We present a fast 3D analytical affine transformation (F3DAAT) method to obtain polygon-based computer-generated holograms (CGHs). CGHs consisting of tens of thousands of triangles from 3D objects are obtained by this method. We have attempted a revised method based on previous 3D affine transformation methods. In order to improve computational efficiency, we have derived and analyzed our proposed affine transformation matrix. We show that we have further increased the computational efficiency compared with previous affine methods. We also have added flat shading to improve the reconstructed image quality. A 3D object from a 3D camera is reconstructed holographically by numerical and optical experiments.
In the analytical method of polygon-based computer-generated holography, the spectrum of the surface function of an arbitrary polygon (triangle) is expressed in terms of the spectrum of a unit right triangle, which is known analytically. We perform texture mapping by dividing the triangle into many unit right sub-triangles which contain the texture information. The method has been verified by computer simulations and optical experiments.
We have developed a full analytical method with texture mapping for polygon-based computer-generated holography. A parallel planar projection mapping for holographic rendering along with affine transformation and self-similar segmentation is derived. Based on this method, we further propose a parallelogram-approximation to reduce the number of polygons used in the polygon-based technique. We demonstrate that the overall method can reduce the computational effort by 50% as compared to an existing method without sacrificing the reconstruction quality based on high precision rendering of complex textures. Numerical and optical reconstructions have shown the effectiveness of the overall scheme.
We propose the use of planar projection mapping to texture fully analytic 3D affine transformed computer-generated holograms. Simulation results show that this is an effective texture mapping method.
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