# Questions tagged [bezier-curve]

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

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### Generalize Finding $y$ value of Bezier curve given a $x$

A quadratic Bezier curve is a parametric curve. Its $x$ value can be represented by the equation: $$(t² × (x_0 - 2 × x_1 + x_2)) + (t × (2 × x_1 - 2 × x_0)) + (x_0 - x) = 0$$ For $0<t<1$ If I ...
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### Fitting a modified Bézier curve

I am connecting various vectors with a Bézier curve, using the De Casteljau algorithm. These vectors have a variety of lengths and directions, and when they are equal and orthogonal the curve (purple) ...
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### Approximate quadratic Bezier by a $1.0-\sqrt{x^2 + y^2}$ distance

Summary: I have a triangle with points at $A=(0, 100); B=(100, 0); C=(100, 100)$ each point also has an $F$ value, this value is linearly interpolated between every other point and used to get the ...
1 vote
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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 ...
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### How to find the inscribed and circumscribed circles from convex region?

Let $\mathbf{P}(t)$ be a piecewise bezier curve of degree $p$, which defines a jordan curve in the plane such the interior region $D$ is convex. Question: How can I find the external $C_e$ and ...
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### NURB curves with interior knot multiplicy higher than curve degree

I have the following question. If I have a NURB curve where one of the interior knots has multiplicity higher than the degree of curve (I did not chose to have such curves, I am writing a code for ...
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### Finding Δt for a Bezier curve following a certain speed

I'm writing an algorithm where I would like a body to move along a Bezier curve at variable speed. My bezier curve So I have a Bezier curve which represents a body's X and Y positions over time. ...
1 vote
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### How to get enough data to draw an arc or a curve from 3 points?

Note: Although I want to accomplish this in java, I think the question is more suitable for this site since it is mostly mathematical. I am in the following scenario. I want to draw a curve and I have ...
1 vote
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### Parametrization relationship between rational Cubic Bezier curve and two curves resulting from subdivision.

I have a following situation: Say I have a rational cubic Bezier curve $B_0$. I then project it into 4D, to make it non-rational, and then use De Casteljau's algorithm to subdivide it into two ...
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### Finding best 2D curve passing by waypoints

For a robotic application, I am looking for a mathematical tool for finding the best curve passing by or near (up to a certain radius) from waypoints as shown below. The pink circles are obstacles ...
25 views

### Decomposing NURBS curve into piecewise Bezier segments

I have a question concerning a paper. In it the authors try to approximate a NURBS curve by biarcs and to do so, they first need to find a polygonal approximation of the NURBS curve. They chose a ...
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1 vote
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### Calculating arc length of Bezier curves by hand

I was wondering if there was a viable method to calculate arc length of a quadratic Bezier curve without using coding. If I know the points of P0, P1 and P2, would it be possible to calculate the arc ...