Inserting Spline Point

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Dominik_We

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Feb 12, 2021
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Hi everyone,

I have a spline and want to insert a point between 2 other points, without changing the spline.

So as in the picture seen (hopefully, sry for using paint), given points A,B and their tangents, and the location of C, which is on the bezier curve, how can I get the tangents from C - C1 and C2, - so that the spline stays the same.

Hope you can help me.

InsertSplinePoint.png
 
Dominik_We said:
Hi everyone,

I have a spline and want to insert a point between 2 other points, without changing the spline.

So as in the picture seen (hopefully, sry for using paint), given points A,B and their tangents, and the location of C, which is on the bezier curve, how can I get the tangents from C - C1 and C2, - so that the spline stays the same.

Hope you can help me.

View attachment 25096
Click to expand...
What software are you using for your spline fit?

The user's manual should instruct you regarding the procedure to insert a point on the curve.
 
Subhotosh Khan said:
What software are you using for you spline fit?

The user's manual should instruct you regarding the procedure to insert a point on the curve.
Click to expand...

I'm using Unreal Engine 4 USplineComponent. There are functions to add and insert into the spline but I can't completely use this, because I want to add points without changing the current splin and the Unreal Engine Splines change the bezier curve before the new added. For inserting the same, the spline changes. For adding at the end I just save the Tangent of the last point before adding and afterwards set it again, so it stays the same. For inserting I can't fix this behaviour
 
You already have the tangents. The line between p0 and pt 1 is a tangent line as well at the line between p2 and p3 is the other tangent on a standard cubic bezier. Your original curve looks like a quartic bezeir or degree 4 or "5th order". After insertion it looks like it will be a quintic. Your second segment of c1 and c2 is the tangent line. You can determine exact tangent line by first finding the derivative at that point and then using this common calculus technique

In general when you have a curve comprised of more than 4 points of degree 3 it is standard practice to use bsplines and not bezier.


pomax.github.io

A Primer on Bézier Curves

A detailed explanation of Bézier curves, and how to do the many things that we commonly want to do with them.
pomax.github.io pomax.github.io
 
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markraz said:
You already have the tangents. The line between p0 and pt 1 is a tangent line as well at the line between p2 and p3 is the other tangent on a standard cubic bezier. Your original curve looks like a quartic bezeir or degree 4 or "5th order". After insertion it looks like it will be a quintic. Your second segment of c1 and c2 is the tangent line. You can determine exact tangent line by first finding the derivative at that point and then using this common calculus technique

In general when you have a curve comprised of more than 4 points of degree 3 it is standard practice to use bsplines and not bezier.


pomax.github.io

A Primer on Bézier Curves

A detailed explanation of Bézier curves, and how to do the many things that we commonly want to do with them.
pomax.github.io pomax.github.io
Click to expand...
Maybe my question is not clear, I will try it again. I have all tangents of the curve. It's not 4. or 5. degree, it is a bezier curve between 2 points always and when I add the point I have 2 bezier curves afterwards.
My problem is, how "long" do the tangents have to be.
So I have given tangents at all points of the spline and need to know the length from A->A1, B->B1, C->C1, C->C2. Because, if the tangents length does not match, the new bezier curves don't match the old one.
 
Dominik_We said:
Maybe my question is not clear, I will try it again. I have all tangents of the curve. It's not 4. or 5. degree, it is a bezier curve between 2 points always and when I add the point I have 2 bezier curves afterwards.
My problem is, how "long" do the tangents have to be.
So I have given tangents at all points of the spline and need to know the length from A->A1, B->B1, C->C1, C->C2. Because, if the tangents length does not match, the new bezier curves don't match the old one.
Click to expand...
the length of the tangent line is the magnitude of the vector (see hermite spline https://www.cubic.org/docs/hermite.htm). The length is whatever you need it to be. Also Bezier curves have to have a minimum of 3 points and 2 hulls since there is no point drawing a bezier line. The number of control points on your bezier IS the degree of the curve. Are you implementing a Bezier in code? what is your goal, that may help explain things having some context
 
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markraz said:
the length of the tangent line is the magnitude of the vector (see hermite spline https://www.cubic.org/docs/hermite.htm). The length is whatever you need it to be. Also Bezier curves have to have a minimum of 3 points and 2 hulls since there is no point drawing a bezier line. The number of control points on your bezier IS the degree of the curve. Are you implementing a Bezier in code? what is your goal, that may help explain things having some context
Click to expand...
So for implementation I'm using Unreal Engines Spline Component. The bezier curve has 2 points + 2 control points.

So my goal is to "divide" one bezier curve into 2 other bezier curves that together match exactly the first curve.

In my picture this would be like this:

I have an existing bezier curve: A to B, with the control points A1, B1

I want to new bezier curves: A to C, with the control points A1 and C1
C to B, with the control points C2 B1

Note that A1, B1 is differentin the existing curve than in the new curves, name is just the same because of better visibility.

So A B C are given. A1,B1 from existing curve are also given. The direction of the tangent in C is also given.

What I need for the new curves: New A1, B1 and C1, C2.

So if we say the tangent in C is c we have C1 = C + x * c. What I need is x. Same for A1, B1, C2.
 
Ok, found the solution. Finding it was harder than implementing it, the solution is just the De Casteljau algorithm.
 
Beer soaked reply follows.
Dominik_We said:
Is there a way to post code here with formatting or just a screenshot?
Click to expand...
There is with just a screenshot.
You can see it just below.
It's an icon of a paperclip that says "Attach files".
You were able to upload a png file in at post #1.
 
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