1. Lapped Solid Textrues Filling a Model with Anisotropic Textures
Kenshi Takayama, Makoto Okabe, Takashi Ijiri, Takeo Igarashi
The University of Tokyo
발표: 이성호

2. Abstract representing solid objects
with spatially varying oriented textures
by repeatedly pasting solid texture exemplars
Extend the 2D lapped textures to 3D solids
creating solid models
whose textural patterns change gradually
along the depth fields
Identify several texture types

3. Procedural approach [Perlin 1985; Cutler et al. 2002]
Difficult for non-expert users

4. 2D texture synthesis on cross sections
[Owada et al. 2004; Pietroni et al. 2007]
Limitations
Inconsistency among different cross-sections
Difficulty in handling textures with discontinuous elements
Such as seeds

5. Example-based 3D solid texture synthesis
[Jagnow et al. 2004; Kopf et al. 2007]
For large-scale solid models
The amount of data and computational cost become problematic

6. Lapped textures

7. Lapped solid textures Arrange solid textures along a tensor field
handle spatially-varying textures
classify solid textures into several types
according to the amount of anisotropy and spatial variation
Designed easily and created efficiently
Little memory and computational cost

8. Classification of solid textures

9. [Kopf et al. 2007] [Owada et al. 2004] This paper Not considered 1-a
1-b
This paper
2-a and 2-b
Not considered
2-c and 2-d

10. User interface: Texture type 0

11. Type 1-a

12. Type 1-b

13. Type 2-a

14. Type 2-b

15. Manual pasting of textures

16. Algorithm: Tetrahedral mesh
The input mesh model is converted to a tetrahedral mesh model
Used the TetGen library [Si 2006]

17. Preparation of solid texture exemplars
Solid texture synthesis [Kopf et al. 2007]
Noise functions [Cook and DeRose 2005]
Volume capturing using slicers [Banvard 2002]
In-house voxel editor (this paper)
Created manually from photographs

18. Rendering an LST model convert tetrahedron model
Into a polygonal model
That consists of surface triangles
with a list of 3D texture coordinates assigned to each of its three vertices
Each surface triangle is rendered multiple times
Approximately 10–20 times
in most of our results
With alpha blending enabled

19. Cutting Constructs a scalar field
Using radial basis function (RBF) interpolation [Turk and O’Brien 1999]
Texture coordinates for each triangle on the cross-section
obtained by linear interpolation

20. Volume rendering Construct a scalar field
over the mesh vertices
To give the distance between the camera and each vertex
Calculate a large number of slices of the model
perpendicular to the camera direction
by iso-surface extraction

21. Creating an alpha mask of the solid texture
Create 3D mask
Using [Nealen et al. 2007]
The alpha value drops off around the boundary of the mask
We assume all the textures in our examples are less structured
Use a constant “splotch” mask shown in Fig. 11
for all the textures

22. Constructing a tensor field
Type 1-a and 1-b
First direction
user-drawn strokes (1-a)
Gradient direction of the depth field (1-b)
Other direction is chosen randomly
when pasting each patch
Type 2-a and 2-b
Gradient direction of the depth field
Second direction
User-drawn strokes
Third direction
Cross product of the two
Magnitudes of tensors
User-specified texture scaling values
Except for types 1-b and 2-b
Set automatically from the depth field

23. Interpolating tensor field (1/3)
Laplacian smoothing [Fu et al. 2007]

24. Interpolating tensor field (2/3)
Minimizing Laplacians (Eq. 1) while satisfying the collection of constraints (Eq. 2) in a least squares sense forms a sparse linear system, which can be solved quickly.

25. Interpolating tensor field (3/3)
Perform Laplacian smoothing
for each x-, y-, and z-component of the vectors
which are later combined and normalized.
Types 2-a and 2-b,
no guarantee that resulting vectors will
always be orthogonal to the first direction
orthogonalize these vectors
To the first direction after smoothing

27. Obtain a depth field Assign depth values Types 1-b and 2-b,
By using thin-plate RBF interpolation in the 3D Euclidean space [Turk and O’Brien 1999]
the depth field must be defined as a smooth function in 3D space
Assign depth values
of 0 and 1 to the outermost (red) and the innermost (blue) regions, respectively
Types 1-b and 2-b,
These depth values are used directly
As one of the three texture coordinates

28. Selecting a seed tetrahedron
Initialize a list of “uncovered” tetrahedra
One is selected at random
For each pasting operation
Tetrahedra are removed from the list
If they are completely covered
Repeat this process
Until the “uncovered” list becomes empty
Manual pasting of the textures
Seed tetrahedron is set to the one
Clicked by the user

29. Growing a clump of tetrahedra

30. Texture optimization

32. Coverage test of tetrahedron
linearly sample the alpha values of the mask
at these discrete points of each tetrahedron
in the clump
which are then accumulated.
Assume that the tetrahedron is completely covered by the overlapping textures
If the accumulated alpha values of all the sampling points of a tetrahedron reach 255

33. Creation of depth-varying solid models
Map the clump of tetrahedra
Into the corresponding depth position
In the texture space
Instead of the central position
alter the positional constraints
from (0.5, 0.5, 0.5)t to (0.5, dseed, 0.5, )t,
dseed is the depth value assigned to Tseed
Assuming the s-axis corresponds to the depth orientation

34. Problem & solution

35. Results

38. Limitations and future work
Patch seams
a texture with strong low-frequency components
Singularities of the tensor field
blurring artifacts
Preparation of exemplar solid textures