Normally after voiding out or dying in water, Amaterasu will warp to the point where she was last standing. However, when loading into a new area, if the player jumps on the first frame of allowable input, Amaterasu's respawn point is initialized to (0, 0, 0) and remains unchanged until she lands. Therefore, if Amaterasu voids out or dies in water before landing on the ground, she will respawn at (0, 0, 0) instead of where she entered the level.
Alternatively, it is possible to jump on the first frame after landing to keep the respawn point at (0, 0, 0). These one frame jumps can be repeated until voiding out.
Documentation explaining when to jump to set it up correctly (only useful for TAS as of now) https://youtu.be/SnGqj1KZSmM
Origin warp is possible in almost every location, but only a few locations have proven to be useful in runs. These are explained in detail, but a complete list of all origin points can be found here: https://docs.google.com/document/d/11VeokQNVGnWjtICilrUVeSxM6hvfzSDiYu1x-nMfJBA
Gale Shrine Origin Warp
This warp is used in NG+ to warp from the entrance of Gale Shrine to the elevator in order to quickly obtain Galestorm. This is done by first entering Gale Shrine to clear the initial cutscene. Exit, re-enter and jump on the first frame. This can be repeated until the jump is successful. Then KT down the hallway and over the invisible wall to void out. After landing in the elevator, KT up one floor and go toward the balcony. KT over the invisible wall and clip into the bottom of the top platform to obtain Galestorm.
Video tutorial for Gale Shrine origin warp: https://youtu.be/zP8QxOk26E4
Gale Shrine Origin Warp was discovered by Lyriati, and proven to be RTA Viable by Cornchunks.
Oni Island Origin Warp
This warp is used in NG+ to warp from the entrance of Oni Island to the top of the mountain in order to quickly obtain Thunderstorm. This is done by jumping on the first frame after entering Oni Island, and doing one KT to get over the invisible wall. Land in the water and swim at full speed to die quickly. This will warp Amaterasu below the mountain and she will be launched into the air. After reaching max height, KT over to the Gekigami statue and rejuvenate the bow and arrow.
Video of the origin warp being performed: https://youtu.be/_IBHsUUgoqA
Origin Warp originally found by: DriftingPancake - ZLAMP
Discovery of 1 Frame Jumping - Lyriati