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Related Concept Videos

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Metallic Solids02:37

Metallic Solids

Metallic solids such as crystals of copper, aluminum, and iron are formed by metal atoms. The structure of metallic crystals is often described as a uniform distribution of atomic nuclei within a “sea” of delocalized electrons. The atoms within such a metallic solid are held together by a unique force known as metallic bonding that gives rise to many useful and varied bulk properties.
All metallic solids exhibit high thermal and electrical conductivity, metallic luster, and malleability. Many...
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...
Ionic Crystal Structures02:42

Ionic Crystal Structures

Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size.
Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result (1) when ions of one charge are surrounded by as many ions as possible of the opposite...
Structures of Solids02:22

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
Unit Cells01:18

Unit Cells

A crystal's internal structure is an orderly array of atoms, ions, or molecules, and the details of this array significantly influence the solid's properties. In a crystal, periodically repeating 'structural motifs' - which could be atoms, molecules, or groups thereof - create a 'space lattice.' This is essentially a three-dimensional, infinite array of points, each surrounded by its neighbors in an identical way, forming the basic structure of the crystal.A 'unit cell' is a theoretical...

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Related Experiment Video

Updated: May 29, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Chain coding with a hexagonal lattice.

D K Scholten1, S G Wilson

  • 1Department of Electrical Engineering, University of Virginia, Charlottesville, VA 22901; The Analytic Sciences Corporation, Reading, MA 01867.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

Hexagonal chain coding offers improved efficiency for curve quantization compared to square lattices. This method reduces bit rates by approximately 15% for similar quantization errors, enhancing data compression for general curves.

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Area of Science:

  • Digital signal processing
  • Image compression
  • Geometric algorithms

Background:

  • Chain code quantization is a method for representing curves digitally.
  • Standard methods often use square lattice structures, which can be inefficient.
  • Exploring alternative lattice structures may yield performance improvements.

Purpose of the Study:

  • To investigate the performance of hexagonal lattice chain code quantization for general curves.
  • To compare the efficiency of hexagonal lattices against traditional square lattices.
  • To develop and evaluate algorithms for hexagonal chain coding.

Main Methods:

  • Theoretical performance analysis using a generalized grid-intersect quantization model for straight lines.
  • Development of a chain coding algorithm specifically for hexagonal lattices.
  • Computer simulations evaluating hexagonal chain coding on various curves (straight lines, circles, stochastic models).

Main Results:

  • Theoretical predictions for straight lines were validated for curves with a radius of curvature approximately twice the lattice constant.
  • Hexagonal coding achieved approximately 15% reduction in bit rate for a given peak quantization error compared to square lattice codes.
  • Qualitative improvements in fidelity were observed with hexagonal chain coding.

Conclusions:

  • Hexagonal lattice chain code quantization provides a more efficient method for representing general curves than square lattices.
  • The developed hexagonal chain coding algorithm demonstrates practical benefits in terms of bit rate reduction and fidelity.
  • This approach is particularly effective for curves with larger radii of curvature relative to the lattice constant.