Fig. 1. Relationship of an arbitrary triangle and the hologram plane.

Fig. 2. Mapping between (unit right triangle) primitive triangle and arbitrary triangle.

Fig. 3. Coordinates and vertex normals of sub-triangles.

Fig. 4. Numerically reconstructed images of the sphere. (a) Park’s shading method: continuous shading. (b) and (c) Proposed shading method: Phong shading approximation. The sphere is subdivided at M = 2 in (b) and M = 3 in (c).

Fig. 5. Numerically and optically constructed images of the teapot. (a) No shading: The brightness of the entire surface is uniform. (b) Flat shading: The brightness within each triangle of the 3D object is uniform. (c) Park et al.’s shading method: continuous shading. (d) Proposed shading method: Phong shading approximation, with subdivision degree M = 3.

Fig. 6. Numerically reconstructed images of the teapot. (a) Wang et al.’s shading method: simulate Phong shading. (b) Proposed shading method: Phong shading approximation. Teapot is subdivided at M = 3, M = 8, M = 16, and M = 32.

Fig. 7. Comparison of the calculation time for five different methods. Note that the no shading, flat shading, and Park et al. methods are independent of M.

Fig. 8. Numerical reconstruction of (a) Park’s method and (b) the proposed method on complicated 3D objects, with subdivision degree M = 3. (c) Optically reconstructed images of 3D objects: proposed shading method, with subdivision degree M = 3.