What is the Difference Between Bezier Curve and B-Spline Curve?
🆚 Go to Comparative Table 🆚The main difference between Bezier curves and B-spline curves lies in the control points and the way they are used to define the shape of the curve. Here are the key differences:
- Control Points: In a Bezier curve, all control points are on the curve itself, and there are handlebars for adjustments. In contrast, B-spline curves have control points off the curve, creating a cage-like system for control.
- Local Control: B-spline curves allow for local control over the curve surface, meaning that changing any control point only affects a specific segment of the curve. In Bezier curves, changing any control point affects the entire curve.
- Flexibility: B-spline curves are specified by Bernstein basis functions, which have limited flexibility. Bezier curves, on the other hand, can be specified with boundary conditions, a characterizing matrix, or blending function.
- Degree: The degree of a Bezier curve is determined by the number of control points used to approximate the curve segment. B-spline curves allow the order of the basis function to change, hence the degree of the resulting curve can vary.
- Smoothness: B-spline curves possess a high degree of smoothness at the places where the polynomial pieces connect. Bezier curves may not have the same level of smoothness.
In summary, Bezier curves use control points on the curve itself, while B-spline curves use control points off the curve. B-spline curves allow for local control and have limited flexibility, whereas Bezier curves offer more flexibility but affect the entire curve when a control point is changed. B-spline curves also provide a higher degree of smoothness compared to Bezier curves.
Comparative Table: Bezier Curve vs B-Spline Curve
The main differences between Bezier curves and B-spline curves are as follows:
Feature | Bezier Curve | B-spline Curve |
---|---|---|
Definition | Specified with boundary conditions or blending functions, with a characterizing matrix | Specified by Bernstein basis function, with limited flexibility |
Control Points | Changing any control point affects the entire curve shape | Changing any control point only affects (degree+1) Bezier segments |
Degree | The degree of the polynomial defining the curve segment is one less than the number of defining control points | The degree of the resulting curve is determined by the order of the basis function |
Flexibility | Limited flexibility | Higher flexibility due to local control over the curve surface |
Global vs. Local Control | Control points impart global control over the curve shape | Control points impart local control over the curve shape |
In summary, Bezier curves are defined using boundary conditions or blending functions, and the shape of the entire curve is affected when any control point is changed. B-spline curves, on the other hand, are specified using Bernstein basis functions, and changing a control point only affects a specific segment of the curve. B-spline curves offer more flexibility and local control over the curve shape compared to Bezier curves.
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