bezier | 易学教程

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

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问题 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

how to make Sprite follow bezier curve

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问题 Im fairly new to objective-c and sprite kit but i've done games development for a while. Im currently working on a 2d game and i have enemy ships moving from right to left on the screen. Ive been following tutorials for different parts of my game and then adding to it where necessary. I found a tutorial where the in game enemies follow a bezier path and i've managed to implement this in my game however as i'm new to bezier curves i do not fully understand them and the algorithm makes my

Dashed Curves on Html5 Canvas Bezier

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For one of my application I would need to draw a dashed curves on the bezier path in Html5 canvas... The dash' length and gaps in between should be variable... It is achivable in JavaFx, see this link ... I would like to achieve same effect using Html5 canvas. I know how to draw dashed straight lines, but not curved lines along the bezier... Though I am not an expert, I know the bezier drawing algorithm , problem I see with this algorithm is, it allows you to identify coordinates on the bezier using the time parameter which ranges from 0 to 1... This is not sufficient because to draw a dashed

Finding a point on a Bézier curve when given the distance from the start point?

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I created a 4 point Bézier curve, and a distance. Starting at the start point, how do I find the x,y coordinates of a point which is that distance away from the start point? I've looked at the other examples, and from what I can tell, they approximate the values by dividing the curve into several thousand points, then finding the nearest point. This will not work for me. For what I'm doing, I'd like to be accurate to only two decimal places. Below is a simple form of what I have to create my Bézier curve. (The y values are arbitrary, the x values are always 352 pixels apart). If it matters, I

Cheap way of calculating cubic bezier length

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问题 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

Find bezier control-points for curve passing through N points

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问题 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? 回答1: This is a really old question, but I'm leaving this here for people who have the same question in the

Bezier curve through three points

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I have read similar topics in order to find solution, but with no success. What I'm trying to do is make the tool same as can be found in CorelDraw, named "Pen Tool". I did it by connecting Bezier cubic curves, but still missing one feature, which is dragging curve (not control point) in order to edit its shape. I can successfully determine the "t" parameter on the curve where dragging should begin, but don't know how to recalculate control points of that curve. Here I want to higlight some things related to CorelDraw''s PenTool behaviour that may be used as constaints. I've noticed that when

How to create a cubic bezier curve when given N points in 3D?

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So I need to find out where the control points would be for a cubic bezier curve when only knowing points on the curve, the points can lie in 3D. It would be ideal if I could do this for any number of points on the curve. Most of what I have found deals only with 2D, or only for 4 points. Let me see if I understand you: you want an interpolating Bezier curve, going through a given set of points P0 P1 ... but drawn as Bezier curves, with a function like bezier4( nstep, Pj, Cj, Dj, Pj+1 ) -- control points Cj, Dj That is, you want to derive two Bezier control points Cj, Dj for each piece Pj --

OpenGL NURBS surface

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问题 I'm learning OpenGL and I want to get a surface with a slight hump in the middle. I'm currently using this code and im not sure how to adjust the ctrl points to make it the way i want. Its currently like and i would like to have it like this: im not entirely sure what control points i should use and i'm confused on how it works. #include <stdlib.h> #include <GLUT/glut.h> GLfloat ctrlpoints[4][4][3] = { {{-1.5, -1.5, 4.0}, {-0.5, -1.5, 2.0}, {0.5, -1.5, -1.0}, {1.5, -1.5, 2.0}}, {{-1.5, -0.5,

How to find out Y coordinate of specific point in bezier curve in canvas?

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问题 I need to find out Y coordinate of specific point of bezier curve in canvas. Do you know, how to find it out? Thank you 回答1: Using de Casteljau's algorithm you can find the coordinates x and y of a bezier curve for any t, the percentage or interpolation step. So a t of .1 would give you the x and y at 10% of the curve from the beginning. A t of .9 would be 90% from the beginning, and so on. In our cubic bezier we have p0 (point 0), cp0 (control point 0), cp1 (control point 1), and p1 (point 1