CHAPTER 4 GENERATION OF TEXTURE MAPPING
4.3 Cells Mapping
4.3.2 Texture Mapping on Model
In this subsection, we process triangles of the model separately to map textures.
At first, we search the cells which intersect the bounding box of a triangle. Then we consider the intersection between these cells and a triangle. If a triangle is inside one cell completely, we use the mapping function of the cell to map textures onto it. If not, we need to acquire the intersectional points by detecting a triangle with the cells.
There are two kinds of points between a triangle and a cell described as follows:
1. Three edges of a triangle and six surfaces of a cell
2. Twelve edges of a cell and the interior of a triangle
Figure 4.11 A triangle is subdivided into four slices by a cell
Some intersectional points are increased in the triangle. A triangle is subdivided into several slices by cells and each slice is included in a cell. An example is shown in Figure 4.11. Then we separately process each slice to map textures onto it according to the mapping function of the cell which includes it.
An interior point of a triangle A point in the edge of a triangle
Four slices of a triangle A triangle and four unit cells
Finally, we accomplish to map textures of the polycube onto the slices which belong to all triangles of the model. And this algorithm is able to reduce distortion.
Chapter 5
Implementation and Results
In this chapter, we demonstrate our implementation results. The input sources are a texture and a 3D model. Our algorithm are implemented in C# language on VC.Net with a Pentium4 3.4GHz PC with 2 GB memory.
(a) (b)
Figure 5.1 (a) example 1: an input texture and (b) a laruana model
An input example with a 183x100 texture image and a laurana model are shown in Figure 5.1. An intermediate result is the polycube of the model with unit cubes, as shown in Figure 5.2(a). Figure 5.2(b) shows that the relation between the polycube and the model. They are intersecting with each other. Figure 5.2(c) shows the polycube with tiled textures and Figure 5.2(d) shows that an image is enlarged from
Example 1
the yellow region in Figure 5.2(c). Each tile is combined by graph cuts algorithm. The final result is shown in Figure 5.3. And Figure 5.5 shows another result with different texture sample.
(a) (b)
(c)
Figure 5.2 (a) a polycube of the laruana model, (b) relation between the polycube and the model, (c) polycube with the tiled textures and (d) an enlarged image
(d)
(b)
(c)
Figure 5.3 (a) Textures map onto the model, (b) and (c) are enlarged images form the portions of (a)
(a)
Figure 5.4 shows a result of Fu and Leung [9]. Table 5.1 shows the comparison with our result.
Table 5.1 Comparison between our result and Fu and Leung [9]
Our algorithm Fu and Leung [9]
Size of a unit cube Small Large
Number of unit cubes Many Few
Size of patterns Small Large
(b)
Figure 5.4 (a) a polycube of the laruana model [20] (b) a result of the laruana model in Fu and Leung [9]
(a)
(b)
(c)
Figure 5.5 A mapping result with the texture example 2, (b) and (c) are enlarged images
Example 2
(a)
Table 5.2 shows the information of Figure 5.3 and 5.5.
Table 5.2 Information during texture mapping by using different examples
Model Laruana
Input texture Example 1 Example 2
Size of the input texture 183x100
Size of a tile 32x32
Number of unit cubes 2555
Number of surfaces on the polycube
4264
Number of different tiles 804 800
Time of constructing the polycube with tiles
5 min. 03 sec. 5 min. 09 sec.
Time of mapping from the polycube to the model
33 sec. 33 sec.
Figure 5.6 shows a synthesized texture by Wang tiles [4]. Figure 5.7 and 5.8 show that the results are mapped with the same input texture but different size of the unit cubes. Example 3 is our input texture and a 400x400 image. Figure 5.8 has lower distortion than Figure 5.7. But the size of
patterns in Figure 5.8 is smaller. We can not avoid some unconnected regions, as compared with Figure 5.6 (b).
Figure 5.6 (a) an input in Wang tiles (b) A synthesized texture from (a) [4]
(a) (b)
(b)
Figure 5.7 A mapping result with the texture example 3 and (b) and (c) are enlarged images
(c) (a) ( ) Example 3
(b)
(c)
Figure 5.8 A mapping result with the texture example 2 and (b) and (c) are enlarged images
(a)
Table 5.3 Information during texture mapping by using dixfferent sizes of unit cubes
Model Laruana
Input texture Example 3
Size of the input texture 400x400
Size of a tile 64x64
Number of different tiles 766 940
Time of constructing the polycube with tiles
8 min. 18 sec. 10 min. 40 sec.
Time of mapping from the polycube to the model
30 sec. 47 sec.
Another input model is a teapot, as shown in Figure 5.9(a), and an input texture is example 2. Figure 5.9(b) shows the polycube of the teapot with tiled textures. The final result is shown in Figure5.10.
(b) Figure 5.9 (a) A teapot model (b) The polycube of teapot with tiled textures
(a)
(b)
(a)
(c)
Figure 5.10 A mapping result with the texture example 2 and (b) and (c) are enlarged images
Example 4 is a 128x128 image, as shown in Figure 5.11. We apply different sizes of a tile. The final result is shown in Figure5.12. And the corresponding information about the teapot model is shown in Table 5.4.
Figure 5.11 Example 4: an input texture
Table 5.4 Information during texture mapping by using different input textures
Model Teapot
Input texture Example 2 Example 4
Size of the input texture 183x100 128x128
Size of a tile 32x32 64x64
Number of unit cubes 1425
Number of surfaces on the polycube
2568
Number of different tiles 648 679
Time of constructing the polycube with tiles
3 min. 56 sec. 8 min 35 sec.
Time of mapping from the polycube to the model
15 sec. 14 sec.
(b)
(a)
(c)
Figure 5.12 A mapping result with the texture example 4 and (b) and (c) are enlarged images
An input example with a 433x640 texture image and a Daba model are shown in Figure 5.13. Figure 5.14 shows the polycube of the model with tiled textures. And final result is shown in Figure 5.15.
(a) (b)
Figure 5.13 (a) a Daba model and (b) example 5: an input texture
Figure 5.14 The polycube of the Daba model with tiled textures
(a)
(b) (c)
Figure 5.15 A mapping result with the example 5 and (b) and (c) are enlarged images
(a)
(b) (c)
Figure 5.16 A mapping result with the example 2 and (b) and (c) are enlarged images
Figure 5.16 and 5.17 show the results with texture Example 2 and 6. The corresponding information about the Daba model is shown in Table 5.5.
(b)
(c) (d)
Figure 5.17 (a) Example 6: A 200x200 input texture (b) A mapping result with the texture example 6 and (c) and (d) are enlarged portions
(a)
Table 5.5 Information during texture mapping by using different input textures
Model Daba
Input texture Example 5 Example 2 Example6
Size of the input texture 433x640 183x100 200x200
Size of a tile 64x64 48x48 64x64
Number of unit cubes 1798
Number of surfaces on the polycube
2730
Number of different tiles 541 561 566
Time of constructing the polycube with tiles
6 min. 15 sec. 5 min 55 sec. 6 min. 13 sec.
Time of mapping from the polycube to the model
27 sec. 31 sec. 28 sec.
There are few apparent distortions in our results. These distortions are usually formed by the configurations of Type 5, Type 3 and Type 6. If we decrease the size of a unit cube, the shape of the polycube is close to the model. Then we reduce the distortions on the model. However, the size of patterns is reduced together. We can decrease the size of a tile so that the size of patterns is enlarged. However, the size of a tile is not too small because a tile should contain the complete structure of a texture.
Chapter 6
Conclusions
In this thesis, we proposed a method to map texture on 3D models automatically.
The proposed approach consists of two important processes: polycube construction and cells mapping. In the first process, we use the triangle-cube intersection algorithm [6] to construct the polycube of a model. Then we tile texture on the polycube seamlessly. Second, we process cells of the polycell separately. The textures of the cell are mappe d on the model according to its mapping direction. Therefore, users may generate texture mapping on the model by using our system easily. Table 6.1 shows the differences between our system and polycube-maps [20].
However, there are still some issues in our system.
1. Our system is not generic for some models which have a portion with large curvature, such as the ear of the bunny model.
2. In our experiment, we found that some cubes intersect only few regions of the model. The textures are compressed seriously when mapping them on these regions.
Table 6.1 Differences between two methods
Our algorithm Polycube-maps
Polycube construction Automatic
Number of unit cubes Many Few
In order to solve these problems, we reduce the size of a unit cube so that the shape of the polycube is close to the model. The distortion and the size of patterns on the model are reduced simultaneously. There is a trade-off between the distortion and the size of patterns on the model.
In the future, we will use different size of the unit cubes to construct the polycube. The shape of the polycube is similar to the model. Not all size of the square surfaces on the polycube is reduced. We can reduce the distortion and maintain the size of patterns at the same time. Another method of inverse warping can be used to reduce the distortion. We estimate the distortion of the cells before mapping on the model. The texture is warped in advance. Then we obtain the better results with the lower distortion.
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