Bézier curve
A Bézier curve is a parametric curve whose shape is determined by control points through Bernstein basis functions.
Math for Web Design
A Bézier curve is a parametric curve defined by control points and polynomial interpolation, commonly used to represent smooth paths or progression.
- How it is used
- Shapes CSS animation timing so interface transitions accelerate, decelerate, anticipate, or overshoot deliberately.
- How deep it goes
- Explains quadratic and cubic construction, polynomial formulas, control-point roles, CSS syntax, and practical curve diagnosis.
- Examples
- Uses product-card entrances, a toggle, mobile menu, dialog bounce, tooltip, shopping-cart feedback, and fade-in debugging.
- What you can do after
- Apply it via CSS cubic-bezier() and easing keywords to tune animation feel and diagnose jumpy timing.
Geometry for Programmers
A Bézier curve is a polynomial parametric curve defined by control points and Bernstein basis functions.
- How it is used
- Models smooth controllable curves for design, engineering, graphics, GIS, and contour smoothing.
- How deep it goes
- Develops linear, quadratic, cubic, and rational forms with coordinate-level Python implementations; defers extended control to NURBS.
- Examples
- Uses numeric linear interpolation, quadratic and cubic coordinate code, and cubic weight variations.
- What you can do after
- Build it from scratch by evaluating coordinate-wise linear, quadratic, cubic, and rational Bézier formulas from control points.
Advanced Algorithms and Data Structures
A Bézier curve is a parametric curve defined by endpoints and one or more control points using Bernstein polynomial interpolation.
- How it is used
- Replaces polylines or straight graph edges when drawings need flexible curves and controllable rendering precision.
- How deep it goes
- Explains quadratic and cubic construction geometrically, then applies subdivision-based intersection checks, while deferring full mathematical details.
- Examples
- Uses quadratic and cubic edge diagrams, symmetric parabolic curves, convex-hull subdivision, and interval-based intersection sketches.
- What you can do after
- Apply it to model curved graph edges and choose subdivision strategies for approximate intersection testing.
Read how Advanced Algorithms and Data Structures explains Bézier curve →
How Computers Make Books
A Bézier curve is a parametric curve defined by endpoints and control points whose positions determine the curve's shape.
- How it is used
- Builds adjustable letterform outlines by shaping strokes and joining them into paths.
- How deep it goes
- Explains endpoint-and-control-point geometry, chaining, smooth joins, circle approximation, and filling complications without presenting curve equations.
- Examples
- Uses an ampersand with three paths, approximate circles, an O-shaped hole, and a trace-and-divide exercise.
- What you can do after
- Practice/perform curve manipulation, construct connected letterform paths, and choose filling rules for holes or self-crossing shapes.
CSS in Depth, Second Edition
A Bézier curve is a parameterized curve whose shape is determined by control points.
- How it is used
- Shapes transition timing functions so property changes accelerate, decelerate, or follow custom motion.
- How deep it goes
- Explains curve direction, endpoints, control handles, and cubic-bezier() values without deriving the underlying mathematics.
- Examples
- Uses linear and keyword curves, custom cubic-bezier() values, and DevTools handle editing.
- What you can do after
- Apply it through cubic-bezier() and DevTools to tune transition motion for different interface effects.
Read how CSS in Depth, Second Edition explains Bézier curve →
Related concepts
- parametric curvekind of · A parametric curve is a curve whose coordinates are expressed as functions of one or more parameters.
- control pointhas part · A control point is a point whose position influences the shape, direction, or local behavior of a curve or other parametric geometric representation.
- cubic-bezier()used by · The CSS cubic-bezier() function defines a timing function using a cubic Bézier curve specified by two control points.
- polylinealternative to · A polyline is an ordered sequence of connected straight line segments represented by successive points.
- CSS animationused by · CSS animation is a stylesheet-defined change in one or more element properties over time, governed by animation timing rules and often specified with keyframes.
- CSSused by · CSS, or Cascading Style Sheets, is a stylesheet language for specifying the presentation and layout of structured documents and user interfaces.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.