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

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

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

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

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

Lapped textures

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

Classification of solid textures

[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

User interface: Texture type 0

Type 1-a

Type 1-b

Type 2-a

Type 2-b

Manual pasting of textures

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

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

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

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

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

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

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

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

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.

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

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

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

Growing a clump of tetrahedra

Texture optimization

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

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

Problem & solution

Results

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