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Hückel's Rule Diagram of π MOs: Frost Circle

Hückel's Rule Diagram of π MOs: Frost Circle

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...

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Related Experiment Video

Updated: Jun 13, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

Viewpoint-dependent lighting on polygonal holograms using bump mapping.

Fan Wang, David Blinder, Yogi Udjaja

|September 13, 2024

Summary

This summary is machine-generated.

This study introduces a novel hologram generation method for 3D displays. It accurately models viewpoint-dependent lighting on polygonal objects, enhancing realism with smooth shading and high computational performance.

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Last Updated: Jun 13, 2025

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Digital Inline Holographic Microscopy DIHM of Weakly-scattering Subjects

Published on: February 8, 2014

Recording Ultra-Realistic Full-Color Analog Holograms for Use in a Moving Hologram Display

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Published on: January 14, 2020

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Published on: September 25, 2020

Area of Science:

Computer graphics
Optics
Holography

Background:

Accurate 3D displays require modeling viewpoint-dependent light reflections.
Existing methods may struggle with dynamic lighting and smooth shading on complex objects.

Purpose of the Study:

To propose a new hologram generation method for polygonal meshes.
To achieve viewpoint-dependent lighting effects and smooth shading with low-polygon objects.

Main Methods:

Leveraging bump mapping to create a bump-phase map.
Encoding light wave propagation frequency.
Spreading reflected light waves for specific viewpoint reception.

Main Results:

Successful generation of holograms with viewpoint-dependent lighting.
Rendering smooth shading on low-polygon objects.
High computational performance confirmed through simulations with small pixel pitches.

Conclusions:

The proposed method effectively generates holograms with dynamic lighting.
It offers a computationally efficient approach for realistic 3D holographic displays.