Bezier Curve
A Bezier curve is a smooth parametric curve controlled by points and handles, widely used for paths, profiles, vector outlines, and animation splines.
What is Bezier Curve?
Bezier Curve is a parametric curve that defines a smooth path by blending a set of control points. The first and last control points usually lie on the curve, while the intermediate control points shape its tangents and curvature. Bezier curves are common in 3D modeling, vector graphics, typography, CAD, and animation editing.
How it works
A Bezier curve is evaluated by weighting its control points with Bernstein polynomials or by using the equivalent de Casteljau interpolation algorithm. A cubic Bezier curve uses four control points and is the most common form in artist tools because it offers predictable handles for shaping smooth arcs. Bezier curves matter in 3D because they can define extrusion paths, bevel profiles, motion paths, trim curves, and clean silhouette guides. They are resolution independent until converted or tessellated into line segments, polygons, or mesh geometry.
Use cases
Drawing a smooth path for a cable, pipe, rail, or tentacle before beveling it into geometry.
Creating a 2D profile that can be extruded, lathed, or used as a trim shape in a 3D scene.
Editing animation handles to control ease-in, ease-out, and smooth motion timing.
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Frequently Asked Questions
A Bezier curve in 3D modeling is a smooth parametric curve controlled by points and handles. Artists use it to define paths, outlines, profiles, and motion curves.
A Bezier curve blends its control points according to mathematical weights. Moving the control points changes the curve shape without directly editing every point along the curve.
A standard Bezier curve passes through its first and last control points. The middle control points usually act as handles that pull the curve and define tangent direction rather than points the curve must cross.
A cubic Bezier curve is a Bezier curve with four control points. It is widely used because it gives artists two endpoint positions and two handle positions for intuitive smooth-curve control.
A spline is a broader class of smooth curves. A Bezier curve is one specific spline type, and longer artist-facing splines are often built by joining multiple Bezier segments.
Bezier handles are control points or tangent controls that set the direction and strength of the curve as it leaves or approaches an anchor point. They are the main interactive tool for shaping a Bezier curve.
Yes. A Bezier curve can be converted or tessellated into mesh geometry, often after adding bevel depth, extrusion, or a surface operation.
Bezier curves are used in vector illustration, font design, user interface drawing, motion graphics, and animation timing. They are a standard way to describe smooth, editable shapes.
Bezier curves let artists create smooth, controllable forms with few editable controls. They are useful for clean silhouettes, repeatable profiles, precise paths, and smooth animation transitions.
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