Lvdi Wang Tsinghua University Microsoft Research Asia Lvdi Wang Tsinghua University Microsoft Research Asia Kun Zhou Zhejiang University Kun Zhou Zhejiang University Yizhou Yu University of Illinois at Urbana-Champaign Yizhou Yu University of Illinois at Urbana-Champaign Baining Guo Tsinghua University Microsoft Research Asia Baining Guo Tsinghua University Microsoft Research Asia

Efficient random access in rendering A choice between resolution and memory Texture mapping Without texture With bitmap texture

Efficient random access in rendering A choice between resolution and memory Resolution: Memory: 0.2 MB Resolution: Memory: 3.0 MB

No need for parameterization Consistent interior & exterior Memory consumption increases cubically! [Kopf et al. 07][Dong et al. 08][Takayama et al. 08]

No need for parameterization Consistent interior & exterior Memory consumption increases cubically! [Dong et al. 08] [Takayama et al. 08] [Kopf et al. 07]

Compact and resolution-independent Limited to 2D content SVG ( Diffusion Curves Diffusion Curves [Orzan et al. 08]

Resolution-independent Efficient rendering Compact storage Benefits of solid textures A VST textured model Rendered at 110 Fps Size: 1.55 MB

Vector Solid Textures

Sharp discontinuities + Smooth variations Sharp discontinuities + Smooth variations 2D texture Bitmap texture (linear interpolation) Vector texture

Sharp discontinuities + Smooth variations Sharp discontinuities + Smooth variations Solid texture Discontinuities highlighted Surfaces formed by discontinuities

Region boundaries Region boundaries Region labels Region labels Color variations Color variations

Region boundaries Region boundaries Region labels Region labels Color variations Color variations » Signed distance function » Stored on a 3D grid » Tricubic interpolation 3D surfaces Signed distance function

Region boundaries Region boundaries Region labels Region labels Color variations Color variations » Conceptually: Stored on the SDF grid » In practice: Efficient compression Region labels

Region boundaries Region boundaries Region labels Region labels Color variations Color variations » Radial Basis Functions (RBF) RBFs illustrated in 2D

Basic rasterization pipeline: Basic rasterization pipeline: SDFLabels Final color RBFs pp Tex. volume tt D(t)D(t)D(t)D(t) D(t)D(t)D(t)D(t) L(t)L(t)L(t)L(t) L(t)L(t)L(t)L(t)

Bitmap Solid Texture

Create SDF Create SDF Label Regions Label Regions RBF Fitting RBF Fitting

Create SDF Create SDF Label Regions Label Regions RBF Fitting RBF Fitting » Does there already exist one? » Texture synthesis algorithms use them as Feature Maps » Texture synthesis algorithms use them as Feature Maps [Lefebvre & Hoppe 06] [Kopf et al. 07] … colormaskSDF colorSDF Input 2D exemplar Output solid texture

Create SDF Create SDF Label Regions Label Regions RBF Fitting RBF Fitting » We can also create one » Image Analogy » Image Analogy [Hertzmann et al. 01] : : : : Solid texture 2D slice 2D mask 2D SDF 3D SDF

Create SDF Create SDF Label Regions Label Regions RBF Fitting RBF Fitting » Find connected components in the signed distance function Signed distance function Region labels

Create SDF Create SDF Label Regions Label Regions RBF Fitting RBF Fitting » Find n RBFs that best approximate the existing color distribution » Techniques: » L-BFGS-B minimizer » L-BFGS-B minimizer [Zhu et al. 97] » Teleportation » Teleportation [Cohen-Steiner et al. 04]

Vector Solid Textures

Bitmap solid texture Resolution: Memory: 6.0 MB Vector solid texture Num. RBFs: 5183 Memory: 1.2 MB

Bitmap solid texture Resolution: Storage: 6.0 MB Vector solid texture Num. RBFs: 5183 Storage: 1.2 MB

Num. RBFs: 7137 Storage: 1.3 MB

Algebraic and Boolean operations on textures Algebraic and Boolean operations on textures += VST #1 VST #2 Hybrid VST

Self-similar textures Self-similar textures 1 scale 2 scales 3 scales

Performance: Fps NVidia GeForce 8800GTX, window Performance: Fps NVidia GeForce 8800GTX, window Storage: 17-26% of the respective input bitmap solid texture Storage: 17-26% of the respective input bitmap solid texture

Store two region labels at every voxel Store two region labels at every voxel Octree compression [Lefebvre et al. 05] Octree compression [Lefebvre et al. 05] Save 70% % storage Save 70% % storage Useful in rendering Useful in rendering

Utilize SDF and region label pairs Utilize SDF and region label pairs High quality anti-aliasing Little performance overhead Without anti-aliasing With anti-aliasing δ

Some boundaries are not that sharp Some boundaries are not that sharp Same as anti-aliasing, but with different δ Same as anti-aliasing, but with different δ

Explicit surface Implicit surface » Random-access » Vectorization » Compactness » Flexibility Root finding Compression 2-colorable constraint Surface fitting Direct & utilizes GPU Robust and efficient Adaptive Less constraint Multiple SDFs

Contribution: A compact random-access vector representation for solid textures Contribution: A compact random-access vector representation for solid textures Future work: Interactive texture authoring tool Future work: Interactive texture authoring tool