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  • An extended Bezier Library or Algorithms of bezier operations

    - by Sorush Rabiee
    Hi, Is there a library of data structures and operations for quadratic bezier curves? I need to implement: bezier to bitmap converting with arbitrary quality optimizing bezier curves common operations like subtraction, extraction, rendering etc. languages: c,c++,.net,python Algorithms without implementation (pseudocode or etc) could be useful too. (especially optimization)

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  • Quaddratic Bezier Curve: Calculate Tangent

    - by stefan.at.wpf
    Hello, I have have a quadratic bezier curve and I want to calculate the slope of the tangent in a given point. For example, let it be the middlepoint of the quadratic bezier curve, therefore t=0.5 (please see the link below for a picture of this). I've calculated the first derivation of the formula for the quadratic bezier curve, however I get 400 as value for the slope, though it should be 0. Maybe I'm using the first derivation in a wrong way? I know I could also calculate the tangents using trigonometric functions, however I'd like to do it using the first derivation, shouldn't this be possible? Thanks for any hint! For clarification / please note: I'm interested in a general way to get the slope in a arbitrary given point on a quadratic bezier curve, not only to get the tangent in the start- and end point. A picture of my problem including the text above: http://cid-0432ee4cfe9c26a0.skydrive.live.com/self.aspx/%c3%96ffentlich/Quadratic%20Bezier%20Curve.pdf Thank you very much for any hint!

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  • Quadratic Bezier Curve: Calculate Tangent

    - by stefan.at.wpf
    I have a quadratic bezier curve and I want to calculate the slope of the tangent in a given point. For example, let it be the middlepoint of the quadratic bezier curve, therefore t=0.5 (please see the link below for a picture of this). I've calculated the first derivative of the formula for the quadratic bezier curve; however I get 400 as value for the slope, though it should be 0. Maybe I'm using the first derivative in a wrong way? I know I could also calculate the tangents using trigonometric functions; however I'd like to do it using the first derivative, shouldn't this be possible? Thanks for any hint! For clarification / please note: I'm interested in a general way to get the slope in a arbitrary given point on a quadratic bezier curve, not only to get the tangent in the start- and end point. A picture of my problem including the text above: http://cid-0432ee4cfe9c26a0.skydrive.live.com/self.aspx/%c3%96ffentlich/Quadratic%20Bezier%20Curve.pdf Thank you very much for any hint!

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  • Reverse engineering a bezier curve

    - by Martin
    Given a few sample points on a bézier curve, is it possible to work out the set of possible parameters of the curve? In my specific application there is a limited set of endpoints the curve may have, so I want to generate the set of possible curves, enumerate all of them and pick out all the ones which may end on a valid end point.

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  • How to convert closed bezier curves to Bitmaps?

    - by Sorush Rabiee
    I need an algorithm to convert a closed bezier curve (perhaps self-crossing) to a binary bitmap: 0 for inside pixels and 1 for outside. I'm writing a code that needs to implement some operations on bezier curves, could anybody give me some resources or tutorials about beziere? Wikipedia and others didn't say anything about optimization, subtracting, union, knot insertion and deletion and other operations :-)

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  • Quadratic bezier curve: Y coordinate for a given X ?

    - by stefan.at.wpf
    Hello, I have a quadratic bezier curve and I need the Y coordinate of a point on the bezier curve for a given X coordinate. I know that in pure maths this can be easily done, but I'm wondering is there's a simple / another way for this in C# / WPF? Is it possible to get the single points used by C# / WPF for drawing the bezier curve and then maybe just loop them and compare the X coordinate of each point with the given X coordinate? BTW for the mathematical way it would be good to know which step for the parameter t of the bezier curve has been choosen by C# / WPF? Any chance to find this out? Probably t is just scaled by / steps for t are 1/(distance of P0 and P2) ? Thank you very much for any hint!

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  • Spring 3 learning curve

    - by Lucian Enache
    I'm coming from a Struts background and I was considering learning the Spring framework. How long would it usually take to get familiarity with Spring Core and Spring MVC modules, keeping in mind that I come from a Struts 1 background ? Beside those two modules are there any other modules that I should focus on ? I know that the time is relative given that everyone has a different learning curve.

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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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  • How can I boost my C# learning curve?

    - by MSU
    I have been learning programming, mostly C# and .net stuff. And I have target to become a fulltime .NET developer. But I am feeling that learning Graph is very slow, I have been learning C# programming, doing some coding everyday, but how I can learn very fast and increase my skills rapidly? I know there should be a balance of coding and reading, as without reading I can't code and without coding I can't increase my skills. SO, I am requesting here suggesting from experts on how I bring more pace to my learning curve? I intend to give 4-6 hours daily for this and on weekends 10+ hours.

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  • Linux Learning curve for a 'Lifetime' windows user [closed]

    - by gary
    I am using windows for almost 8-10 years and have never worked on linux. Mostly i used to work in VB, VC++ MFC and little bit of .NET(C# and VB) so i didn't bother about Linux. But now when i got an opportunity to work with linux i dont want to miss it, here are my questions : Where can i find useful resources for Linux newbies? Which books/Tutorials will you suggest to start? Which distro shall i use? What was your experience while moving from Windows to Linux?

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  • ASP.NET and C# learning curve [closed]

    - by Mashael
    My friend wants to become a web developer. However, he doesn't know how to start if he is going to become ASP.NET developer. He found a book which is titled ' Beginning ASP.NET 4: in C# and VB (Wrox Programmer to Programmer) by Imar Spaanjaars' but he is not sure if this will be right start or not because he has know knowledge in OOP programming and whether he has to learn C# first and read such book or is it OK to start with such that book assuming that the book will teach some fundamentals in C#!

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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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  • How do I draw part of parabola using iText ? Or how do I create quadratic bezier curves from cubic b

    - by drasto
    I need to draw a shape whose boundaries are parts of parabola (that is quadratic bezier curves) using iText. I have found only method for drawing cubic bezier curves in PdfContentByte class. So how do I draw quadratic bezier curves using iText ? One way would be to use method for cubic bezier curves. Is it possible to draw quadratic bezier curves as a cubic bezier curves (with 2 control points). I gues it is but I cannot make up the formula. If somebody states the formula tu "translate" cubic bezier curves to quadratic that would solve the problem. Any other ways to draw quadratic bezier(parts of parabola) curves in iText (and filled shapes made of them) is also the solution. Thanks

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  • Drawing path by Bezier curves

    - by OgreSwamp
    Hello. I have a task - draw smooth curve input: set of points (they added in realtime) current solution: I use each 4 points to draw qubic Bezier curve (1 - strart, 2 and 3rd - control points, 4- end). End point of each curve is start point for the next one. problem: at the curves connection I often have "fracture" (angle) Can you tell me, how to connect my points more smooth? Thanks!

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  • Modifying and Manipulating a interactive bezier curve

    - by rachel
    This is a homework question and I'm having a lot of trouble with it - I've managed to do some of it but still cant finish it - can i Please get some help. Q1. Bezier Curves The following example allows you to interactively control a bezier curve by dragging the control points Cubic.java Replace the call to draw the cubic shape (big.draw(cubic)), by your own function to draw a bezier by the recursive split method. Finally, add the ability to create a longer Bezier curve by adding more control points to create a second curve. Cubic.java import java.awt.*; import javax.swing.*; import java.awt.event.*; import java.applet.Applet; import java.awt.geom.*; import java.awt.image.BufferedImage; public class Cubic extends JApplet{ static protected JLabel label; CubicPanel cubicPanel; public void init(){ //Initialize the layout. getContentPane().setLayout(new BorderLayout()); cubicPanel = new CubicPanel(); cubicPanel.setBackground(Color.white); getContentPane().add(cubicPanel); label = new JLabel("Drag the points to adjust the curve."); getContentPane().add("South", label); } public static void main(String s[]) { JFrame f = new JFrame("Cubic"); f.addWindowListener(new WindowAdapter() { public void windowClosing(WindowEvent e) {System.exit(0);} }); JApplet applet = new Cubic(); f.getContentPane().add(applet, BorderLayout.CENTER); applet.init(); f.setSize(new Dimension(350,250)); f.setVisible(true); } } class CubicPanel extends JPanel implements MouseListener, MouseMotionListener{ BufferedImage bi; Graphics2D big; int x, y; Rectangle area, startpt, endpt, onept, twopt, rect; CubicCurve2D.Double cubic = new CubicCurve2D.Double(); Point2D.Double start, end, one, two, point; boolean firstTime = true; boolean pressOut = false; public CubicPanel(){ setBackground(Color.white); addMouseMotionListener(this); addMouseListener(this); start = new Point2D.Double(); one = new Point2D.Double(); two = new Point2D.Double(); end = new Point2D.Double(); cubic.setCurve(start, one, two, end); startpt = new Rectangle(0, 0, 8, 8); endpt = new Rectangle(0, 0, 8, 8); onept = new Rectangle(0, 0, 8, 8); twopt = new Rectangle(0, 0, 8, 8); } public void mousePressed(MouseEvent e){ x = e.getX(); y = e.getY(); if(startpt.contains(x, y)){ rect = startpt; point = start; x = startpt.x - e.getX(); y = startpt.y - e.getY(); updateLocation(e); } else if(endpt.contains(x, y)){ rect = endpt; point = end; x = endpt.x - e.getX(); y = endpt.y - e.getY(); updateLocation(e); } else if(onept.contains(x, y)){ rect = onept; point = one; x = onept.x - e.getX(); y = onept.y - e.getY(); updateLocation(e); } else if(twopt.contains(x, y)){ rect = twopt; point = two; x = twopt.x - e.getX(); y = twopt.y - e.getY(); updateLocation(e); } else { pressOut = true; } } public void mouseDragged(MouseEvent e){ if(!pressOut) { updateLocation(e); } } public void mouseReleased(MouseEvent e){ if(startpt.contains(e.getX(), e.getY())){ rect = startpt; point = start; updateLocation(e); } else if(endpt.contains(e.getX(), e.getY())){ rect = endpt; point = end; updateLocation(e); } else if(onept.contains(e.getX(), e.getY())){ rect = onept; point = one; updateLocation(e); } else if(twopt.contains(e.getX(), e.getY())){ rect = twopt; point = two; updateLocation(e); } else { pressOut = false; } } public void mouseMoved(MouseEvent e){} public void mouseClicked(MouseEvent e){} public void mouseExited(MouseEvent e){} public void mouseEntered(MouseEvent e){} public void updateLocation(MouseEvent e){ rect.setLocation((x + e.getX())-4, (y + e.getY())-4); point.setLocation(x + e.getX(), y + e.getY()); checkPoint(); cubic.setCurve(start, one, two, end); repaint(); } public void paintComponent(Graphics g){ super.paintComponent(g); update(g); } public void update(Graphics g){ Graphics2D g2 = (Graphics2D)g; Dimension dim = getSize(); int w = dim.width; int h = dim.height; if(firstTime){ // Create the offsecren graphics to render to bi = (BufferedImage)createImage(w, h); big = bi.createGraphics(); // Get some initial positions for the control points start.setLocation(w/2-50, h/2); end.setLocation(w/2+50, h/2); one.setLocation((int)(start.x)+25, (int)(start.y)-25); two.setLocation((int)(end.x)-25, (int)(end.y)+25); // Set the initial positions of the squares that are // drawn at the control points startpt.setLocation((int)((start.x)-4), (int)((start.y)-4)); endpt.setLocation((int)((end.x)-4), (int)((end.y)-4)); onept.setLocation((int)((one.x)-4), (int)((one.y)-4)); twopt.setLocation((int)((two.x)-4), (int)((two.y)-4)); // Initialise the CubicCurve2D cubic.setCurve(start, one, two, end); // Set some defaults for Java2D big.setColor(Color.black); big.setStroke(new BasicStroke(5.0f)); big.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); area = new Rectangle(dim); firstTime = false; } // Clears the rectangle that was previously drawn. big.setColor(Color.white); big.clearRect(0, 0, area.width, area.height); // Set the colour for the bezier big.setPaint(Color.black); // Replace the following line by your own function to // draw the bezier specified by start, one, two, end big.draw(cubic); // Draw the control points big.setPaint(Color.red); big.fill(startpt); big.setPaint(Color.magenta); big.fill(endpt); big.setPaint(Color.blue); big.fill(onept); big.setPaint(new Color(0, 200, 0)); big.fill(twopt); // Draws the buffered image to the screen. g2.drawImage(bi, 0, 0, this); } /* Checks if the rectangle is contained within the applet * window. If the rectangle is not contained withing the * applet window, it is redrawn so that it is adjacent to the * edge of the window and just inside the window. */ void checkPoint(){ if (area == null) { return; } if((area.contains(rect)) && (area.contains(point))){ return; } int new_x = rect.x; int new_y = rect.y; double new_px = point.x; double new_py = point.y; if((rect.x+rect.width)>area.getWidth()){ new_x = (int)area.getWidth()-(rect.width-1); } if(point.x > area.getWidth()){ new_px = (int)area.getWidth()-1; } if(rect.x < 0){ new_x = -1; } if(point.x < 0){ new_px = -1; } if((rect.y+rect.width)>area.getHeight()){ new_y = (int)area.getHeight()-(rect.height-1); } if(point.y > area.getHeight()){ new_py = (int)area.getHeight()-1; } if(rect.y < 0){ new_y = -1; } if(point.y < 0){ new_py = -1; } rect.setLocation(new_x, new_y); point.setLocation(new_px, new_py); } }

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  • Drawing half of a Bezier path in Raphael

    - by Fibericon
    Let's say I have a cubic Bezier path as follows (formatted for use with the Raphael path function): M55 246S55 247 55 248 Just an example. This was taken from my drawing application, where I use the cursor to draw a line when the user holds the mouse button down, kind of like a pencil or marker. I'm using jquery's mousemove event to draw the line between two points every time the user moves the mouse. There is another (the reference point) that is taken before the line is drawn, so that the Bezier curve can be created. Here's my question: is it possible to make Raphael only draw half of a given path? I'm aware of the getSubpath() function, but if my understanding of Bezier curves is correct, it would be rather difficult to calculate the second argument. The problem with the animate function is that it creates double lines (that is, it creates the curved line that I want, and the boxy line around it which should not be shown, possibly because the mouse is being moved faster than the animation can handle). Of course, if my approach itself is flawed in some way (or my understanding of the possible solutions), I'd like to hear it. Any help would be appreciated.

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  • Finding the Formula for a Curve

    - by Mystagogue
    Is there a program that will take "response curve" values from me, and provide a formula that approximates the response curve? It would be cool if such a program would take a numeric "percent correct" (perhaps with a standard deviation) so that it returns simplified formulas when laxity is permissable, and more precise (viz. complex) formulas when the curve needs to be approximated closely. My interest is to play with the response curve values and "laxity" factor, until such a tool spits out a curve-fit formula simple enough that I know it will be high performance during machine computations.

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  • Generating Bezier Control Points for an object

    - by E.F
    Hello everyone, I'm trying to draw objects using Bezier surfaces with openGL's evaluators. I am struggling with defining the control points for my objects. Can anyone please suggest ways to get the control points for an object? Is there some program that I can use to design my object then import the control points into a file that I can use in my application?

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  • Drawing a clamped uniform cubic B-spline using Cairo

    - by Tamás
    I have a bunch of coordinates which are the control points of a clamped uniform cubic B-spline on the 2D plane. I would like to draw this curve using Cairo calls (in Python, using Cairo's Python bindings), but as far as I know, Cairo supports Bézier curves only. I also know that the segments of a B-spline between two control points can be drawn using Bézier curves, but I can't find the exact formulae anywhere. Given the coordinates of the control points, how can I derive the control points of the corresponding Bézier curves? Is there any efficient algorithm for that?

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  • How do bezier handles work?

    - by user146780
    On Wikipedia I found information about bezier curves and made a function to generate the inbetween points for a bezier polygon. I noticed that Expression Design uses bezier handles. This allows a circle to be made with 4 points each with a bezier handle. I'm just not sure mathematically how this works in relation with the formula for bezier point at time T. How do these handle vectors work to modify the shape? Basically what's there relation to the bezier formula? Thanks

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  • What is the maximum distance from an anchor point to a bezier curve?

    - by drawnonward
    Given a cubic bezier curve P0,P1,P2,P3 with the following properties: • Both P1 and P2 are on the same side of the line formed by P0 and P3. • P2 can be projected onto the line segment formed by P0 and P3 but P1 cannot. What is the T value for the point on the curve farthest from P3? Here is an image with an example curve. The curve bulges on the left, so there is a point on the curve farther from P3 than P0. I found this reference for finding the minimum distance from an arbitrary point to a curve. Is trial and error the only way to solve for maximum distance as well? Does it make any difference that the point is an anchor on the curve? Thanks

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