What Is the Difference Between Control Points and Fit Points in B-Splines?

[basty]

What I learned from a book, B-spline is constructed by knowing some control points.

However, below video showing that a B-spline is not constructed by a control point instead of fitpoints and tangent weight (handle).



Anyone know what is the name of the theory of it in a book and how to solve the equation?

 

[jvicens]

Hello there,

Thank you for sharing your thoughts on B-splines. It is true that B-splines are not constructed solely by control points, but also by fit points and tangent weights. This is because B-splines are a type of mathematical curve that is used to represent and smooth data points. They are commonly used in computer graphics, computer-aided design, and other fields where smooth curves are needed.

The theory behind B-splines is called "B-spline basis functions" and it is a fundamental concept in the field of computer-aided geometric design (CAGD). These basis functions are used to calculate the coordinates of the curve at any given parameter value. The equation used to calculate these basis functions is called the "de Boor algorithm" and it involves a recursive process that takes into account the control points, fit points, and tangent weights.

To solve the equation and construct a B-spline curve, you would need to use a computer program or software that has the capability to calculate the basis functions and plot the resulting curve. There are also mathematical formulas and algorithms that can be used to manually calculate the coordinates of the curve, but they can be quite complex and time-consuming.

I hope this helps to answer your question about the theory behind B-splines and how to solve the equation. If you are interested in learning more about B-splines, I recommend checking out some books on computer graphics or CAGD. They often have detailed explanations and examples of how B-splines are used and constructed. Best of luck in your studies!