B-Spline Curve Generator
Drag the green control points to shape your B-Spline curve in real time. Uses authentic cubic B-spline (degree 3) with uniform knot vector.
C(t) = Σ Pᵢ × Nᵢ,ₖ(t) where Nᵢ,ₖ are basis functions
Uniform knot vector • Open curve • Local control • C² continuity (for k=3)
About the B-Spline Curve Generator
The B-Spline Curve Generator is a scientifically precise, interactive online tool that creates smooth curves using authentic B-Spline Curve mathematics — the foundation of modern CAD systems (AutoCAD, SolidWorks), animation software (Blender, Maya), and scientific visualization. Unlike Bézier curves, B-Splines offer local control, C² continuity, and do not pass through control points (except endpoints), making them ideal for engineering, design, and agriculture mapping. This free tool uses the exact de Boor algorithm with uniform knots, delivering results identical to professional software. For precision farming applications, visit Agri Care Hub.
What is a B-Spline Curve?
A B-Spline (Basis Spline) is a generalization of Bézier curves that uses a sequence of control points and basis functions to create smooth, flexible curves. Key properties:
- Local Control: Moving one point affects only a small region
- C² Continuity: Smooth curvature (perfect for motion paths)
- Convex Hull Property: Curve stays inside control polygon
- Invariant under affine transformations
Scientific Accuracy
This generator implements the exact de Boor recursive algorithm as defined in Piegl & Tiller (1997), “The NURBS Book”, and used in OpenGL, WebGL, and all major CAD systems. It supports degree 3 (cubic) by default — the industry standard for smooth curves.
Why B-Splines Are Superior
- No unwanted oscillations
- Easy to extend with new points
- Used in fonts (TrueType), car design, aircraft
- Foundation of NURBS surfaces
Applications
- CAD/CAM: Product design, CNC paths
- Animation: Character motion, camera paths
- Agriculture: Field boundary mapping, irrigation planning
- GIS: Road networks, river modeling
- Robotics: Smooth trajectory planning
When to Use This Tool
Use it when you need:
- Smooth curves with local control
- Professional-grade design without software
- Teaching B-spline theory
- Planning farm layouts or irrigation paths
User Guidelines
- Drag green points to shape the curve
- Use buttons to add/remove points
- Change degree for different smoothness
- Curve updates instantly!
Agricultural Applications
In precision agriculture — supported by Agri Care Hub — B-splines are used to:
- Draw smooth field boundaries from GPS points
- Plan curved irrigation pivot paths
- Model crop rows and drainage systems
- Create professional farm maps
Conclusion
The B-Spline Curve Generator is the most advanced free tool available for creating professional smooth curves. With real-time interaction, mathematical precision, and beautiful visualization, it serves designers, engineers, educators, and farmers worldwide. Learn more at the B-Spline Curve Wikipedia page or explore farming solutions at Agri Care Hub.