Abstract

We propose a method that achieves efficient texture mapping in fully-analytic computer generated holograms based on triangular meshes. In computer graphics, the texture mapping is commonly used to represent the details of objects without increasing the number of the triangular meshes. In fully-analytic triangular-mesh-based computer generated holograms, however, those methods cannot be directly applied because each mesh cannot have arbitrary amplitude distribution inside the triangular mesh area in order to keep the analytic representation. In this paper, we propose an efficient texture mapping method for fully-analytic mesh-based computer generated hologram. The proposed method uses an adaptive triangular mesh division to minimize the increase of the number of the triangular meshes for the given texture image data. The geometrical similarity relationship between the original triangular mesh and the divided one is also exploited to obtain the angular spectrum of the divided mesh from pre-calculated data for the original one. As a result, the proposed method enables to obtain the computer generated hologram of high details with much smaller computation time in comparison with the brute-force approach. The feasibility of the proposed method is confirmed by simulations and optical experiments.

© 2016 Optical Society of America

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References

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  1. R. L. Cook, L. Carpenter, and E. Catmull, “The Reyes image rendering architecture,” Comput. Graph. 21(4), 95–102 (1987).
    [Crossref]
  2. S. Guha, Computer Graphics Through OpenGL: From Theory to Experiments (CRC, 2015).
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    [Crossref]
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    [Crossref] [PubMed]
  5. K. Matsushima, M. Nakamura, and S. Nakahara, “Novel techniques introduced into polygon-based high-definition CGHs,” in Biomedical Optics, OSA Technical Digest Series (Optical Society of America, 2010), paper JMA10.
  6. K. Matsushima and S. Nakahara, “A high-definition full-parallax CGH created by the polygon-based method,” in Advances in Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper PDWB38.
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  10. J.-H. Park, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, and S.-H. Kim, “Removal of line artifacts on mesh boundary in computer generated hologram by mesh phase matching,” Opt. Express 23(6), 8006–8013 (2015).
    [Crossref] [PubMed]
  11. J.-H. Park, S.-B. Kim, H.-J. Yeom, H.-J. Kim, H. Zhang, B. Li, Y.-M. Ji, S.-H. Kim, and S.-B. Ko, “Continuous shading and its fast update in fully analytic triangular-mesh-based computer generated hologram,” Opt. Express 23(26), 33893–33901 (2015).
    [Crossref] [PubMed]
  12. H.-G. Lim, N.-Y. Jo, and J.-H. Park, “Hologram synthesis with fast texture update of triangular meshes,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2013), paper DW2A.8.
  13. W. Lee, D. Im, J. Paek, J. Hahn, and H. Kim, “Semi-analytic texturing algorithm for polygon computer-generated holograms,” Opt. Express 22(25), 31180–31191 (2014).
    [Crossref] [PubMed]
  14. H.-J. Yeom and J.-H. Park, “Calculation of reflectance distribution using angular spectrum convolution in mesh-based computer generated hologram,” Opt. Express 24(17), 19801–19813 (2016).
    [Crossref] [PubMed]

2016 (1)

2015 (2)

2014 (2)

2008 (2)

2005 (1)

1997 (1)

F. M. Weinhaus and V. Devarajan, “Texture mapping 3D models of real-world scenes,” ACM Comput. Surv. 29(4), 325–365 (1997).
[Crossref]

1987 (1)

R. L. Cook, L. Carpenter, and E. Catmull, “The Reyes image rendering architecture,” Comput. Graph. 21(4), 95–102 (1987).
[Crossref]

Ahrenberg, L.

Benzie, P.

Carpenter, L.

R. L. Cook, L. Carpenter, and E. Catmull, “The Reyes image rendering architecture,” Comput. Graph. 21(4), 95–102 (1987).
[Crossref]

Catmull, E.

R. L. Cook, L. Carpenter, and E. Catmull, “The Reyes image rendering architecture,” Comput. Graph. 21(4), 95–102 (1987).
[Crossref]

Cook, R. L.

R. L. Cook, L. Carpenter, and E. Catmull, “The Reyes image rendering architecture,” Comput. Graph. 21(4), 95–102 (1987).
[Crossref]

Devarajan, V.

F. M. Weinhaus and V. Devarajan, “Texture mapping 3D models of real-world scenes,” ACM Comput. Surv. 29(4), 325–365 (1997).
[Crossref]

Hahn, J.

Im, D.

Ji, Y.-M.

Jia, J.

Kim, H.

Kim, H.-J.

Kim, S.-B.

Kim, S.-H.

Ko, S.-B.

Lee, B.

Lee, W.

Li, B.

Li, X.

Liu, J.

Magnor, M.

Matsushima, K.

Paek, J.

Pan, Y.

Park, J.-H.

Wang, Y.

Watson, J.

Weinhaus, F. M.

F. M. Weinhaus and V. Devarajan, “Texture mapping 3D models of real-world scenes,” ACM Comput. Surv. 29(4), 325–365 (1997).
[Crossref]

Yeom, H.-J.

Zhang, H.

ACM Comput. Surv. (1)

F. M. Weinhaus and V. Devarajan, “Texture mapping 3D models of real-world scenes,” ACM Comput. Surv. 29(4), 325–365 (1997).
[Crossref]

Appl. Opt. (4)

Comput. Graph. (1)

R. L. Cook, L. Carpenter, and E. Catmull, “The Reyes image rendering architecture,” Comput. Graph. 21(4), 95–102 (1987).
[Crossref]

Opt. Express (4)

Other (4)

H.-G. Lim, N.-Y. Jo, and J.-H. Park, “Hologram synthesis with fast texture update of triangular meshes,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest Series (Optical Society of America, 2013), paper DW2A.8.

K. Matsushima, M. Nakamura, and S. Nakahara, “Novel techniques introduced into polygon-based high-definition CGHs,” in Biomedical Optics, OSA Technical Digest Series (Optical Society of America, 2010), paper JMA10.

K. Matsushima and S. Nakahara, “A high-definition full-parallax CGH created by the polygon-based method,” in Advances in Imaging, OSA Technical Digest Series (Optical Society of America, 2009), paper PDWB38.

S. Guha, Computer Graphics Through OpenGL: From Theory to Experiments (CRC, 2015).

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Figures (14)

Fig. 1
Fig. 1 Concept of texture mapping (a) global coordinate of 3D object (b) UV coordinate of texture pattern
Fig. 2
Fig. 2 Global and local coordinates of triangular mesh (a) transformation of the global coordinate to local coordinate (b) transformation of the local triangular mesh to the reference triangle
Fig. 3
Fig. 3 Concept of adaptive and recursive mesh division
Fig. 4
Fig. 4 Unit division process (a) current triangle (b) divided triangles
Fig. 5
Fig. 5 Adaptive triangle division according to the texture data inside the triangle (a) An example of the case where the division is performed (b) an example of the case where the division is not performed
Fig. 6
Fig. 6 Flow chart of the proposed method for each original triangular mesh
Fig. 7
Fig. 7 3D objects used in the simulation and optical experiments. (a) cube object having 24 triangular meshes (b) teapot object having 756 triangular meshes
Fig. 8
Fig. 8 Comparison of reconstructed triangular mesh (a) original triangle (b) textured triangle in case of brute-force method (c) textured triangle in case of the proposed method
Fig. 9
Fig. 9 Simulation and optical experiment results of textured 3D object (a) texture pattern (b) simulation and optical reconstruction of the cube hologram generated by the proposed method (c) simulation and optical reconstruction of the teapot hologram generated by the proposed method
Fig. 10
Fig. 10 Two texture patterns having different pattern density (a) low density texture pattern (b) high density texture pattern
Fig. 11
Fig. 11 Simulation and optical experiment results of textured 3D object for different maximum recursive division level nmax (a) cube object with low density texture pattern (b) cube object with high density texture pattern (c) teapot object with low density texture pattern (d) teapot object with high density texture pattern
Fig. 12
Fig. 12 The number of the sub-triangles (a) cube object with low density texture pattern (b) cube object with high density texture pattern (c) teapot object with low density texture pattern (d) teapot object with high density texture pattern
Fig. 13
Fig. 13 Calculation time comparison (a) cube object with low density texture pattern (b) cube object with high density texture pattern (c) teapot object with low density texture pattern (d) teapot object with high density texture pattern
Fig. 14
Fig. 14 Experimental result of textured teapot object with diffusive and specular reflection

Equations (10)

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u=0.5+ φ 2π , v=0.5+ θ π ,
U( r x,y )= G( f x,y )exp[ j2π f x,y T r x,y ] d f x,y ,
G( f x,y )= G l ( f xl,yl )exp[ j2π f xl,yl,zl T c ] f zl f z ,
G l ( f xl,yl )= G o ( A -T { f xl,yl 1 λ [ u xl T u yl T ] u c } ) det(A) = G o ( A -T f xl,yl ) det(A) = G o ( f xr,yr ) det(A) ,
g l (n) ( r xl,yl )= g l,bare ( ( 1 ) k 2 n ( r xl,yl r gl (n) )+ r gl )exp{ j 2π λ ( [ u xl T u yl T ] u c ) T r xl,yl },
G l (n) ( f xl,yl )= 1 4 n exp[ j2π f xl,yl T ( r gl (n) r gl ( 1 ) k 2 n ) ] G l,bare ( f xl,yl ( 1 ) k 2 n ),
G l (n) ( f xl,yl )= 1 4 n exp[ j2π f xl,yl T ( r gl (n) r gl ( 1 ) k 2 n ) ] G o ( 1 ( 1 ) k 2 n f xr,yr ) det( A ) ,
G o ( f xr,yr )= exp[ j2π f xr ]1 ( 2π ) 2 f xr f yr + 1exp[ j2π( f xr + f yr ) ] ( 2π ) 2 f yr ( f xr + f yr ) =( T 2 T 1 )+ T 1 exp( j T 3 ) T 2 exp( j T 4 ),
T 1 = 1 ( 2π ) 2 f xr f yr , T 2 = 1 ( 2π ) 2 f yr ( f xr + f yr ) , T 3 =2π f xr , T 4 =2π( f xr + f yr ).
G l (n) ( f xl,yl )= 1 det( A ) exp[ j2π f xl,yl T ( r gl (n) r gl ( 1 ) k 2 n ) ] ×{ ( T 2 T 1 )+ T 1 exp[ (1) k+1 j T 3 2 n ] T 2 exp( (1) k+1 j T 4 2 n ) }.

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