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• GraphDisplay : a Bezier based control for graphing functions and curves

  A WPF control for graphing functions, parametric curves, and polar curves

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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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• Calculate cubic bezier T value where tangent is perpendicular to anchor line.

  - by drawnonward

  Project a cubic bezier p1,p2,p3,p4 onto the line p1,p4. When p2 or p3 does not project onto the line segment between p1 and p4, the curve will bulge out from the anchor points. Is there a way to calculate the T value where the tangent of the curve is perpendicular to the anchor line? This could also be stated as finding the T values where the projected curve is farthest from the center of the line segment p1,p4. When p2 and p3 project onto the line segment, then the solutions are 0 and 1 respectively. Is there an equation for solving the more interesting case? The T value seems to depend only on the distance of the mapped control points from the anchor line segment. I can determine the value by refining guesses, but I am hoping there is a better way.

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• How can I draw the control points of a Bézier Path in Java?

  - by Sanoj

  I have created a Path of Bézier curves and it works fine to draw the path. But I don't know How I can draw the Control Points together with the Path. Is that possible or do I have to keep track of them in another datastructure? I am creating the path with: Path2D.Double path = new Path2D.Double(); path.moveTo(0,0); path.curveTo(5, 6, 23, 12, 45, 54); path.curveTo(34, 23, 12, 34, 2, 3); And drawing it with: g2.draw(path);

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• How can I modify my code to line through the bezier control points?

  - by WillyCornbread

  HI all - I am using anchor points and control points to create a shape using curveTo. It's all working fine, but I cannot figure out how to get my lines to go through the center of the control points (blue dots) when the line is not straight. Here is my code for drawing the shape: // clear old line and draw new / begin fill var g:Graphics = graphics; g.clear(); g.lineStyle(2, 0, 1); g.beginFill(0x0099FF,.1); //move to starting anchor point var startX:Number = anchorPoints[0].x; var startY:Number = anchorPoints[0].y; g.moveTo(startX, startY); // Connect the dots var numAnchors:Number = anchorPoints.length; for (var i:Number=1; i<numAnchors; i++) { // curve to next anchor through control g.curveTo(controlPoints[i].x,controlPoints[i].y, anchorPoints[i].x, anchorPoints[i].y); } // Close the loop g.curveTo(controlPoints[0].x,controlPoints[0].y,startX,startY); And the shape I'm drawing for reference: How can I modify my code so that the lines go directly through the blue control points? Thanks in advance! b

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• draw ios quartz 2d path with a varying alpha component

  - by Giovanni

  Hi, I'd like to paint some Bezier curves with the alpha channel that is changing during the curve painting. Right now I'm able to draw bezier paths, with a fixed alpha channel. What I'd like to do is to draw a single bezier curve that uses a certain value of the alpha channel for the first n points of the path another, alpha value for the subsequent m points and so on. The code I'm using for drawing bezier path is: CGContextSetStrokeColorWithColor(context, curva.color.CGColor); .... CGContextAddCurveToPoint(context, cp1.x, cp1.y, cp2.x, cp2.y, endPoint.x, endPoint.y); .... CGContextStrokePath(context); Is there a way to achieve what I'm describing? Many thanks, Giovanni

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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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• how to tesselate bezier triangles?

  - by Cheery

  My concern are quadratic bezier triangles which I'm trying to tesselate for rendering them. I've managed to implement this by subdividing the triangle recursively like described in a wikipedia page. Though I'd like to get more precision to subdivision. The problem is that I'll either get too few subdivisions or too many because the amount of surfaces doubles on every iteration of that algorithm. In particular I would need an adaptive tesselation algorithm that allows me to define the amount of segments at the edges. I'm not sure whether I can get that though so I'd also like to hear about uniform tesselation techniques. Hardest trouble I have trouble with calculating normals for a point in bezier surface, which I'm not sure whether I need, but been trying to solve out.

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• Cocos2d: Move a Sprite along a path/bezier ?

  - by eemceebee

  Hi I need to move a sprite from one CGPoint to another using Cocos2d for the Iphone. The problem is that the animation should be along a bezier. Basically I would use this : id move = [CCMoveTo actionWithDuration:.5f position:ccp(100,200)]; [sprite runAction:move]; Now how can I do this in a non linear path ? Thx

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• How to achieve uniform speed of movement on a bezier curve in cocos 2d?

  - by Andrey Chernukha

  I'm an absolute beginner in cocos2 , actually i started dealing with it yesterday. What i'm trying to do is moving an image along Bezier curve. This is how i do it - (void)startFly { [self runAction:[CCSequence actions: [CCBezierBy actionWithDuration:timeFlying bezier:[self getPathWithDirection:currentDirection]], [CCCallFuncN actionWithTarget:self selector:@selector(endFly)], nil]]; } My issue is that the image moves not uniformly. In the beginning it's moving slowly and then it accelerates gradually and at the end it's moving really fast. What should i do to get rid of this acceleration?

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• Drag and drop in as3 on specific path (ex bezier curve)

  - by abinop

  I need to implement a drag and drop functionality, where I can define and constraint the route of the draggable object. Like in http://www.kirupa.com/forum/showthread.php?t=330302 , only that i have the paths designed and not calculated by a math function. So, in fact, as mouse moves I need to tell the object to follow the custom path/movieclip.

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• How to write outline data into .otf files?

  - by Sorush Rabiee

  I need to edit or completely replace outline data (bezier curves) of OpenType fonts. the input data is an EPS file that i have to write it into one specified glyph of an otf file with a certain scaling. (The glyph is specified by PostScript name OR Unicode value.) I need something like an encoder (or just a library of file structure of OpenType)? where to find about structure of otf and ttf files? Note: python-realated tools and libraries are performed :-?

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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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• UIBezierPath too many paths = too slow?

  - by HHHH

  I have a loop in which I'm adding many (10000+) lines to a UIBezierPath. This seems to be fine, but once I try and render the bezierpath, my device becomes extremely slow and jerky. Is this because I've added too many lines to my path? Adding lines to UIBezierPath - simplified: (this seems fine) [path moveToPoint:CGPointZero]; for (int i = 0; i < 10000; i++ ) { [path addLineToPoint:CGPointMake(i, i)]; } Rendering BeizerPath (Suggested by Rob) - this seems slow. - (void)drawBezierAnimate:(BOOL)animate { UIBezierPath *bezierPath = path; CAShapeLayer *bezier = [[CAShapeLayer alloc] init]; bezier.path = bezierPath.CGPath; bezier.strokeColor = [UIColor blueColor].CGColor; bezier.fillColor = [UIColor clearColor].CGColor; bezier.lineWidth = 2.0; bezier.strokeStart = 0.0; bezier.strokeEnd = 1.0; [self.layer addSublayer:bezier]; if (animate) { CABasicAnimation *animateStrokeEnd = [CABasicAnimation animationWithKeyPath:@"strokeEnd"]; animateStrokeEnd.duration = 100.0; animateStrokeEnd.fromValue = [NSNumber numberWithFloat:0.0f]; animateStrokeEnd.toValue = [NSNumber numberWithFloat:1.0f]; [bezier addAnimation:animateStrokeEnd forKey:@"strokeEndAnimation"]; } } Qs: 1) Is this because I'm adding too many paths too quickly? 2) I want to eventually draw many different lines of different colors, so I assume I would need to create multiple (10000+) UIBezierPaths - would this help or greatly slow the device as well? 3) How would I get around this? Thanks in advance for your help.

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• How could I make geometry advanced operations on bezier paths?

  - by yizzreel

  I have a library that draws regular bezier path figures (complex paths formed of a lot of bezier points), using midpoint approximation. I can draw them without problem, but I need to add support for advanced geometry operations: Nearest point of a curve, intersection, figure contains point, and more importantly, path combinations: difference, intersection, exclusive-or, union, ... Is there any good source to get all this? Thanks

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• How to convert any text/font to its bezier path representation?

  - by yizzreel

  I have a bezier path library to draw complex bezier paths without problem. Now, I need to know how to read a text or font and extract its path information to draw it as a path instead of as text. I came across a C applicaiton, FontForge. It does exactly what I need, picks any font and extract its path information. But what I need to know is how it does it to add that feature to my drawing library.

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• Multiple circles -> One Polygon?

  - by Josh

  Using Google Maps API v3, I was able to create multiple google.maps.Circle objects on my map. However, I now need to "connect" them somehow. I have the following map with multiple circles: I now need to get it to look something like this: I've looked all over the Internet for solutions, but to no avail. Any ideas?

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• Draw an Inset NSShadow and Inset Stroke

  - by Alexsander Akers

  I have an NSBezierPath and I want to draw in inset shadow (similar to Photoshop) inside the path. Is there anyway to do this? Also, I know you can -stroke paths, but can you stroke inside a path (similar to Stroke Inside in Photoshop)? Update This is the code I'm using. The first part makes a white shadow downwards. The second part draws the gray gradient. The third part draws the black inset shadow. Assume path is an NSBezierPath instance and that clr(...) returns an NSColor from a hex string. NSShadow * shadow = [NSShadow new]; [shadow setShadowColor: [NSColor colorWithDeviceWhite: 1.0f alpha: 0.5f]]; [shadow setShadowBlurRadius: 0.0f]; [shadow setShadowOffset: NSMakeSize(0, 1)]; [shadow set]; [shadow release]; NSGradient * gradient = [[NSGradient alloc] initWithColorsAndLocations: clr(@"#262729"), 0.0f, clr(@"#37383a"), 0.43f, clr(@"#37383a"), 1.0f, nil]; [gradient drawInBezierPath: path angle: 90.0f]; [gradient release]; [NSGraphicsContext saveGraphicsState]; [path setClip]; shadow = [NSShadow new]; [shadow setShadowColor: [NSColor redColor]]; [shadow setShadowBlurRadius: 0.0f]; [shadow setShadowOffset: NSMakeSize(0, -1)]; [shadow set]; [shadow release]; [path stroke]; [NSGraphicsContext restoreGraphicsState]; Here you can see a gradient fill, a white drop shadow downwards, and a black inner shadow downwards.

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• Cocos2d rotating sprite while moving with CCBezierBy

  - by marcg11

  I've done my moving actions which consists of sequences of CCBezierBy. However I would like the sprite to rotate by following the direction of the movement (like an airplane). How sould I do this with cocos2d? I've done the following to test this out. CCSprite *green = [CCSprite spriteWithFile:@"enemy_green.png"]; [green setPosition:ccp(50, 160)]; [self addChild:green]; ccBezierConfig bezier; bezier.controlPoint_1 = ccp(100, 200); bezier.controlPoint_2 = ccp(400, 200); bezier.endPosition = ccp(300,160); [green runAction:[CCAutoBezier actionWithDuration:4.0 bezier:bezier]]; In my subclass: @interface CCAutoBezier : CCBezierBy @end @implementation CCAutoBezier - (id)init { self = [super init]; if (self) { // Initialization code here. } return self; } -(void) update:(ccTime) t { CGPoint oldpos=[self.target position]; [super update:t]; CGPoint newpos=[self.target position]; float angle = atan2(newpos.y - oldpos.y, newpos.x - oldpos.x); [self.target setRotation: angle]; } @end However it rotating, but not following the path...

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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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• How do I rotate a sprite with ccbezierTo in cocos2d-x?

  - by user1609578

  In cocos2d-x, I move a sprite with ccbezierTo like this: // use for ccbezierTo bezier.controlPoint_1 = ccp(m_fish->getPositionX() + 200, visibleSize.height/2 + 300); bezier.controlPoint_2 = ccp(m_fish->getPositionX() + 400, visibleSize.height/2 - 300); bezier.endPosition = ccp(m_fish->getPositionX() + 600,visibleSize.height/2); bezier1.controlPoint_1 = ccp(m_fish->getPositionX() + 800, visibleSize.height/2 + 300); bezier1.controlPoint_2 = ccp(m_fish->getPositionX() + 1000, visibleSize.height/2 - 300); bezier1.endPosition = ccp(m_fish->getPositionX() + 1200,visibleSize.height/2); bezierForward = CCBezierTo::create(6, bezier); nextBezier = CCBezierTo::create (6,bezier1); m_fish->runAction(CCSequence::create( bezierForward, nextBezier, NULL)); How can I make my sprite rotate while moving it with CCBezierTo?

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• How do I cache jQuery selections?

  - by David

  I need to cache about 100 different selections for animating. The following is sample code. Is there a syntax problem in the second sample? If this isn't the way to cache selections, it's certainly the most popular on the interwebs. So, what am I missing? note: p in the $.path.bezier(p) below is a correctly declared object passed to jQuery.path.bezier (awesome animation library, by the way) This works $(document).ready(function() { animate1(); animate2(); }) function animate1() { $('#image1').animate({ path: new $.path.bezier(p) }, 3000); setTimeout("animate1()", 3000); } function animate2() { $('#image2').animate({ path: new $.path.bezier(p) }, 3000); setTimeout("animate2()", 3000); } This doesn't work var $one = $('#image1'); //problem with syntax here?? var $two = $('#image2'); $(document).ready(function() { animate1(); animate2(); }) function animate1() { $one.animate({ path: new $.path.bezier(p) }, 3000); setTimeout("animate1()", 3000); } function animate2() { $two.animate({ path: new $.path.bezier(p) }, 3000); setTimeout("animate2()", 3000); }

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• How to implement curved movement while tracking the appropriate angle?

  - by Vexille

  I'm currently coding a 2D top-down car game which will be turn-based. And since it's turn-based, the cars won't be controlled directly (i.e. with a simple velocity vector that adjusts its angle when the player wants to turn), but instead it's movement path has to be planned beforehand, and then the car needs to follow the path when the turn ends (think Steambirds). This question has some interesting information, but its focus is on homing-missile behaviour, which I kinda had figured out, but doesn't really apply to my case, I think, since I need to show a preview of the path when the player is planning his turn, then have the car follow that path. In that same question, there's an excellent answer by Andrew Russel which mentions Equations of Motion and Bézier's Curve. Some of his other suggestions of implementation are specific to XNA though, so they don't help much (I'm using Marmalade SDK). If I assume Bézier's Curve as the solution of choice, I'm left with one specific problem: I'll have the car's position (the first endpoint) and the target/final position (the last endpoint), but what should I use as the control point (assuming a square/quadratic curve)? And whether I use Bézier's Curve or another parametric equation, I'd still be left with another issue: the car can't just follow the curve, it must turn (i.e. adjust its angle) accordingly. So how can I figure out which way the car should be pointing to at any given point in the curve?

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• How to prevent latex memory overflow

  - by drasto

  I've got a latex macro that makes small pictures. In that picture I need to draw area. Borders of that area are quadratic bezier curves and that area is to be filled. I did not know how to do it so currently I'm "filling" the area by drawing a plenty of bezier curves inside it... This slows down typeseting and when a macro is used multiple times (so tex is drawing really a lot of quadratic bezier curves) it produces following error: ! TeX capacity exceeded, sorry [main memory size=3000000]. How can I prevent this error ? (by freeing memory after macro or such...) Or even better how do I fill the area determined by two quadratic bezier curves? Code that produces error: \usepackage{forloop} \usepackage{picture} \usepackage{eepic} ... \linethickness{\lineThickness\unitlength}% \forloop[\lineThickness]{cy}{\cymin}{\value{cy} < \cymax}{% \qbezier(\ax, \ay)(\cx, \value{cy})(\bx, \by)% }% Here are some example values for variables: \setlength{\unitlength}{0.01pt} \lineThickness=20 %cy is just a counter - inital value is not important \cymin=450 \cymax=900 %from following only the difference between \ax and \bx is important \ax=0 \ay=0 \bx=550 \by=0 Note: To reproduce the error this code have to execute approximately 150 times (could be more depending on your latex memory settings). Thanks a lot for any help

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• Transform shape built of contour splines to simple polygons

  - by Cheery

  I've dumped glyphs from truetype file so I can play with them. They have shape contours that consist from quadratic bezier curves and lines. I want to output triangles for such shapes so I can visualize them for the user. Traditionally I might use libfreetype or scan-rasterise this kind of contours. But I want to produce extruded 3D meshes from the fonts and make other distortions with them. So, how to polygonise shapes consisting from quadratic bezier curves and lines? There's many contours that form the shape together. Some contours are additive and others are subtractive. The contours are never open. They form a loop. (Actually, I get only contour vertices from ttf glyphs, those vertices define whether they are part of the curve or not. Even though it is easy to decompose these into bezier curves and lines, knowing the data is represented this way may be helpful for polygonizing the contours to triangles)

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