Curve drawing, not Bezier - curves

As a kid I would draw curves like the red line below, hopefully it is reasonably clear how I have constructed that.
I understand that the green line is the quadratic Bezier curve, what is the red line called?
Curves


The red curve in your picture is a parabola (which still can be represented as a quadratic Bezier curve). See this link for more details.

Related

Pixi.JS Dashed (or dotted) Bezier Curve

I'm working on a network graph and would like to use bezier curves to represent multiple edges between and two given nodes.
I would like to animated a dashed line to represent this edge.
There are quite a few examples and conversations floating around regarding dashed lines but not dashed curves.
I'm very new to Pixi.JS and am struggling to even find which direction to go to explore figuring out this topic.
Hopefully someone can point me in the right direction and give a few examples of dashed curves in Pixi.JS

How to fit a ellipse to given points in Octave

I would like to know how to fit a bunch of (x,y) points in an ellipse shape. I've got two vectors, both the same size [1001,1], but I don't know how to fit an ellipse. Every time I tried the least squares it ends in some different approximation. I was using trigonometric polynomials by the way.
Here is an image of the graphic plot.
I will appreciate any help :)
Image plot: https://i.stack.imgur.com/P4vnt.png

Closest point on a B-Spline Curve?

This thread asks how to get the closest point on a Bezier curve given an arbitrary point on the same plane: Closest point on a cubic Bezier curve?
How can I accomplish the same thing but for a B-SPline curve?

Using bezier curves to draw variable width paths

Given two points and a control point, one can easily draw a bezier path between the two points. What I would like to do use a bezier curve to draw a path that with changing width, by a assigning a "weight" to a the points of the curve which will determine its width. For example, if I give weight=0 to the first point of the curve and weight = 1 to the second point of the curve then something like the following path should be generated (the curve in the picture is cubic, but I am working with quadratic bezier curves):
In order to do this I would need to find the control points of the "edge" curves that determine the shape and then fill the shape that is found between the two new curves. However, I am quite unsure on how this can be done. One thing I thought about was to determine the starting and ending points of the new curves by simple drawing perpendicular segments to the line connecting the original control point and the original end points, but this still doesn't solve the problem of finding the new control points for the new curves.

I would use cubics instead of quadratics.
Yes you offset the control points perpendicularly by your weight but not the control points of BEZIER but control points of interpolation cubic (or catmull-rom) and then just convert that into Bezier control points. See related QAs:
How can i produce multi point linear interpolation?
How to create bezier curves for an arc with different start and end tangent slopes
draw outline for some connected lines
However much easier would be to directly render curve using Shaders and (perpendicular) distance. See:
Draw Quadratic Curve on GPU
That way you would not need to offset anything just interpolate the width of your curve ...

Maybe this could help, also there is an example on variable offseting
https://microbians.com/mathcode

Draw a parabola y^2=x using the mid point algorithm?

i need to how parabola is drawn using midpoint algorithm. i got how to obtain the circle and line and also ellipse but couldn't get proper method for parabola. can anyone help me out for doing it from beginning to end.

Resources