Mark a point Gaussian Splatting on WEBGL

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I've been experimenting with Gaussian Splatting neural networks after reading about them on Hugging Face's blog. I've utilized one of the available open-source models to create a 3D file from a collection of 1k 2D images. The outcome has been quite impressive, as seen in this example: Excavator.

Being relatively new to the 3D realm, I'm eager to enhance my project by enabling users to mark points in space using their mouse. Converting mouse clicks on the canvas to coordinates in the 3D world is straightforward. However, I'm unsure how to mark a point in space at a distance from the camera's location. Clicking on the screen and converting to 3D space yields coordinates on the camera plane, but how can I extend this to mark a point in 3D space at a certain distance from the camera?

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