bezier

What is the best way to approximate a cubic Bezier curve? Ideally I would want a function y(x) which would give the exact y value for any given x, but this would involve solving a cubic equation for every x value, which is too slow for my needs, and there may be numerical stability issues as well with this approach. Would this be a good solution? Die in Sente Just solve the cubic. If you're talking about Bezier plane curves, where x(t) and y(t) are cubic polynomials, then y(x) might be undefined or have multiple values. An extreme degenerate case would be the line x= 1.0, which can be

I need to find the 2 points of the visual horizon , of a curved face. I have: XYZ of the 4 corner points XYZ of the 2 curved edge bezier points And I need to calculate either: XY of the 2 horizon points XYZ of the 2 horizon points Note: I got a solution the last time I asked this question, but it only found the extrema of the curves, not the horizon points , which changes based on the position and rotation of both curves in respect to each other. You don't say how your surface is defined, only that it is bounded by two quadratic Bézier curves. There are lots of ways to build such a surface,

I have a quadratic bezier curve described as (startX, startY) to (anchorX, anchorY) and using a control point (controlX, controlY). I have two questions: (1) I want to determine y points on that curve based on an x point. (2) Then, given a line-segment on my bezier (defined by two intermediary points on my bezier curve (startX', startY', anchorX', anchorY')), I want to know the control point for that line-segment so that it overlaps the original bezier exactly. Why? I want this information for an optimization. I am drawing lots of horizontal beziers. When the beziers are larger than the screen

Given an arbitrary sequence of points in space, how would you produce a smooth continuous interpolation between them? 2D and 3D solutions are welcome. Solutions that produce a list of points at arbitrary granularity and solutions that produce control points for bezier curves are also appreciated. Also, it would be cool to see an iterative solution that could approximate early sections of the curve as it received the points, so you could draw with it. The Catmull-Rom spline is guaranteed to pass through all the control points. I find this to be handier than trying to adjust intermediate control

I have a cubic bezier curve where the first and last points are given (namely P0(0,0) and P3(1,1)). The other two points are defined like this: cubic-bezier(0.25, 0.1, 0.25, 1.0) (X1, Y1, X2, Y2, also those values must not be smaller or larger than 0 or 1, respectively) Now what would I have to do to get the Y coordinate for a given X, assuming there's only one? (I know that under certain circumstances there can be multiple values, but let's just put them aside. I'm not doing rocket science over here, I just want to be able to get Y multiple times per second to do transitions) I managed to dig

I have a cubic bezier with 2 control points. Starting point and control points are known. Need to get all the points of the curve, given the control, starting and ending points. What I wanna to achieve is ..given a value i from 1 to length of curve.. get the X and Y and alpha (angle) of each point in that position. I cannot find a good reference or working code for that. I'm using javascript. Rahul Banerjee If I understand correctly, you are trying to determine the position and slope (tangent to the curve) of the Bezier, at every point. Let's assume that your start point is (ax, ay), the end