Visualizing 3D models with fine-grain surface depth Author: Roi Méndez Fernández Supervisors: Isabel Navazo (UPC) Roger Hubbold (University of Manchester) _________________________________________________________________________Index Index 1. Introduction ..................................................................................................................... 7 2. Main goal .......................................................................................................................... 9 3. Depth hallucination ........................................................................................................ 11 3.1. Background ............................................................................................................. 11 3.2. Output .................................................................................................................... 14 4. Displacement mapping .................................................................................................. 15 4.1. Background ............................................................................................................. 15 4.1.1. Non-iterative methods ................................................................................... 17 a. Bump mapping ...................................................................................... 17 b. Parallax mapping ................................................................................... 18 c. Parallax mapping with offset limiting .................................................... 19 d. Parallax mapping taking into account the slope ................................... 19 4.1.2. Unsafe iterative methods ............................................................................... 20 a. Iterative parallax mapping .................................................................... 20 b. Binary search ......................................................................................... 21 c. Secant method ...................................................................................... 22 4.1.3. Safe iterative methods ................................................................................... 22 a. Linear search ......................................................................................... 22 b. Other methods ...................................................................................... 23 4.2. Displacement mapping implementation ................................................................ 24 4.2.1. Relief mapping ................................................................................................ 24 4.2.2. Interval mapping............................................................................................. 25 4.2.3. Relaxed Cone stepping ................................................................................... 27 4.3. Results of implementation ..................................................................................... 31 5. Illumination .................................................................................................................... 37 5.1. Background ............................................................................................................. 38 5.2. HDR Images ............................................................................................................ 39 5.2.1. Environment map creation ............................................................................. 40 5.2.2. Median cut sampling ...................................................................................... 44 a. Implementation ..................................................................................... 44 5.3. Results of implementation ..................................................................................... 52 6. Geometry images ........................................................................................................... 55 6.1. Background ............................................................................................................. 55 6.2. Implementation and use ........................................................................................ 55 6.3. Results of implementation and use........................................................................ 57 6.4. Conclusions and future work.................................................................................. 59 7. Acknowledgements ........................................................................................................ 61 References ...................................................................................................................... 63 Appendices ..................................................................................................................... 65 3 Visualizing 3D models with fine-grain surface depth___________________________________ 4 __________________________________________________________________ Figures index Figures index Figure 1: Model reconstructed from a set of photographs ............................................ 7 Figure 2: Model reconstructed from photographs lit with one point light ......................... 9 Figure 3: Original photograph from a real Mayan building, derived model relighted with different light conditions and the same model with another illumination ....................... 11 Figure 4: Flow chart showing the steps in the process ............................................... 12 Figure 5: Example of an input photograph pair ....................................................... 12 Figure 6: Example of a profile of a textured surface and the separation between the above- plane and below-plane surface models .................................................................. 13 Figure 7: Difference between a render using a depth hallucinated map and a render using a laser scanned map ........................................................................................... 13 Figure 8: Original photograph and reconstructed and relighted model .......................... 14 Figure 9: Depth map and computed normal map using the Sobel operator ...................... 14 Figure 10: Displacement mapping scheme .............................................................. 15 Figure 11: Displacement mapping process scheme .................................................... 16 Figure 12: Displacement mapping ........................................................................ 16 Figure 13: Bump mapping .................................................................................. 17 Figure 14: Texture mapping and Bump mapping ...................................................... 17 Figure 15: Parallax mapping ............................................................................... 18 Figure 16: Comparison between bump mapping and parallax mapping ........................... 18 Figure 17: Parallax mapping with offset limiting ..................................................... 19 Figure 18: Parallax mapping and Parallax mapping with offset limiting ......................... 19 Figure 19: Parallax mapping taking into account the slope ......................................... 20 Figure 20: Comparison between parallax mapping with offset limiting and parallax mapping taking into account the slope ............................................................................. 20 Figure 21: Comparison between parallax mapping with slope and iterative parallax mapping .................................................................................................................. 21 Figure 22: Binary search .................................................................................... 21 Figure 23: Binary search results .......................................................................... 21 Figure 24: Secant method .................................................................................. 22 Figure 25: Linear search .................................................................................... 22 Figure 26: Linear search results .......................................................................... 23 Figure 27: Cone stepping ................................................................................... 23 Figure 28: Interval mapping ............................................................................... 25 Figure 29: Comparison between interval mapping and relief mapping with two steps in the interval mapping and binary search step respectively ............................................... 26 Figure 30: Comparison between conservative and relaxed cones .................................. 27 Figure 31: An intermediate step during computation of a cone ratio ............................. 28 Figure 32: Some viewing directions and relaxed cone ................................................ 28 Figure 33: Cone map and relaxed cone map ........................................................... 29 Figure 34: Ray-relaxed cone intersection process ..................................................... 29 Figure 35: Relief mapping artifacts with 10 linear search steps and relief mapping with 20 linear search steps .......................................................................................... 32 Figure 37: Interval mapping using 10 linear search steps and interval mapping using 20 search steps. .........................................................................................................