Radius

As explained in Geometry for Programmers

A radius is a line segment or distance from the center of a circle to a point on its circumference.

A radius is the distance from a circle’s center to its circumference. Geometrically, it controls how tightly a circle bends: a smaller radius produces stronger curvature, while a very large radius makes an arc resemble a straight line. section 5.2.3

Figure 5.16 The smaller the radius, the larger the curvature.

Compare circles with different radii to see why curvature increases as radius decreases. section 5.2.3

Radius becomes especially useful when constructing smooth curve segments:

• Approximate a curve near a point with a fitting circle whose radius reflects the curve’s local bending. section 5.2.3
• Use tangent-vector changes, not merely a shared point and tangent, to determine the appropriate radius. section 5.2.3
• For a biarc, solve for two radii and two circle centers so the arcs meet continuously and smoothly. section 5.3.1

A radius in a biarc

A biarc connects two points while following specified tangent vectors. Its construction represents each point-to-center vector as a rotated, normalized tangent vector scaled by its radius, then constrains the circles’ center distance to equal the sum of their radii. SymPy can solve the resulting system for the centers and radii. section 5.3.1

How Geometry for Programmers covers it

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 it assumes

Assumes familiarity with curves and tangent vectors while connecting radius to derivatives through curvature.

What you can do after

Evaluate/understand how radius controls curvature and supports symbolic construction of smooth biarcs.

How it connects

Ties radius to curvature, circles, tangent vectors, derivatives, parametric curves, and biarcs.

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Also explained in

• 

  liveBookmanning.com
  Advanced Algorithms and Data StructuresA radius is the maximum distance from a center to the boundary or an included point of a geometric region.
• 

  liveBookmanning.com
  Math for Web DesignA radius is the distance from the center of a circle to any point on its circumference.
• 

  liveBookmanning.com
  D3.js in Action, Third EditionA radius is the distance from the center or origin of a geometric figure to a point on its boundary.

Compare how 4 books explain radius →

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.

This explainer was generated by Manning's knowledge graph from the text of Geometry for Programmers. The section links point to the parts of the book it draws on.