Mathematics Stack Exchange
Mathematics Stack Exchange

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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How to draw circle using Quadratic Bézier curves

I am trying to draw a circle using 4 Quadratic Bézier curves. By referring https://www.degruyter.com/document/doi/10.1515/math-2016-0012/html. $$C(t) = (1-t)^2P_0 + 2(1-t)tP_1 + t^2P_2.$$ If the arc is like this, the $t = 0.5$ and $C(t) = Radius$,…
JustWe
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I have a function which depends on four parameters and a target value, how can I discover the value for the four parameters that hits my target value?

So I have an equation: $$F(s,t,u,v)=A$$ Where $A$ is some given value. Is there an iterative method to discover the four parameters that will obtain my given $A$? If it helps, my function $F$ is a quintic bezier where most of the parameters are…
prismofeverything
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Minimum (or mean?) radius of a cubic bezier curve

I'm trying to calculate the minimum radius in a cubic Bezier curve (in C#). I know this question is around on StackExchange, and have thoroughly browsed the answers and tried different implementations. However, the results are not what I…
mennowo
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Can a cubic Bézier curve be accurately represented by a series of $f(x)$ functions (i.e. traditional non-parametric)?

Please forgive my naive assumptions, if these come across as such -- I am not a mathematician by the standards of this community. Allow me to elaborate: for what's it worth, intuitively I feel convinced that if we divide a cubic Bézier spline $B(t)$…
Armen Michaeli
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How can I find the point(s) where the tangent to a Bézier is horizontal?

I am working on cubic Béziers, and need to find the points where the tangent to the curve is vertical or horizontal. So far I've managed to: convert the Bézier to a cubic polynomial find the derivative find the root(s) of the derivative This…
simone
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Link points on a bicubic bezier patch

A bicubic bezier patch is defined by 16 control points. Given two points both lying on the patch boundaries, I think that if you link the two points you will end up with a cubic bezier curve in 3D. Is that true ? If yes, how can I find the two…
Ensis
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Bezier curve, X position of reference points outside [Xstart, Xend]

Not quite sure whether this belongs here or on stackoverflow, but considering it's about the formula itself and not the implementation I'm placing it here. I'm required to implement bezier curves in 2 ways: using de Casteljau's algorithm and the…
Kevinson
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Build a hyperbola using cubic or quadratic Bézier curves

I have a hyperbola defined with an equation y = A/x. How to build approximation of this hyperbola in a given rectangular area 0 < x <= x1, 0 < y <= y1 using cubic or quadratic Bézier curves, so that the difference between approximation and hyperbola…
Eugene Mala
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How to move the control points of the cubic Bézier curve, to keep the curve invariant?

I have 3 cubic Bézier curves with different control points: https://cubic-bezier.com/#.17,.8,.77,1 https://cubic-bezier.com/#.18,.59,.5,1 https://cubic-bezier.com/#.12,.41,.41,1 They look similar to each other. Assuming the anchor points…
zhangxaochen
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Find the cubic bezier control points from end points and tangents

If i have 2 end points and two unit vectors as tangents at the two end points is it possible to find the cubic bezier curve control points that make the curve ? Is there one solution or many solutions ? Visual of what i am trying to find:
WDUK
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given a polynomial how can you derive its bezier representation

I am developing an application that renders ECG rhythms that need to be animatable in response to user input. That part is not relevant to this site3, however I am starting with hand drawn rhythms, determining their polynomial representation and…
user74091
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Symmetric bezier curve with unsymmetric control points

I'm solving this problem about Cubic Bezier Curve which have $4$ control points $C_0,C_1,C_2,C_3$. $$ C_0 = (0,0),\: C_1 = (x_1,y_1),\: C_2=(x_2,y_2),\: C_3=(1,0) $$ where $0 < x_1 < x_2 < 1$ and $y_1, y_2>0$. If $C_1$ and $C_2$ are symmetric with…
Donguk Jung
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Help me understand Rational Bézier curve

Example: Given a rational linear Bézier curve between points $(x=0,y=0)$ and $(x=0,y=1)$, with weights of $1$ and $2$ respectively, for a given value of $t$, how do I find $y$? I can understand Bézier curves okay, the equations go over my head but I…
Peter Chaplin
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Bézier curve from three different y values

So I want to graph the Bézier curve below, but all I can find on how to do it is if two of the points are on the same y coordinate. How would I do it for this? Would I have to create the bottom part of the parabola from two of the same y…
Ethan Rappaport
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Polar Bezier Curves? Bezier Curves on a Torus?

Background: I am (trying) to use bezier curves to model an angle of a linkage. As an angle, it $\in \left\{-180, 180\right\}$. So my coordinate system is angle being y, time being x. To be continuous in looping time, the angle (y) at the start must…
Kurbo Matematikon
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