# Tagged Questions

Questions on Bézier curves, curves that are frequently used in computer graphics.

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### How to calculate the controls of this Bézier curve?

How to calculate the controls of this curve if I know three points: start, one on the curve and the end? Here is the curve with the coordinates I know: The curve with the points I've never done this ...
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### Are Bezier curves invariant under conformal mapping?

I've spent quite a bit of time on google trying to find information on whether or not Bezier curves are invariant under conformal mapping (i.e. a conformal mapping of all points on the curve is the ...
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### Bézier Curve and b spline curves.

Well I am learning about curves. I have come across Bézier and Spline curves. I want to know which one should be learned first? Are their concepts independent? or I need to know about one before ...
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### How to set control points for spline curves

I've written a program that calculates points on spline curves (including Hermite, Bezier, and B-splines) and plot the curve on the screen (the curve is plotted on an html canvas using javascript). ...
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### Passing an ellipse through 3 points (where 2 two points lie on the ellipse axes)? [Updated with alternative statement of problem and new picture]

Update Alternative Statement of Problem, with New Picture Given three points $P_1$, $P_2$, and $P_3$ in the Cartesian plane, I would like to find the ellipse which passes through all three points, ...
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### How do I fill in points in an equation?

I'm doing research for Bézier curves for school, and I don't really understand how to fill in a point in an equation. I mean, I'd like to represent this on an x,y (or t,y) curve, but what do I need to ...
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### Do Bezier control points aproximate their curve?

I was just reading here about degree elevation in Bezier curves and I noticed that in the diagrams of the progressively higher degree curve, that the control points began to approximate the curve ...
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### Convert segment of parabola to quadratic bezier curve

How do I convert a segment of parabola to a cubic Bezier curve? The parabola segment is given as a polynomial with two x values for the edges. My target is to convert a quadratic piecewise ...
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### Convert quadratic bezier curve to parabola

A quadratic Bézier curve is a segment of a parabola. If the $3$ control points and the quadratic Bézier curve are known, how do you calculate the equation of the parabola (which is an $y=f(x)$ ...
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### What does the 2nd degree derivative of a cubic Bezier curve actually represent?

I have a $3D$ Bezier curve. Each co-ordinate along its path is defined by the equation: $$f(t) = t^3 \bigl(a_2+3(c_1-c_2)-a_1\bigr) + 3t^2 (a_1-2c_1+c_2) + 3t(c_1-a_1) + a_1$$ where $a_1, a_2$ are ...
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### Equation for control point distance for fixed-length cubic Bézier path (with specific constraints)

A particular Stack Overflow question asks how to construct a specific cubic Bézier path of constant length. I have experimentally determined the ideal distances of the control points from the nearest ...
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### Is there anything interesting about this figure constructed from a set of points and their barycentre?

Playing with the TikZ package for (La)TeX, I made a nice figure. Well, I think it is nice, anyway. You can ignore the distracting colours and the concentric circles, they are not important for this ...