    - by xEnOn
    Is it possible to tell OpenGL to draw a 4 degree (5 control points) bezier curve with 10 subdivisions? I was trying with this: point ctrlpts[] = {..., ..., ..., ...}; glMap1f(GL_MAP1_VERTEX_3, 0, 1, 3, 5, ctrlpts); glBegin(GL_LINE_STRIP); for (i = 0; i <= 30; i++) glEvalCoord1f((GLfloat) i/30.0); glEnd(); But this just draws the curve nicely. I am thinking that I want the algorithm inside the bezier curve to draw only until 10 subdivisions and then stop. The line should look a little facet.

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  • Move an object in the direction of a bezier curve?

    - by Sent1nel
    I have an object with which I would like to make follow a bezier curve and am a little lost right now as to how to make it do that based on time rather than the points that make up the curve. .::Current System::. Each object in my scene graph is made from position, rotation and scale vectors. These vectors are used to form their corresponding matrices: scale, rotation and translation. Which are then multiplied in that order to form the local transform matrix. A world transform (Usually the identity matrix) is then multiplied against the local matrix transform. class CObject { public: // Local transform functions Matrix4f GetLocalTransform() const; void SetPosition(const Vector3f& pos); void SetRotation(const Vector3f& rot); void SetScale(const Vector3f& scale); // Local transform Matrix4f m_local; Vector3f m_localPostion; Vector3f m_localRotation; // rotation in degrees (xrot, yrot, zrot) Vector3f m_localScale; } Matrix4f CObject::GetLocalTransform() { Matrix4f out(Matrix4f::IDENTITY); Matrix4f scale(), rotation(), translation(); scale.SetScale(m_localScale); rotation.SetRotationDegrees(m_localRotation); translation.SetTranslation(m_localTranslation); out = scale * rotation * translation; } The big question I have are 1) How do I orientate my object to face the tangent of the Bezier curve? 2) How do I move that object along the curve without just setting objects position to that of a point on the bezier cuve? Heres an overview of the function thus far void CNodeControllerPieceWise::AnimateNode(CObject* pSpatial, double deltaTime) { // Get object latest pos. Vector3f posDelta = pSpatial->GetWorldTransform().GetTranslation(); // Get postion on curve Vector3f pos = curve.GetPosition(m_t); // Get tangent of curve Vector3f tangent = curve.GetFirstDerivative(m_t); } Edit: sorry its not very clear. I've been working on this for ages and its making my brain turn to mush. I want the object to be attached to the curve and face the direction of the curve. As for movement, I want to object to follow the curve based on the time this way it creates smooth movement throughout the curve.

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  • Drawing a Dragons curve in Python

    - by Connor Franzoni
    I am trying to work out how to draw the dragons curve, with pythons turtle using the An L-System or Lindenmayer system. I no the code is something like the Dragon curve; initial state = ‘F’, replacement rule – replace ‘F’ with ‘F+F-F’, number of replacements = 8, length = 5, angle = 60 But have no idea how to put that into code.

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  • How do I get points on a curve in PHP with log()?

    - by Erick
    I have a graph I am trying to replicate: I have the following PHP code: $sale_price = 25000; $future_val = 5000; $term = 60; $x = $sale_price / $future_val; $pts = array(); $pts[] = array($x,0); for ($i=1; $i<=$term; $i++) { $y = log($x+0.4)+2.5; $pts[] = array($i,$y); echo $y . " <br>\n"; } How do I make the code work to give me the points along the lower line (between the yellow and blue areas)? It doesn't need to be exact, just somewhat close. The formula is: -ln(x+.4)+2.5 I got that by using the Online Function Grapher at http://www.livephysics.com/ Thanks in advance!!

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  • Unexpected performance curve from CPython merge sort

    - by vkazanov
    I have implemented a naive merge sorting algorithm in Python. Algorithm and test code is below: import time import random import matplotlib.pyplot as plt import math from collections import deque def sort(unsorted): if len(unsorted) <= 1: return unsorted to_merge = deque(deque([elem]) for elem in unsorted) while len(to_merge) > 1: left = to_merge.popleft() right = to_merge.popleft() to_merge.append(merge(left, right)) return to_merge.pop() def merge(left, right): result = deque() while left or right: if left and right: elem = left.popleft() if left[0] > right[0] else right.popleft() elif not left and right: elem = right.popleft() elif not right and left: elem = left.popleft() result.append(elem) return result LOOP_COUNT = 100 START_N = 1 END_N = 1000 def test(fun, test_data): start = time.clock() for _ in xrange(LOOP_COUNT): fun(test_data) return time.clock() - start def run_test(): timings, elem_nums = [], [] test_data = random.sample(xrange(100000), END_N) for i in xrange(START_N, END_N): loop_test_data = test_data[:i] elapsed = test(sort, loop_test_data) timings.append(elapsed) elem_nums.append(len(loop_test_data)) print "%f s --- %d elems" % (elapsed, len(loop_test_data)) plt.plot(elem_nums, timings) plt.show() run_test() As much as I can see everything is OK and I should get a nice N*logN curve as a result. But the picture differs a bit: Things I've tried to investigate the issue: PyPy. The curve is ok. Disabled the GC using the gc module. Wrong guess. Debug output showed that it doesn't even run until the end of the test. Memory profiling using meliae - nothing special or suspicious. ` I had another implementation (a recursive one using the same merge function), it acts the similar way. The more full test cycles I create - the more "jumps" there are in the curve. So how can this behaviour be explained and - hopefully - fixed? UPD: changed lists to collections.deque UPD2: added the full test code UPD3: I use Python 2.7.1 on a Ubuntu 11.04 OS, using a quad-core 2Hz notebook. I tried to turn of most of all other processes: the number of spikes went down but at least one of them was still there.

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  • Mapping Hilbert values to 3D points

    - by Alexander Gladysh
    I have a set of Hilbert values (length from the start of the Hilbert curve to the given point). What is the best way to convert these values to 3D points? Original Hilbert curve was not in 3D, so I guess I have to pick by myself the Hilbert curve rank I need. I do have total curve length though (that is, the maximum value in the set). Perhaps there is an existing implementation? Some library that would allow me to work with Hilbert curve / values? Language does not matter much.

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  • Does anyone really understand how HFSC scheduling in Linux/BSD works?

    - by Mecki
    I read the original SIGCOMM '97 PostScript paper about HFSC, it is very technically, but I understand the basic concept. Instead of giving a linear service curve (as with pretty much every other scheduling algorithm), you can specify a convex or concave service curve and thus it is possible to decouple bandwidth and delay. However, even though this paper mentions to kind of scheduling algorithms being used (real-time and link-share), it always only mentions ONE curve per scheduling class (the decoupling is done by specifying this curve, only one curve is needed for that). Now HFSC has been implemented for BSD (OpenBSD, FreeBSD, etc.) using the ALTQ scheduling framework and it has been implemented Linux using the TC scheduling framework (part of iproute2). Both implementations added two additional service curves, that were NOT in the original paper! A real-time service curve and an upper-limit service curve. Again, please note that the original paper mentions two scheduling algorithms (real-time and link-share), but in that paper both work with one single service curve. There never have been two independent service curves for either one as you currently find in BSD and Linux. Even worse, some version of ALTQ seems to add an additional queue priority to HSFC (there is no such thing as priority in the original paper either). I found several BSD HowTo's mentioning this priority setting (even though the man page of the latest ALTQ release knows no such parameter for HSFC, so officially it does not even exist). This all makes the HFSC scheduling even more complex than the algorithm described in the original paper and there are tons of tutorials on the Internet that often contradict each other, one claiming the opposite of the other one. This is probably the main reason why nobody really seems to understand how HFSC scheduling really works. Before I can ask my questions, we need a sample setup of some kind. I'll use a very simple one as seen in the image below: Here are some questions I cannot answer because the tutorials contradict each other: What for do I need a real-time curve at all? Assuming A1, A2, B1, B2 are all 128 kbit/s link-share (no real-time curve for either one), then each of those will get 128 kbit/s if the root has 512 kbit/s to distribute (and A and B are both 256 kbit/s of course), right? Why would I additionally give A1 and B1 a real-time curve with 128 kbit/s? What would this be good for? To give those two a higher priority? According to original paper I can give them a higher priority by using a curve, that's what HFSC is all about after all. By giving both classes a curve of [256kbit/s 20ms 128kbit/s] both have twice the priority than A2 and B2 automatically (still only getting 128 kbit/s on average) Does the real-time bandwidth count towards the link-share bandwidth? E.g. if A1 and B1 both only have 64kbit/s real-time and 64kbit/s link-share bandwidth, does that mean once they are served 64kbit/s via real-time, their link-share requirement is satisfied as well (they might get excess bandwidth, but lets ignore that for a second) or does that mean they get another 64 kbit/s via link-share? So does each class has a bandwidth "requirement" of real-time plus link-share? Or does a class only have a higher requirement than the real-time curve if the link-share curve is higher than the real-time curve (current link-share requirement equals specified link-share requirement minus real-time bandwidth already provided to this class)? Is upper limit curve applied to real-time as well, only to link-share, or maybe to both? Some tutorials say one way, some say the other way. Some even claim upper-limit is the maximum for real-time bandwidth + link-share bandwidth? What is the truth? Assuming A2 and B2 are both 128 kbit/s, does it make any difference if A1 and B1 are 128 kbit/s link-share only, or 64 kbit/s real-time and 128 kbit/s link-share, and if so, what difference? If I use the seperate real-time curve to increase priorities of classes, why would I need "curves" at all? Why is not real-time a flat value and link-share also a flat value? Why are both curves? The need for curves is clear in the original paper, because there is only one attribute of that kind per class. But now, having three attributes (real-time, link-share, and upper-limit) what for do I still need curves on each one? Why would I want the curves shape (not average bandwidth, but their slopes) to be different for real-time and link-share traffic? According to the little documentation available, real-time curve values are totally ignored for inner classes (class A and B), they are only applied to leaf classes (A1, A2, B1, B2). If that is true, why does the ALTQ HFSC sample configuration (search for 3.3 Sample configuration) set real-time curves on inner classes and claims that those set the guaranteed rate of those inner classes? Isn't that completely pointless? (note: pshare sets the link-share curve in ALTQ and grate the real-time curve; you can see this in the paragraph above the sample configuration). Some tutorials say the sum of all real-time curves may not be higher than 80% of the line speed, others say it must not be higher than 70% of the line speed. Which one is right or are they maybe both wrong? One tutorial said you shall forget all the theory. No matter how things really work (schedulers and bandwidth distribution), imagine the three curves according to the following "simplified mind model": real-time is the guaranteed bandwidth that this class will always get. link-share is the bandwidth that this class wants to become fully satisfied, but satisfaction cannot be guaranteed. In case there is excess bandwidth, the class might even get offered more bandwidth than necessary to become satisfied, but it may never use more than upper-limit says. For all this to work, the sum of all real-time bandwidths may not be above xx% of the line speed (see question above, the percentage varies). Question: Is this more or less accurate or a total misunderstanding of HSFC? And if assumption above is really accurate, where is prioritization in that model? E.g. every class might have a real-time bandwidth (guaranteed), a link-share bandwidth (not guaranteed) and an maybe an upper-limit, but still some classes have higher priority needs than other classes. In that case I must still prioritize somehow, even among real-time traffic of those classes. Would I prioritize by the slope of the curves? And if so, which curve? The real-time curve? The link-share curve? The upper-limit curve? All of them? Would I give all of them the same slope or each a different one and how to find out the right slope? I still haven't lost hope that there exists at least a hand full of people in this world that really understood HFSC and are able to answer all these questions accurately. And doing so without contradicting each other in the answers would be really nice ;-)

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