Title: **6 order Bezier Spline**

Post by:**mogn** on **April 01, 2012, 06:25:48 am**

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A paper about Bezier Splines can be found here: http://processingjs.nihongoresources.com/bezierinfo/ (http://processingjs.nihongoresources.com/bezierinfo/)

This special Spline, takes as Input a number between 0 and zero, and a vector with 3 Numbers [A, B, C]

The spline is controlled by 7 points along the Input line:

(0, 0) (1/6, 0) (1/3, a) (1/2, b) (2/3, c) (5/6, 1) (1, 1)

The two first points ensures that the Spline starts with a value of 0 and zero slope.

The two last points ensures that the Spline ends with a value of 1 and zero slope.

The values a,b,c is calculated so that the Spline passes through the points (1/3, A) (1/2, B) (2/3, C).

Shown here is an application for visually determine the numbers input vector [A, B, C]:

1. View the settings for "Constant vector 01"

2. Right click "Surface layer 01" and view in another window.

You will now see two instances of the curve (The line between red and black). The two instances are seperated by the vertical line.

If you place the cursor near this line you can see spline output as the y value.

In the picture is shown that the value near the top is 1.202

No you can change the numbers in "Constant vector 01" until you are satiesfied by the curve.

This special Spline, takes as Input a number between 0 and zero, and a vector with 3 Numbers [A, B, C]

The spline is controlled by 7 points along the Input line:

(0, 0) (1/6, 0) (1/3, a) (1/2, b) (2/3, c) (5/6, 1) (1, 1)

The two first points ensures that the Spline starts with a value of 0 and zero slope.

The two last points ensures that the Spline ends with a value of 1 and zero slope.

The values a,b,c is calculated so that the Spline passes through the points (1/3, A) (1/2, B) (2/3, C).

Shown here is an application for visually determine the numbers input vector [A, B, C]:

1. View the settings for "Constant vector 01"

2. Right click "Surface layer 01" and view in another window.

You will now see two instances of the curve (The line between red and black). The two instances are seperated by the vertical line.

If you place the cursor near this line you can see spline output as the y value.

In the picture is shown that the value near the top is 1.202

No you can change the numbers in "Constant vector 01" until you are satiesfied by the curve.

Title: **Re: 6 order Bezier Spline**

Post by:**Hetzen** on **April 11, 2012, 06:29:01 pm**

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Why the hell couldn't I have had this program to help understand the use of this stuff at school?!

Thank you Mogn. I need to study that link a little more.

Thank you Mogn. I need to study that link a little more.

Title: **Re: 6 order Bezier Spline**

Post by:**Kadri** on **April 12, 2012, 12:55:02 am**

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Thanks for the file Mogn!

Quote from: mogn on April 01, 2012, 06:25:48 am

A paper about Bezier Splines can be found here: http://processingjs.nihongoresources.com/bezierinfo/ (http://processingjs.nihongoresources.com/bezierinfo/)

...

The link is great!

This is what i think of a good...awesome use of the web!

When i ask my students how they use the internet they think the web is Facebook :(