Feng Shui

Feng shui (風水 (ふうすい) ) is a Chinese system of beliefs and principles that is aiming to create harmony with one's surroundings through the proper arrangement of objects and the siting and construction of establishments.

In Toaru Majutsu no Index, Tsuchimikado Motoharu, is the only currently known practitioner of Feng shui, and is referred to as an expert in it, as part of being an Onmyoudou specialist.

Principles
Feng shui is a magic system that focuses on the arrangement of things in a certain location to create a magic circle for a spell that activates the moment the circle is created, and its composition is dependent of its contents. The spell makes use of the energy (ch'i) of the world instead of the spellcaster's mana, as such, any person can create a spell using the principles of Feng shui.

An apt analogy for this would be is that the power of the world is a generator, the spellcaster is a transformer, and the magic circle is the circuitry, which is switched on the moment the magic circle is created.

Feng shui is explained by Idol Theory, as it still subscribes to the four elements, most specifically, its usage of the various colors, elements, cardinal directions, stars, and guardian deities, to find harmony with the world with the constructed magic circle.

Background
According to Motoharu, Feng shui originated in China, and there were originally no one who was specifically an expert of Feng shui, as such, the Taoist priest would handle the aspects of arranging objects and other things, to find harmony with nature, this task is intended for the Onmyouji in Japan.

Angel Fall Arc
Kamijou Touya amasses thousands of souvenirs and charms, believing that it would bring his son, Touma, good luck. Although, incredibly innocuous on their own, Touya arranges the various charms according to the principles of Feng shui, making his home a temple, and activating the Grand Magic, Angel Fall, after leaving his house.

Due to the danger posed by moving or destroying part of the magic circle created by Touya, Motoharu, a Feng shui expert, is forced to destroy Touya's house in order to stop Angel Fall.

Document of Constantine Arc
Feng shui is used by Tsuchimikado and Itsuwa to help Touma understand how ley lines and in particular of how the Vatican–Avignon Ley line works.

Homecoming Arc
GREMLIN's Radiosonde Castle used Feng shui as a means of tracking the Imagine Breaker, by observing the repairing of "altered" ley lines that are destroyed by Imagine Breaker. When Radiosonde Castle appears in the sky over Academy City, Accelerator uses his newly acquired knowledge of magic and Feng shui to locate the crystal "transmitter" which was calling the flying fortress.

Magic God Othinus Arc
Fenrir is able to distort the space around him as by a combination of Idol Theory and in using a principle similar from Feng shui where the existence of mountains and rivers changes the flow of energy through ley lines and the like. In his case he can create a ‘ditch’ that draws in the surrounding energy by creating a new mountain or river. The spell creates a number of black cracks, forcibly swallows up the magic power that constructed magic and sweeps it away.