Mathematics Stack Exchange
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Questions tagged [bezier-curve]

Questions on Bézier curves, which are used for numerical analysis with applications in computer graphics.

Bézier curves are widely used in computer graphics to model smooth curves by using control points. Affine transformations of the curve correspond to affine transformations of the control points. The curve is contained in the convex hull of its control points. On computers, these points are often graphically displayed and used to manipulate the curve by dragging the control points.

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Bezier Control points problem

I would like to construct a cubic Bezier curve. For this, I assume a known starting point $K_0$ as well as a known end point $K_2$. I would like my resulting curve to pass through another known point $K_1$. I also know the angles of the curve at the…
user729921
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get 2nd and 3rd control points of a Cubic Bezier Curve fit in a rectangle

I would like to fit a Cubic Bezier Curve in a rectangle, and wondering how to get the 2nd and 3rd control points's Y value, illustrated below: (Sorry the rectangle is bit distorted.) Basically, given the position of first point (x1, y1), fourth…
dli
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Model Bézier curve of N control points with more Bézier curve of n-1 points.

Given a Bézier curve defined by N control points. Is it possible to model that curve using a finite amount of Bézier points with less than N control points? eg. Model a 4 control point Bézier with 2, 3 control points Bézier.
user2475269
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approximating a b-spline with a single bezier curve of any degree

suppose we have b-spline composed of several bezier curves with known control points and nodes and is not necessarily smooth. Is there a way to create a single bezier curve of any degree that will fairly accurately approximate the b-spline? I…
Om Nomni
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Bézier curve for some nodes

How do I write the Bézier curve with the nodes $(x_1,y_1),(x_2,y_2)$and control points $(x_3,y_3),(x_4,y_4)$? I know how to write it as parametric form with $x(t)$ and $y(t)$, but I have no idea how to write it directly
user135671
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Approximation with Bézier curves

I have just completed basic research on Bézier curves, mainly focused on the characteristics of Bernstein polynomials and the de Casteljau algorithm. Now I am supposed to approximate $\sin(x)$ and $\frac{\sin(x)}{x}$ using Bézier curves. How is…
Diego Ibarra
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Bezier Curve and derivatives

Consider the following polynomial in Bezier form: $$p(u)=\sum_{i=0}^n b_i B_i^n \Big(\frac{u-a}{b-a}\Big)$$ I am supposed to derive Bezier points $b_i$ for $i=0,1,...,n$ in general form, assuming that I know the values of the function, first…
Ekber
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Calculate new points after Bezier Curve

I have this graph: graph without tension I'm using linearGradient to color the areas between the lines. I'm calculating the cutting point's x, and then calculating the offset for where I want to stop the previous color and start the new one (it will…
Ben
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Cubic Bezier curve - how to make height always the same as a given vertical line

I have a cubic bezier curve that is always drawn from a source to a destination. but its not always drawn on a horizontal line. anyway ideally it looks like this: but the PEEK of the curve should touch the height of the black line. info: i will…
j2emanue
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