Rotations in three dimensions as elements of the special orthogonal group SO(3). Explore Euler angles, quaternions, axis-angle, and Rodrigues–Frank vectors — all updated simultaneously in real time.
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Visualise a crystal unit cell in 3D and apply rotations interactively. See how symmetry operations map the lattice onto itself, and compare orientations before and after each transformation.
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Visualise the region of orientation space bounded by crystal point-group symmetry in 3D Rodrigues–Frank space. Explore how orientation equivalence classes collapse into a compact convex domain.
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Explore crystallographic directions as unit vectors on the sphere. Interactively pick Miller indices [hkl], visualise the corresponding lattice direction, and measure inter-direction angles.
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Project crystal poles onto a stereographic plane to produce pole figures — the standard representation of preferred orientation (texture) in polycrystalline materials. Visualise single-crystal and texture distributions.
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