Preset Planes: Custom zw-plane yw-plane xw-plane xy-plane A diagonal plane Vector u: Vector v: Angle: Play Pause Random Day Mode What is going on

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This visualization represents the projection of a four-dimensional hypercube (tesseract) into three dimensions. The algorithm works as follows:

1. Four-Dimensional Representation: The tesseract is defined in ℝ⁴ with vertices at all points (±1, ±1, ±1, ±1).
2. Rotation in Four Dimensions: The animation rotates the tesseract around a plane spanned by two user-defined orthonormal vectors u, v.
3. Projection to Three Dimensions: The rotated tesseract is projected into ℝ³ using a central projection.
4. Rendering with WebGL: The projected 3D vertices are used to draw the edges of the tesseract using Three.js.