Optical ModelsSlide 2Transport of LightSlide 4Max - 1995Blinn - AssumptionsSlide 7Blinn – transparency (1)Blinn – transparency (2)Max - absorption onlySlide 11Slide 12Max - cloud modelMax - self-emitting glowSlide 15Slide 16PowerPoint PresentationVolume Ray Integration (2)g(s)Slide 20Slide 21Slide 22Volume Ray Integration EquationMax - reflectionSlide 25Blinn - Phase FunctionSlide 27Slide 28Max - shadowsSlide 30Max - multiple scatteringSlide 32Slide 33Slide 34Slide 35Slide 36Volumetric Ray IntegrationRay-casting - revisitedVolume Rendering Pipeline (Levoy’88)Volume Rendering Pipeline (Wittenbrink et. al. 98)Optical ModelsJian Huang, CS 594, Spring 2002This set of slides are modified from slides used by Prof. Torsten Moeller, at Simon Fraser University, BC, Canada.Optical Models•Nelson Max, “Optical Models”, IEEE Transactions on Visualization and Computer Graphics, Vol. 1, No. 2, 1995.•Jim Blinn’s 1982 SIGGRAPH paper on scattering.•The mathematical framework for light transport in volume rendering.Transport of Light•Determination of Intensity•Local - Diffuse and Specular•Global - Radiosity, Ray Tracing, Ultimate Physcial•Mechanisms in Ultimate Model–Emittance (+)–Absorption (-)–Scattering (+) (single vs. multiple)LightObserverTransport of Light•Typically based on - S. Chandrasekhar “Radiative Transfer”, Oxford Universtiy Press 1950•Mathematically challenging •Approximate models required -Blinn et al to the rescue•Over Operator -only emission and absorptionLightObserverMax - 1995•Several cases:–Completely opaque or transparent voxels–Variable opacity correction–Self-emitting glow–Self-emitting glow with opacity along viewing ray–Single scattering of external illumination–Multiple scatteringBlinn - Assumptions•Assumptions:–N - surface normal–E - eye vector–L - light vector–T - surface thickness–e - angle btw. E and N–a - angle btw. E and Laka phase angle–I - angle btw. N and LaLENeiParticlesTBlinn - Assumptions•Assumptions (contd.):–particles are little spheres with radius p–n - number density (number of particles per unit volume)– - cosine of angle e, i.e. N.E–D - proportional volume of the cloud occupied by particlesaLENeiParticlesT334pnD Blinn – transparency (1)•Expected particles in a volume will be nV•Probability that there are no particles in the way can be modeled as a Poisson process:•Hence the probability that the light is making it through those tubes is:E LtCylindersmust be empty nVeVP,0ELCylindersof IntegrationtBottom LitTop Lit TpnTpneeVP202,0Blinn – transparency (2)•Transparency through the cloud:• is called the optical deptheTrE-ETpn2TMax - absorption only•I(s) = intensity at distance s along a ray• (s) = extinction coefficient•T(s) = transparency between 0 and s sIsdsdI sTIdttIsIs00exp0Max - absorption only•Linear variation of 20expexp0DDdttsTDtDD)0)Max - absorption only•On the opacity •assuming to be constant in the interval ...2/exp1exp1120DDDdttsTDMax - cloud model•Using fractal structure (Perlin)Max - self-emitting glow•Without extinction: sgdsdI sdttgIsI00Max - self-emitting glow•Without extinction:Max - self-emitting glow•With extinction: sIssgdsdI dsdttsgdttIDID DsD 000expexp dssTsgDTIDID00•The continuous form:•In general case, can not compute analytically dsdttsgdttIDID DsD 000expexpVolume Ray Integral (1)Volume Ray Integration (2)•Practical Computation Method:»note: x can be xi (different everywhere)–which leads to the familiar BTF or FTB compositing … dsdttsgdttIDID DsD 000expexp xxixxiti 1exp 0112111110ItggtgtggttIDInnnnnniinijjniig(s)•g(s) could be:–Self-emitting particle glow–Reflected color, obtained via illumination•The color is usually the sum of emitted color E and reflected color RMax - self-emitting glow•Identical glowing spherical particles:•projected area a = r2•surface glow color = C•number per unit volume = N• •extinction coefficient = a N•added glow intensity per unit lengthg = C a N = C AaNAdlarea totalarea occludeddlAMax - self-emitting glow•Special Case g=C: (and C constant)•This is compositing color C on top of background I0 DTCDTIDI 10 DD DsD DsdttCdsdttsCdsdttsg000exp1expexpMax - self-emitting glow•For I0=0 and : varying according to f:Volume Ray Integration Equation•Self-emitting glow, none constant color dsdttssCdsdttsgD DsD Ds 00exp)(expMax - reflection•i(x) = illumination reaching point x• = unit reflection direction vector• ’ = unit illumination direction vector•r(x,,’): BRDF– for conventional surface shading effects xixrxg ,, xfOXMax - reflection•For particle densities:–w(x) = albedo•Blinn: assuming that the primary effect is from interaction of light with one single particle•albedo - proportion of light reflected from a particle: in the range of 0..1–p(,’) = phase function•still unrealistic external reflection of outside illumination ,,, pxxwxrOXBlinn - Phase
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