2018年1月10日 · It is not clear whether the "control points" you need is for Bezier curve or for B-spline curve. Since many graphic toolkits only take quadratic/cubic Bezier curves, I will assume this is what you want. For creating multiple Bezier curves interpolating a given set of data points, you can go with Catmull-Rom spline interpolation or natural spline interpolation. Both schemes …

Of course, a point in 4 4 -space can be expressed as a pair of points in 2 2 -space, and they could be thought of as control points. The use of control points really is mainly for the purposes of visualization, to let a person look at a shape and understand how moving the control points around would change the shape.

I have all points where my curve pass through, but I need to get the coordinates of the control points to be able to draw the curve. How can I do to calculate this points?

2017年5月3日 · The simplest heuristic approximation method is the one proposed by Tiller and Hanson. They just offset the legs of the control polygon in perpendicular directions: The blue curve is the original one, and the three blue lines are the legs of its control polygon. We offset these three lines, and intersect/trim them to get the points A and B. The red curve is the offset. …

Could someone give me a reason/proof why the control points do not lie on the Bézier Curve? Perhaps involving Bernstein Polynomials, if possible? Thanks!

2014年10月6日 · So, compute r − 4 r − 4 points on the curve, and compute the b-spline curve that interpolates these points. This requires that you set up a linear system of equations, and solve for the control points. You have to be careful where you put the interpolation points, or you'll get a linear system that's not solvable.

2014年12月20日 · I'm going to describe how to find the control points for the part of the curve between M1 M 1 and M2 M 2, so as to avoid any negative indices. The four control points will be P0,P1,P2,P3 P 0, P 1, P 2, P 3.

2019年5月9日 · I just wish to clarify one thing: you mean the control point positions or the control point values? Because in my experience (where I use B-splines for interpolation, not drawing, so it might be different) they are separate things. More precisely, the control point position is whatever I want, and their value is given by the interpolation procedure.

2021年1月9日 · Is it possible to find the control points of a quadratic bezier curve, given the starting, ending and stationary point?

2016年9月6日 · The parabolas part is easy, because quadratic bezier curves are parabolas. Such curves have only one intermediate control point Q Q, which is the intersection of the tangents at the end points. Cubic bezier curves can emulate the quadratic ones: From each end point, go two-thirds of the line segment toward Q Q, this gives the two cubic control points. Approximating …