Radius
A radius is the distance from the center of a circle or geometric region to its boundary in a specified direction.
Advanced Algorithms and Data Structures
A radius is the maximum distance from a center to the boundary or an included point of a geometric region.
- How it is used
- Defines spherical bounds for SS-tree nodes and ε-neighborhoods for DBSCAN cluster expansion.
- How deep it goes
- Works through centroid-based radius updates and neighbor checks, but defers the smallest-enclosing-sphere approximation algorithm.
- Examples
- Uses an enlarging leaf envelope, a skew-sensitive split, contrasting enclosing spheres, and DBSCAN neighborhood expansion.
- What you can do after
- Build it from scratch: update SS-tree covering radii, or practice/perform DBSCAN neighbor checks using ε.
Read how Advanced Algorithms and Data Structures explains radius →
Geometry for Programmers
A radius is a line segment or distance from the center of a circle to a point on its circumference.
- How it is used
- Connects circle geometry to curvature measurement and smooth curve construction.
- How deep it goes
- Explains local fitting circles, tangent constraints, signed curvature, and symbolic biarc equations.
- Examples
- Uses straight lines, circles of varying size, sine-graph curvature, and smoothly joined biarc segments.
- What you can do after
- Evaluate/understand how radius controls curvature and supports symbolic construction of smooth biarcs.
Math for Web Design
A radius is the distance from the center of a circle to any point on its circumference.
- How it is used
- Uses radius to position and animate web elements along circular or curved paths.
- How deep it goes
- Defines radius through the unit circle and applies it in coordinate formulas and animations, without developing circle geometry further.
- Examples
- Demonstrates unit-circle coordinates, inward spirals, circular animation, and elliptical motion using independent horizontal and vertical radii.
- What you can do after
- Build it from scratch by calculating element positions for circular, spiral, or elliptical browser animations.
D3.js in Action, Third Edition
A radius is the distance from the center or origin of a geometric figure to a point on its boundary.
- How it is used
- Positions points and shapes in polar-coordinate SVG visualizations, especially arcs.
- How deep it goes
- Defines radius as origin-to-point distance and applies it through D3 arc boundaries and related accessors.
- Examples
- Uses a centered SVG arc chart and D3’s innerRadius() and outerRadius() accessors as concrete applications.
- What you can do after
- Apply it via D3’s arc generator to define SVG arc geometry with inner and outer radii.
Related concepts
- curvaturecontrasts with · Curvature is a measure of how a curve or surface bends locally, or, for a function, how its slope changes across its input space.
- polar coordinatepart of · A polar coordinate specifies a point in two-dimensional space by its distance from an origin and its angle relative to a reference direction.
- circle()configured by · The CSS circle() function defines a circular basic shape using a radius and optionally a center position.
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