• Jiří Filip · ÚTIA AV ČR · ANI-PG2
• Veřejně dostupná data měřených materiálů a jejich vizualizace.
• PDF exportováno 7. 10. 2026; staré datum 8. 9. 2018 v textové vrstvě je údaj šablony, nikoli ověřený termín přednášky.

• MERL [Matusik et al., SIGGRAPH 2003]: 100 isotropic BRDFs. Fitted models: Ngan et al.
• UTIA [Vávra & Filip, PG 2014]: 150 anisotropic BRDFs.
• RGL [Dupuy & Jakob, 2018]: 36 spectral BRDFs, including 4 anisotropic; wavelengths 310–1100 nm.

• CURET (Columbia & Utrecht): 61 BTFs with limited sampling directions.
• Yale University BTF database.
• Bonn BTF database: 100 BTFs.
• UTIA BTF database: 22 BTFs.

• OpenSVBRDF: 1000+ isotropic PBR maps.
• ChaosScans V-Ray and xRite TAC7: custom BTF formats.
• SIGHTTEX Q: open BTF formats BIG and MIF.

• 150 materials: 16 wood, 6 carpet, 96 fabric, 16 leather, 6 plastic and 10 other materials.
• Fabric: upholstery, apparel and cushion. Leather includes genuine and imitation materials.
• Other materials include plaster, paper and paint.

• The source shows the complete material overview.
• Elevation step: 15°. Azimuthal step: 7.5°.
• Counts and sampling figures describe the lecture dataset snapshot.

• 6 BTFs as collections of images.
• 16 BTFs in BIG data format.
• The source panel shows the measured samples.

• Texture mapping.
• World-to-local coordinate transformation and local texture space.
• Local texture-space and measured-direction interpolation.
• Point light versus environment illumination.
• Anti-aliasing.

• 3D geometry v is paired with per-vertex 2D texture coordinates (s,t).
• The unwrapped triangle mesh maps the 2D texture onto the 3D surface.
• The original illustration shows the mapping and seams.

• World-space light and view directions must be expressed in the local texture frame.
• The local frame follows the surface and texture orientation.
• The source contrasts world light/view positions Lw,Vw with local directions L,V.

• Obtain illumination and view directions in the local texture frame.
• For an orthonormal frame: Llocal = (T·Lw, B·Lw, N·Lw); likewise for the view direction.
• The original matrix and geometric construction are retained in the source panel.

Poznámka GRAFIT: interpolace vektorů obecně nezachová jejich jednotkovou délku ani kolmost. Při použití lokálního rámce je potřeba jeho normalizace a případná ortogonalizace.

• The source compares a 1000-triangle model using a per-triangle frame and an interpolated per-pixel frame.
• The original renderings show how interpolation changes the appearance.
• Source credit: Haindl & Filip, Material Appearance.

• Weights describe a point as p = w1·v1 + w2·v2 + w3·v3, with w1+w2+w3=1.
• All three weights strictly positive: point inside the triangle.
• A zero weight: point on the opposite edge when the other weights are nonnegative. Two zero weights: the corresponding vertex.
• A negative weight places the point outside across the opposite edge. Source: Möbius 1827; Coxeter 1969; Fauvel et al. 1999.

Poznámka GRAFIT: interpolace vektorů obecně nezachová jejich jednotkovou délku ani kolmost. Při použití lokálního rámce je potřeba jeho normalizace a případná ortogonalizace.

• Compare no interpolation, local texture-space interpolation and LTS + BTF interpolation.
• Analytical reflectance models evaluate arbitrary directions; measured BTF samples require interpolation between measured directions.

• The source combines three nearby illumination directions with three nearby view directions.
• The interpolated value is the weighted sum of nine BTF images.
• Each coefficient is the product of the illumination and viewing barycentric weights.

• Interpolate for each rendered pixel or fragment.
• Indices and weights for the three closest directions can be precomputed and stored, for example in cube maps.
• The source describes graphics-hardware implementation. Directions above the measured elevation range require special treatment.

• Outgoing radiance consists of emitted and reflected radiance. The source crosses out the emitted term for its non-emissive example.
• The rendering equation combines surface reflectance, incident radiance and the projected-area cosine over incident directions.
• The source panel preserves the original equation and labels.

• Integrate reflected radiance over the hemisphere. The source notes that the foreshortening term is included in its BTF data convention.
• A single directional-light evaluation is a limited illumination approximation.
• Approximate the integral by a finite weighted sum of directional-light contributions.
• The original plot compares mean pixel luminance for a leather BTF.

• The source contrasts a fast idealized point-light rendering with more demanding environment illumination.
• The original images show the difference in appearance under these two illumination setups.

• Approximate the environment by a set of light contributions.
• The source describes smoother images through convolution with the lighting.
• Rendering is slower; optimization techniques are available.

• Rasterization may introduce aliasing artifacts.
• Mip-mapping downsamples the image to lower resolutions (Gaussian pyramid).
• Select an appropriate pyramid level for the projected texture footprint; the source describes this in terms of observer distance.

• The source compares mip-mapping and anisotropic filtering visually.
• Its illustrative overhead figures are 50% and 100%; these are source figures for its setup, not universal memory costs.
• Mip-map storage depends on representation; a complete 2D power-of-two mip chain is about one third extra texels before compression and padding.

Upřesnění GRAFIT k nákladům paměti: čísla na původním snímku jsou závislá na konkrétním uspořádání dat.

• Disney BRDF Explorer.
• Blender.
• SIGHTTEX Studio.
• Mitsuba 2 (C++) and Mitsuba 3 (Python).
• Versions and links are those in the source PDF; they are not claims about the latest software release.