bezier

I have 2 points in X,Y + Rotation and I need to calculate a bezier spline (a collection of quadratic beziers) that connects these 2 points smoothly. (see pic) The point represents a unit in a game which can only rotate slowly. So to get from point A to B, it has to take a long path. The attached picture shows quite an exaggeratedly curvy path, but you get the idea. What formulas can I use to calculate such a bezier spline? Just saw that I misunderstood your question. Couldn't you use a single cubic hermite splines instead since you have a start and end point and two directions (tangents)? Are

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 =

To implement a 2D animation I am looking for interpolating values between two key frames with the velocity of change defined by a Bezier curve. The problem is Bezier curve is represented in parametric form whereas requirement is to be able to evaluate the value for a particular time. To elaborate, lets say the value of 10 and 40 is to be interpolated across 4 seconds with the value changing not constantly but as defined by a bezier curve represented as 0,0 0.2,0.3 0.5,0.5 1,1. Now if I am drawing at 24 frames per second, I need to evaluate the value for every frame. How can I do this ? I

I draw lots of quadratic Bézier curves in my OpenGL program. Right now, the curves are one-pixel thin and software-generated, because I'm at a rather early stage, and it is enough to see what works. Simply enough, given 3 control points ( P 0 to P 2 ), I evaluate the following equation with t varying from 0 to 1 (with steps of 1/8) in software and use GL_LINE_STRIP to link them together: B( t ) = (1 - t ) 2 P 0 + 2(1 - t ) t P 1 + t 2 P 2 Where B , obviously enough, results in a 2-dimensional vector. This approach worked 'well enough', since even my largest curves don't need much more than 8

Considering the following nice solution for finding cubic Bézier control points for a curve passing through 4 points: How to find control points for a BezierSegment given Start, End, and 2 Intersection Pts in C# - AKA Cubic Bezier 4-point Interpolation I wonder, if there is a straightforward extension to this for making the Bézier curve pass through N points, for N > 2 and maybe N ≤ 20? This is a really old question, but I'm leaving this here for people who have the same question in the future. @divanov has mentioned that there's no Bezier curve passing through N arbitrary points for N >4. I

An analytical solution for cubic bezier length seems not to exist, but it does not mean that coding a cheap solution does not exist. By cheap I mean something like in the range of 50-100 ns (or less). Does someone know anything like that? Maybe in two categories: 1) less error like 1% but more slow code. 2) more error like 20% but faster? I scanned through google a bit but it doesn't find anything which looks like a nice solution. Only something like divide on N line segments and sum the N sqrt - too slow for more precision, and probably too inaccurate for 2 or 3 segments. Is there anything

绘制过多点的曲线意义重大。但通过试验，QT的PainterPath不是很如意。当多段曲线围成一个区域时，PainterPath内并不包含该区域的所有面积，只包含曲线和其弦构成的面积。 为了解决这一问题，采用如下方法： 1. 生成自己的bezier曲线点集 2. 将多个bezier曲线头尾相联，形成整个polygon的点集 3. 将这个polygon放入一个PainterPath，然后绘制； 4. 这个PainterPath返回留待下次使用。 下面是代码： 1. 头文件graphic.h #ifndef GRAPHIC_H #define GRAPHIC_H #include < QPainter > #include < QPoint > #include < QColor > #include < QVector > //step是步长，即t每次的递增量，traceSet返回本曲线的所有生成点 void getBezier3 ( const QPointF & startPos , const QPointF & controlPos1 , const QPointF & controlPos2 , const QPointF & endPos , const double step , QVector < QPointF >& traceSet ); //画一个多边形的外接曲线