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  • How to calculate the normal of points on a 3D cubic Bézier curve given normals for its start and end points?

    - by Robert
    I'm trying to render a "3D ribbon" using a single 3D cubic Bézier curve to describe it (the width of the ribbon is some constant). The first and last control points have a normal vector associated with them (which are always perpendicular to the tangents at those points, and describe the surface normal of the ribbon at those points), and I'm trying to smoothly interpolate the normal vector over the course of the curve. For example, given a curve which forms the letter 'C', with the first and last control points both having surface normals pointing upwards, the ribbon should start flat, parallel to the ground, slowly turn, and then end flat again, facing the same way as the first control point. To do this "smoothly", it would have to face outwards half-way through the curve. At the moment (for this case), I've only been able to get all the surfaces facing upwards (and not outwards in the middle), which creates an ugly transition in the middle. It's quite hard to explain, I've attached some images below of this example with what it currently looks like (all surfaces facing upwards, sharp flip in the middle) and what it should look like (smooth transition, surfaces slowly rotate round). Silver faces represent the front, black faces the back. Incorrect, what it currently looks like: Correct, what it should look like: All I really need is to be able to calculate this "hybrid normal vector" for any point on the 3D cubic bézier curve, and I can generate the polygons no problem, but I can't work out how to get them to smoothly rotate round as depicted. Completely stuck as to how to proceed!

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  • Learning curve regarding the transition from Windows to Linux from a Java developer perspective [closed]

    - by Geek
    I am a Java developer who has worked on windows platform all through . Now I have shifted job and my new job requires me to do the development work in Red Hat Linux environment . The IDE they use is JDeveloper . I do not have any prior experience in Linux and JDeveloper . So what suggestion would you guys give me so that I can have a smooth and incremental transition from Windows to Linux ? I do not want to short circuit my learning curve . I want to learn it the correct way . Any suggestions regrading any good books,links etc that will help to get started is welcome .

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  • Staying Ahead of the Curve - Deloitte's 2012 Human Capital Trends Webcast | June 13th

    - by Jay Richey, HCM Product Marketing
    Businesses today are calling on HR to leap ahead and help to manage change in the face of complex challenges that touch so many parts of the enterprise. This webinar will provide an overview of eight major Human Capital Trends surfacing in 2012. Understanding the trends — what they mean for both leading HR and for leading the business — is an opportunity for organizations to be proactive and stay ahead of the curve. June 13, 2012 12:00 p.m. – 2:00 p.m. CT Online Featured Speakers: Michael Gretczko Principal, Deloitte Consulting LLP, Human Capital Practice Dan Helfrich Principal, Deloitte Consulting LLP, Federal Human Capital Practice Leader Greg Vert Senior Consultant, Deloitte Consulting Evite & Registration:  http://www.oracle.com/us/dm/75810-wwmk11040178mpp035c007-oem-1633667.html

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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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