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Volumes of irregularly shaped objects can be systematically determined using the concept of solids of revolution. This approach begins with a region defined by a curve in a two-dimensional plane. When this region is rotated about a fixed line, known as the axis of revolution, it generates a three-dimensional object with rotational symmetry. Such objects frequently arise in mathematical modeling, physics, and engineering applications.When the region being rotated lies directly against the axis...

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Updated: May 29, 2026

High-throughput Image Analysis of Tumor Spheroids: A User-friendly Software Application to Measure the Size of Spheroids Automatically and Accurately

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Published on: July 8, 2014

Packing volumes by spheres.

R Mohr¹, R Bajcsy

¹Unite d'Enseignement et de Recherche Sciences Mathematiques, Université de Nancy, Nancy, France.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This summary is machine-generated.

This study introduces a novel sphere packing algorithm for arbitrary volumes, achieving greater data reduction than existing methods by fitting only tangential spheres. The algorithm generates a graph representing sphere relationships and offers a hierarchy of intrinsic volume properties.

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Area of Science:

Computational geometry
Geometric algorithms
Data visualization

Background:

Sphere packing is a fundamental problem in geometry and computer science.
Existing methods like Blum's transform have limitations in data reduction.
Efficiently representing complex volumes requires advanced packing techniques.

Purpose of the Study:

To present a new algorithm for packing spheres within arbitrary volumes.
To improve data reduction compared to existing sphere packing methods.
To enable the derivation of a hierarchy of intrinsic volume properties.

Main Methods:

Developing an algorithm that fits only tangential spheres of variable radii.
Generating a graph representation where nodes are sphere centers and arcs connect tangent spheres.
Analyzing computational complexity, time, and error considerations.

Main Results:

The algorithm achieves larger data reduction than Blum's transform.
Variable radii spheres allow for a hierarchy of intrinsic volume properties.
The output is a graph detailing sphere center positions and tangent connections.

Conclusions:

The proposed sphere packing algorithm offers enhanced data reduction for arbitrary volumes.
The variable radii approach provides a multi-scale analysis of volume properties.
The resulting graph structure is valuable for geometric analysis and visualization.