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    A Bezier curve is a parametric curve widely used in computer graphics and CAD applications for modeling smooth and flexible shapes. Introduced by Pierre Bézier, it is defined by a set of control points that determine its shape. The curve is particularly valued for its simplicity, precision, and ease of implementation.

    Key Characteristics of Bezier Curves

    A Bezier curve is defined by control points, where the first and last points are the endpoints of the curve, and the intermediate points influence its shape. The degree of the curve is one less than the number of control points. For example, a cubic Bezier curve has four control points and is of degree three.

    The mathematical representation of a Bezier curve is:

    P(u) = Σ (k=0 to n) [ pk * BEZk,n(u) ], where 0 ≤ u ≤ 1
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    Here:

    • pk are the control points.

    • BEZk,n(u) is the blending function, calculated using the binomial coefficient.

    • u is a parameter that varies between 0 and 1, controlling the position along the curve.

    The blending function is:

    Can Bézier curves be joined up?
    Like the Hermite, Bézier curves are easily joined up. We can easily get continuity through a joint by making sure that the last two control points of the first curve line up with the first two control points of the next. Even better, the interior control points should be equally distant from the joint.
    cs.wellesley.edu
    TutorialsPoint
    https://www.tutorialspoint.com/computer_graphics/computer_graphic…
    Bezier Curves and Surfaces in Computer Graphics
  1. Wikipedia
    https://en.wikipedia.org › wiki › Bézier_curve

    Bézier curve - Wikipedia

    Cubic Bézier curve with four control points The basis functions on the range t in [0,1] for cubic Bézier curves: blue: y = (1 − t)3, green: y = 3 (1 − t)2t, red: y …

  2. TutorialsPoint
    https://www.tutorialspoint.com › computer_graphics …

    Bezier Curves and Surfaces in Computer Graphics

    Bezier curves are widely used in various CAD (Computer-Aided Design) and graphics software due to their flexibility and ease of implementation. Read …

  3. Number Analytics
    https://www.numberanalytics.com › blog › mastering-bezier-curves-in-cg

    Mastering Bezier Curves in CG - numberanalytics.com

    Jun 17, 2025 · Bezier curves are used to create smooth curves and surfaces in computer graphics and design. They are used in various applications, including curve fitting, surface creation, and …

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  5. GeeksForGeeks
    https://www.geeksforgeeks.org › cpp › bezier-curves …

    Bezier Curves in OpenGL - GeeksforGeeks

    Jul 23, 2025 · The concept of Bezier curves was discovered by the French engineer Pierre Bézier. Bezier curves are basically used in computer …

  6. raw.org
    https://raw.org › book › computer-graphics › bezier-curves

    Introduction to Bézier Curves • RAW

    Mar 27, 2025 · Bézier curves: from simple lines to smooth shapes. Learn the math, explore their power, and see why they’re everywhere in graphics and animation.

  7. Computer Hope
    https://www.computerhope.com › jargon › bezier-cur…

    What Is a Bezier Curve? - Computer Hope

    Feb 7, 2022 · A Bézier curve is a parametric curve frequently used with computer graphics. It is a mathematical description of a smooth curve …

  8. MUO
    https://www.makeuseof.com › bezier-curves-comput…

    What Are Bézier Curves in Computer Graphics? - MUO

    Dec 3, 2021 · Bézier curves are vectors by nature—unlike rasterized bitmap curves, they're scalable, which means that they retain certain properties as …

  9. Mozilla Developer
    https://developer.mozilla.org › en-US › docs › Glossary › Bezier_curve

    Bézier curve - Glossary | MDN

    Nov 6, 2025 · A Bézier curve (pronounced [bezje]) is a mathematically described curve used in computer graphics and animation. In vector images, they are used to model smooth curves that …

  10. UMA Technology
    https://umatechnology.org › what-are-bezier-curves-in-computer-graphi…

    What Are Bézier Curves in Computer Graphics? - UMA Technology

    Dec 29, 2024 · Bézier curves are a fundamental tool in computer graphics for creating smooth and aesthetically pleasing curves. They are widely used in graphic design, CAD, animation, …

  11. amazingalgorithms.com
    https://amazingalgorithms.com › definitions › bezier-curve

    What is Bézier Curve? - Definition from Amazing Algorithms

    A Bézier curve is a parametric curve used in computer graphics and typography to define smooth curves. It is defined by a set of control points that determine the shape and curvature of the …