Does anyone have an idea why it is called B-Spline: Degree X (X=3,5 or 7) instead of Bezier Curve: Degree X ?
Does anyone have an idea why it is called B-Spline: Degree X (X=3,5 or 7) instead of Bezier Curve: Degree X ?
...yeah.. I guess I see the b-spline degree X as bezier curve(s) controlled X times?
Hi Maha,
Because they are two different types of industry standard curve types and each have different characteristics. A Style spline uses a Bezier function (prevalent in vector drawing programs like Adobe Illustrator) but within the Style Spline PM it can be characterized as a 3, 5 or 7th degree B-spline function. The differences between the two are noticeable. Here is a good overview from GeeksforGeeks:
1. Spline :
A spline curve is a mathematical representation for which it is easy to build an interface that will allow a user to design and control the shape of complex curves and surfaces.
2. B-Spline :
B-Spline is a basis function that contains a set of control points. The B-Spline curves are specified by Bernstein basis function that has limited flexibility.
3. Bezier :
These curves are specified with boundary conditions, with a characterizing matrix or with blending function. A Bezier curve section can be filled by any number of control points. The number of control points to be approximated and their relative position determine the degree of Bezier polynomial.
Difference between Spline, B-Spline and Bezier Curves :
Spline B-Spline Bezier
A spline curve can be specified by giving a specified set of coordinate positions, called control points which indicate the general shape of the curve. The B-Spline curves are specified by Bernstein basis function that has limited flexibility. The Bezier curves can be specified with boundary conditions, with a characterizing matrix or with blending function.
It follows the general shape of the curve. These curves are a result of the use of open uniform basis function. The curve generally follows the shape of a defining polygon.
Typical CAD application for spline include the design of automobile bodies, aircraft and spacecraft surfaces and ship hulls. These curves can be used to construct blending curves. These are found in painting and drawing packages as well as in CAD applications.
It possesses a high degree of smoothness at the places where the polynomial pieces connect. The B-Spline allows the order of the basis function and hence the degree of the resulting curve is independent of the number of vertices. The degree of the polynomial defining the curve segment is one less than the number of defining polygon point.
A spline curve is a mathematical representation for which it is easy to build
an interface that will allow a user to design and control the shape of complex
curves and surfaces.
Thanks for the detail explanation.
Choosing any of those "B-spline" options will actually generate a B-spline of that degree, using the Style spline tool
2020 SOLIDWORKS Help - Style Spline Support for B-Splines
I've always struggled to find a use case for that though.
The Bezier curve degree is always 1 less than the number of Control Vertices so that's pretty straightforward, and you can see it displayed when you select a Style spline (using the default Bezier curve option)
Hi Maha,
Because they are two different types of industry standard curve types and each have different characteristics. A Style spline uses a Bezier function (prevalent in vector drawing programs like Adobe Illustrator) but within the Style Spline PM it can be characterized as a 3, 5 or 7th degree B-spline function. The differences between the two are noticeable. Here is a good overview from GeeksforGeeks:
1. Spline :
A spline curve is a mathematical representation for which it is easy to build an interface that will allow a user to design and control the shape of complex curves and surfaces.
2. B-Spline :
B-Spline is a basis function that contains a set of control points. The B-Spline curves are specified by Bernstein basis function that has limited flexibility.
3. Bezier :
These curves are specified with boundary conditions, with a characterizing matrix or with blending function. A Bezier curve section can be filled by any number of control points. The number of control points to be approximated and their relative position determine the degree of Bezier polynomial.
Difference between Spline, B-Spline and Bezier Curves :
Spline B-Spline Bezier
A spline curve can be specified by giving a specified set of coordinate positions, called control points which indicate the general shape of the curve. The B-Spline curves are specified by Bernstein basis function that has limited flexibility. The Bezier curves can be specified with boundary conditions, with a characterizing matrix or with blending function.
It follows the general shape of the curve. These curves are a result of the use of open uniform basis function. The curve generally follows the shape of a defining polygon.
Typical CAD application for spline include the design of automobile bodies, aircraft and spacecraft surfaces and ship hulls. These curves can be used to construct blending curves. These are found in painting and drawing packages as well as in CAD applications.
It possesses a high degree of smoothness at the places where the polynomial pieces connect. The B-Spline allows the order of the basis function and hence the degree of the resulting curve is independent of the number of vertices. The degree of the polynomial defining the curve segment is one less than the number of defining polygon point.
A spline curve is a mathematical representation for which it is easy to build
an interface that will allow a user to design and control the shape of complex
curves and surfaces.