bezier

问题 I want to split a bezier curve into a polygonal chain with n straight lines. The number of lines being dependent on a maximum allowed angle between 2 connecting lines. I'm looking for an algorithm to find the most optimal solution (ie to reduce as much as possible the number of straight lines). I know how to split a bezier curve using Casteljau or Bernstein polynomals. I tried dividing the bezier into half calculate the angle between the straight lines, and split again if the angle between

问题 The quadratic/cubic bézier curve code I find via google mostly works by subdividing the line into a series of points and connects them with straight lines. The rasterization happens in the line algorithm, not in the bézier one. Algorithms like Bresenham's work pixel-by-pixel to rasterize a line, and can be optimized (see Po-Han Lin's solution). What is a quadratic bézier curve algorithm that works pixel-by-pixel like line algorithms instead of by plotting a series of points? 回答1: A variation

问题 I'm writing a BezierPath class that contains a list of BezierPoints. Each BezierPoint has a position, an inTangent and an outTangent: BezierPath contains functions for getting linear positions and tangents from the path. My next step is to provide functionality for getting the normals from the path. I'm aware that any given line in 3D is going to have an unlimited number of lines that are perpendicular, so there isn't going to be a set answer. My aim is for the user to be able to specify

问题 This is what I am trying to achieve--GRASS Animation(Desired animation) This is where the project is standing currently --My hair animation This is a more structurised code of the above code --My hair animation(by markE)--markE`s code of hair animation PROBLEM:-- I am able to give movements to hairs but animation should be more like wavy grass like freeflowing.Its not very smooth now.What can be done to make the hairs flow in more natural manner. Please provide me with a small sample if

问题 I've been struggling looking for an understandable way to do this. I have four points, a StartPt, EndPoint, and Intersection points to represent the peak and valley in the bezier. The BezierSegment in C# requires start, controlPoint 1, controlPoint 2, endpoint - however I don't have any control points I only have these two points that lie along the bezier curves (i'm calling them intersection points above)... how can I calculate the two control points? Thanks in advance, this has been driving

问题 By stroke of the cubic bezier curve I mean rendering a curve 'A' with a specific line width 'w'. How can I derive other cubic bezier curves that describe the outline of the stroke of bezier 'A' ? 回答1: Ohhh. You want to get the offset-curves of an bezier curve. Bad news. this is hard because these curves can't be simply derived numerical. They contain all kinds of intersections, loops and other nasty stuff. There are some approximations though. The best approach I've read so far is from a

问题 Suppose I have a set of x,y coordinates that mark points along contour. Is there a way that I can build a spline representation of the contour that I can evaluate at a particular position along its length and recover interpolated x,y coordinates? It is often not the case that there is a 1:1 correspondence between X and Y values, so univariate splines are no good to me. Bivariate splines would be fine, but as far as I can tell all of the functions for evaluating bivariate splines in scipy

问题 I need to draw concentric arcs of various sizes using raphael.js. I tried to understand the code behind http://raphaeljs.com/polar-clock.html, which is very similar to what I want, but, whithout comments, it is quite difficult to fathom. Ideally, I would need a function that creates a path that is at a given distance from some center point, starts at some angle and ends at some other angle. 回答1: That answer is ok, but cant be animated. I ripped the important stuff out of polar-clock for you.

问题 We have a start point (x, y) and a circle radius. There also exists an engine that can create a path from Bézier curve points. How can I create a circle using Bézier curves? 回答1: As already said: there is no exact representation of the circle using Bezier curves. To complete the other answers : for Bezier curve with n segments the optimal distance to the control points, in the sense that the middle of the curve lies on the circle itself, is (4/3)*tan(pi/(2n)) . So for 4 points it is (4/3)*tan

问题 I originally posted a much simpler (and less helpful) question, and have edited this to be more specific. This animation from wikipedia shows basically what I want to accomplish, however - I'm hoping to have it flipped around, where it starts progressing more towards the destination and "up" (in this image), and then arcs more directly to the end point. However, I only have access to a starting point and ending point, what I am hoping to do is be able to determine the other points by