Computer Graphics. - Shading & Texturing -

Transcription

1 Computer Graphics - Shading & Texturing -

2 Empirica BRDF Approximation Purey heuristic mode Initiay without units (vaues [0,1] r = r,a + r,d + r,s ( + r,m + r,t r,a : Ambient term Approximate indirect iumination r,d : Diffuse term (ambert Uniform refection r,s : Specuar term Mirror-refection on a rough surface r,m : Perfect refection Ony possibe with Ray-Tracing r,t : Perfect transmission Ony possibe with Ray-Tracing

3 Phong Iumination Mode Extended ight sources: point ight sources Coor of specuar refection equa to ight source Heuristic mode Contradicts physics Purey oca iumination Ony direct ight from the ight sources No further refection on other surfaces Constant ambient term Often: ight sources & viewer assumed to be far away (Binn ( ( (Phong ( ( (, r, r + + = + + = s d a i a s d a i a e e N H N I V I R N I

4 Microfacet Mode Isotropic microfacet coection Microfacets assumed as perfecty smooth refectors BRDF Distribution of microfacets Often probabiistic distribution of orientation or V-groove assumption Panar refection properties Sef-masing, shadowing

5 Ward Refection Mode BRDF f r = ρ π d + ρ s ( I 1 N( V N 2 2 exp( tan ( H, N / σ 2 4πσ σ standard deviation (RMS of surface sope Simpe expansion to anisotropic mode (σ x, σ y Empirica, not physics-based Inspired by notion of refecting microfacets Convincing resuts Good match to measured data N viewer V H θ I surface microfacet

6 Physics-inspired BRDFs Notion of refecting microfacet Specuar refectivity of the form f r = D G F ( λ, θi π N V λ D : statistica microfacet distribution G : geometric attenuation, sef-shadowing F : waveength, ange dependency of refection aong mirror direction N V : faring effect at ow ange of incidence Coo-Torrance mode F : waveength- and ange-dependent refection Meta surfaces

7 Coo-Torrance Refection Mode Coo-Torrance refectance mode is based on the microfacet mode. The BRDF is defined as the sum of a diffuse and specuar components: f r = d ρd + sρs; d + s 1 where s and d are the specuar and diffuse coefficients. Derivation of the specuar component ρ s is based on a physicay derived theoretica refectance mode

8 Coo-Torrance Specuar Term ρ s Fλ DG = π ( N V ( N I N viewer V H θ surface microfacet I D : Distribution function of microfacet orientations G : Geometrica attenuation factor represents sef-masing and shadowing effects of microfacets F λ : Fresne term computed by Fresne equation reates incident ight to refected ight for each panar microfacet N V : Proportiona to visibe surface area N I : Proportiona to iuminated surface area

9 Microfacet Distribution Functions Isotropic Distributions D ( ω D( α α = N H α : ange to average norma of surface Characterized by haf-ange β Binn Torrance-Sparrow D D ( β ( α = cos α ( = 1 2 D α = e n 2 ncos β 2 α β 2 viewer surface N V H θ I microfacet Becmann m : root mean square Used by Coo-Torrance D 1 m [ tanα / ] ( α = e 2 4m 2 cos 4 α

10 Geometric Attenuation Factor V-shaped grooves Fuy iuminated and visibe G =1 Partia masing of refected ight 2( N H ( N G = ( V H V Partia shadowing of incident ight G = 2( N H ( N ( V H I G = min 1, 2( N H ( N ( V H V, 2( N H ( N ( V H I

11 Becman Microfacet Distribution Function m=0.2 m=0.6

12 Comparison Phong vs. Torrance

13 Poygon-Shading Methods Appication of an iumination mode to compute intensity for every pixe has been time consuming. Intensity of adjacent pixes is usuay very simiar (the so caed shading coherence, which aows for ess frequent shading evauations. Each poygon can be rendered with a singe intensity or intensity can be obtained at each point of the surface using an interpoation scheme: Fat shading, singe intensity is cacuated for each poygon Gouraud shading (per vertex shading, intensity cacuated at vertices is interpoated across the surface Phong shading (per pixe shading, norma vectors are cacuated at vertices; then norma vectors are interpoated across the surface and an iumination mode using these norma vectors is appied for every point of the surface With modern hardware this is no big issue any more Often even the norma is cacuated per pixe Bump or dispacement maps

14 Probems in Interpoated Shading Probems Poygona sihouette may not match the smooth shading Perspective distortion Interpoation may be performed after perspective transformation in the 2-D screen coordinate system, rather than word coordinate system. Orientation dependence. This probem does not concern trianges for which inear interpoation is rotation-invariant. Shading discontinuities at shared vertices (T-edges. Unrepresentative norma vectors. P P Shading at P is interpoated aong different scan-ines when poygon rotates. T-edges Vertex normas are a parae