Difference between B-Spline and Bezier Curves

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SUMMARY

The discussion clarifies the fundamental differences between B-Spline curves and Bezier curves. A B-Spline is defined as a more general interpolation curve that passes through its control points, while a Bezier curve is a cubic polynomial approximation that only passes through its endpoints. Under specific conditions, a B-Spline can degenerate into a Bezier curve. This distinction is crucial for understanding their applications in computer graphics and modeling.

PREREQUISITES
  • Understanding of curve types in computer graphics
  • Familiarity with polynomial expressions
  • Knowledge of interpolation vs. approximation concepts
  • Basic grasp of control points in curve modeling
NEXT STEPS
  • Research the mathematical foundations of B-Spline curves
  • Explore the applications of Bezier curves in graphic design software
  • Learn about the implementation of B-Spline and Bezier curves in programming languages like Python
  • Investigate the conditions under which B-Splines degenerate into Bezier curves
USEFUL FOR

This discussion is beneficial for graphic designers, computer graphics programmers, and anyone involved in digital modeling and animation who seeks to understand the nuances between different types of curves.

kmgraju
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Dear friends
What is the difference between B-Spline curve and Bezier curve?
Regards
Govind
 
Mathematics news on Phys.org
Hey kmgraju and welcome to the forums.

A B-Spline is an interpolation curve that is a lot more general whereas a bezier curve is a cubic polynomial expression (for each dimension, example curve, surface, volume, etc) that is an approximation curve given control points.

Interpolation curves go through the control points whereas approximation curves don't necessarily go through the points. You'll note that a bezier curve/surface/volume goes through only the end-points and in general is only 'pulled' towards the middle two points and doesn't go through them (like an interpolation curve does).
 

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