How deeply does D3.js in Action, Third Edition cover centroid?

Explains centroid calculation, returned coordinates, and SVG alignment, but defers general shape-centroid mathematics.

Centroid

As explained in D3.js in Action, Third Edition

A centroid is the geometric center of a shape or region.

A centroid is the geometric center, or center of mass, of a shape or region. For an arc, D3 calculates it as a two-value array containing horizontal and vertical coordinates relative to the chart origin. section 4.4.3 section 4.5

Use an arc centroid to place labels accurately:

Configure the arc generator with its start and end angles. section 4.4.3
Call centroid() to obtain the label position. section 4.5
Assign the returned coordinates to an SVG text element and center its text with text-anchor and dominant-baseline. section 4.4.3

const centroid = arcGenerator
  .startAngle(0)
  .endAngle(angleDaysWithPrecipitation_rad)
  .centroid();

This listing shows the compact D3 method chain for calculating an arc centroid from its angular bounds. section 4.4.3

Labeling a donut arc

For an arc representing 35% of days with precipitation, calculate its centroid and use the two returned values as the x and y coordinates of a white percentage label. Apply the same pattern to every donut-chart arc. section 4.4.3 section 5.1.4

How D3.js in Action, Third Edition covers it

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Also explained in

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Advanced Algorithms and Data StructuresA center of mass is the point representing the coordinate-weighted average location of a body or collection of points.
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Data Without LabelsA centroid is the arithmetic mean position of a set of points and represents a cluster in centroid-based clustering.
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Outlier Detection in PythonA cluster center is a representative location or point associated with a cluster and used to measure observations' proximity to that cluster.
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Statistics Slam DunkA centroid is the central position of a set of points, commonly calculated as the coordinate-wise mean.
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Classic Computer Science Problems in Swift: Essential techniques for practicing programmersA centroid is a representative center of a cluster, typically computed as the mean position of its member points.
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Cyber Threat HuntingA centroid is the arithmetic mean of the data points assigned to a cluster and represents that cluster's center.

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Related concepts

K-means clusteringused by · K-means clustering partitions data into a specified number of groups by assigning observations to representative centers and iteratively updating those centers to reduce within-group distances.
meanuses · A mean is a measure of central tendency, calculated as the arithmetic average of values or, for a random variable, as the probability-weighted average of its possible values.
k-means++ initializationused by · K-means++ initialization is a procedure that selects initial centroids using probability proportional to squared distance from previously selected centroids.
getBoundingClientRectproduced by · getBoundingClientRect is a DOM method that returns an element's size and position relative to the viewport.

This explainer was generated by Manning's knowledge graph from the text of D3.js in Action, Third Edition. The section links point to the parts of the book it draws on.