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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Bezier curve coefficients intuition

I understand that the coefficients for a Bezier curve falls easily from its recursive definition. However, looking at the polynomial unto itself, I'm struggling to understand why we need the additional weighting provided by the binomial…
Zach
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Finding the Control Point in a bezier curve

This is a basic (and probably a stupid) question, math is not my forte and I don't know much about math, in this site: http://www.ams.org/samplings/feature-column/fcarc-bezier in the bezier curves column, specifically in the cubic bezier curve there…
jane
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Which side of a 2d curve is a point on?

Given a point $Q$ and $2d$ Cubic Bezier Curve: $$P = A(1-t)^3 + 3Bt(1-t)^2 + 3Ct^2(1-t) + Dt^3$$ Is there a way to know which side of the curve the point lies on? I know that the term "side" is a bit strange since there can be a loop, but I'm…
Alan Wolfe
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Approximating a cubic Bézier curves with a collection of quadratic ones

I need to approximate a cubic Bézier curve with a minimal collection of quadratic ones given a maximum acceptable error. Trying to read up on this problem, it seems like there are about as many approaches as there are people trying to solve it.…
Markus A.
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Bézier curve - higher order - detect "sharpness" (serpentine or cusp) in curve

I have high order Bézier curve (n > 5). I would like to detect points of self intersection or too pointy ones. In lower degrees, I could use derivative of curve equation and solve roots for valeu = 0, but in higher dimensions, that would take too…
Martin Perry
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How to find the N control point of a bezier curve with N+1 points on the curve

I have a the set of points my curve has to pass through, 2 of those are the start and end points. I'm looking for a way to find the control points of my bezier curve (mostly quadratic and cubic) by using points on the curve. ex: I have 4 points:…
user183776
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Control Points of Bézier Curve?

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!
John
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How to tell if a 2d point is within a set of Bézier curves?

I have a set of Bézier curves defined like pictured: They make a closed shape like so: Given a point $\left(x,y\right)$ I need to tell if it is inside this set of Bézier curves, each defined by four points. Edit: pseudocode can be given too :)
Aly
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What is the degree of a Bezier curve?

A question regarding control points in a practice exam asks to find the relationship between Bezier control points and degrees of the curves. How many control points are required to specify a Bezier curve of degree x? What is the degree of a Bezier…
user3168961
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Finding Y given X on a Cubic Bezier Curve?

I just asked this in the Computing sections but they sent me here: "So I've been looking around for some sort of method to allow me to find the Y-coordinate on a Cubic Bezier Curve, given an x-coordinate on it. I've come across lots of places…
CyrusFiredawn
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Detect “Kinks” in Parallel Lines to Bezier Curves [x-post]

I feel like this is just as much a mathematics question as it is a programming question so I figured it couldn't hurt to cross post my question here. Original Post:…
Spencer Ruport
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Moving along a bezier curve in time T, factoring in acceleration from X to Y

OK, so I got my ships moving along the bezier in time T, now I need to factor in acceleration, but I don't really know how to do it. I'm using the DeCasteljau Algorithm, that's what my code looks like: function linp(d, a, b, t) { d.x = a.x +…
Ivo Wetzel
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Reparametrize of cubic bezier curve in arclength

I am looking for a way to re-parametrize the cubic Bezier curve in t domain to cubic bezier curve in S (arclength) domain. Thanks
Mahsa Ghaffari
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Finding two Bézier control points given three points

My apologies if this is asked in the wrong spot, I believe that this problem has a fairly simple solution... but it is beyond me. Given three points (A,B,C) drawn at random, how do you figure out the middle point's (B) control points (B1?, B2?) for…
RANGER
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Equation for a surface given N points in 3d space?

In 2D it is fairly well established how to generate a smooth curve from arbitrary points à la Bézier curves. Is there an equivalent to this for a smooth surface with arbitrary 3d points?
Tim Morris
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