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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.

630 questions
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Is there a relationship between the length of the inner and outer edges of a curve with a given width?

If you have an arbitrary line, say a bezier curve, that has a width, is there a relationship between the length of the curve at the inner and outer edges? Given the width of the curve at the centerline, can you determine the length at ±width/2…
IanLarson
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Equation for subsection of Bezier curve

Say I have a cubic Bezier curve, with a starting point s, an ending point e and control points c1 and c2. Given t between 0-1, I want to find the equation of the subsection of the curve between 0 and t. Is this possible without being too…
berry120
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Bézier Curves: where the 3 (or 1/3) constant comes from when moving from Hermite curves?

I'm learning Bézier Curves, and I'm stuck at the reason why they use 3 (or 1/3) constant when moving from Hermite curves? Like in this, this, and this source. e.g. why t0 = 3(q1 - q0) ? or why v1 = v0 + 1/3 d0 in the first link: x0 → v0 →…
Maverick Meerkat
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Bezier unit tangent

What is the explicit formula for a unit tangent vector to a Bezier curve? I.e. if the formula for a Bezier curve is $\mathbf{B}(t) = \sum_{i=0}^n\binom{n}i(1-t)^{n-i}t^i\mathbf{P}_i$, what is its unit tangent?
lwiseman
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Sum w.r.t Y axis of two Bézier curves with different control points

Suppose two 2D Bézier curves of the same degree but different control points. $\gamma_1(t) = \Sigma_{i=0}^n B_{i,n}(t) q_i$ and $\gamma_2(t) = \Sigma_{i=0}^n B_{i,n}(t) Q_i$ where $q_0 = Q_0 = (0;0), q_n = Q_n = (1;0)$ and $q_i \neq Q_i$ Let…
FineUser
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Calculate Cubic Bezier Curve passing through 6 points

I know this question has been asked before, but the answers I have come across I need a little more help understanding how to implement. I came across this answer here, but the cited link does not appear to be valid anymore. Also searching elsewhere…
ksmith
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Join two bezier curves so that the result is two-times continuously differentiable

I have a task to join two bezier curves, so that the resulting curve is two-times continuously differentiable. I have the cubic bezier Curve C with control points: $c_0 = (1,1)$ $c_1 = (3,4)$ $c_2 = (7,5)$ $c_3 = (8,2)$ I shall continue this curve…
DeDo
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Offset the Bezier curve by the approximate the circle

Suppose we for any interval of the unit circle, we can approximate by some cubic Bezier curves($B_3(t)$). Q: Can we use above method(or curve $B_3(t)$) to approximate the offset of any cubic Bezier curve? The (exact) offset curve, to the known…
DLIN
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Find the Length of the Bezier Curve having 4 Control Points

I am unable to get the exact length of Bezier curve having 4 Control points. Please give your suggestion to calculate exact length of Bezier curve. Please explain more about k1, k2, k3, k4 in the below code. double BezierArcLength(point2d p1,…
Nathan
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High Degree Bézier Curve For Curve Fitting

I have the feeling that I'm way out of my element here, and that maybe this question will be obvious to most of you. Nonetheless, here goes: I have an example set of 22 two-dimensional points, ordered in increasing x-axis value: 319.48067 …
user2062604
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How can I calculate all possible Bézier handle points in order to make the curve to a given length?

Given two anchor points and a handle point of a cubic Bézier curve, how can I calculate the other handle point in order to make the curve length to a fixed value? What kind of orbit will it be? NOTE: Ultimately I will make a solution in C++ for my…
h5nc
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Convert Bézier curve to equation

How to convert for example this Bézier curve: cubic-bezier($.65,0,.65,1$) (plot) to an equation like $f(x) = x...$ ?
Sony
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How can I prove in general form that the tangent at the start point of a Bézier curve goes through control point 1?

I need to prove that the tangent to the start point of any Bézier curve goes through the control point. I have proven this for specific Bézier curves but I am struggling to do it in general, thank you.
Georgia Jane
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Moving a control points on a bezier curve to best fit a moved end point

I have a bezier curve, which I am wanting to manipulate in a certain way. So that it is clear what part of the curve I am wanting to adjust, here is an illustration that labels the parts of the curve that are relevant to my problem. The…
Mark
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Calculating control points of Cubic Bézier curve

I'm trying to draw different arcs with a Cubic Bezier curve and my problem is that after reading different blogs that explain it, I can draw only a 90degree arc using this article. Is it possible if I have the starting X/Y coordinates, the circle…
Lexx
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