Photorealism Steve Ash, Rhodes College 2006 Photorealism The goal - - PowerPoint PPT Presentation

Photorealism

Steve Ash, Rhodes College 2006

Photorealism

The goal is to model the interaction between light source and surface materials ambient light diffuse reflection specular reflection transparency

Photorealism

The goal is to model the interaction between light source and surface materials ambient light diffuse reflection scattered light illuminating the object (the light source has no direction) point -light illuminating the object light is reflected equally in all directions

Photorealism

The goal is to model the interaction between light source and surface materials specular reflection transparent interaction between light and a highly reflective (shiny) surface interaction between light and a highly transparent surface

Algorithm

For each pixel P in the canvas: shoot a ray V from the eye E to P find intersection point Q with object find color of object at Q which depends on: * object material and light source properties set pixel P to computed color

(x,y,0) (ex,ey,ez)

L V N

(lx,ly,lz)

Light and Materials

Light sources will be modeled by their intensity I = (R, G, B) and position P = (X, Y, Z) no position for ambient light, just intensity Material properties of objects will be modeled by O = (R, G, B) coeff. of reflection e.g. high R coefficient will imply material that appears more Red The color, I, observed on the object will be the sum total of the interactions of all light sources and the material properties of the object I = Ambient + Diffuse + Specular + Transparent

Light and Materials

Point light sources modeled by their intensity Ip = (R, G, B) and position P = (X, Y, Z) no position for ambient light, just intensity Ia Intrinsic color of the object specified by O = (R, G, B) Material properties of objects modeled by various coefficients of reflection ka – ambient coefficient kd – diffuse coefficient ks – specular coefficient n – specular highlight kt – transparency coefficient η – index of refraction The intensity observed on the object will be the sum total of the interactions of all light sources and the color and material properties of the object I = Ambient + Diffuse + Specular + Transparent

Ambient Component

To model the ambient intensity determine how much ambient light is reflected Ambient = ka IaOa This is done for each color channel λ = (R, G, B) Ambientλ = ka IaλOλ AmbientR = ka IaROR AmbientG = ka IaGOG AmbientB = ka IaBOB

Diffuse Component

Diffuse describes matte surfaces light is reflected equally in all directions amount of reflected light depends on amount of surface area hit independent of viewer pos smaller area hit, so more intensity per unit area, but viewer sees less larger area hit, so viewer sees more, but less intensity per unit area

Diffuse Component

Diffuse describes matte surfaces light is reflected equally in all directions amount of reflected light depends on amount of surface area hit smaller area hit, so more intensity per unit area, but viewer sees less larger area hit, so viewer sees more but less intensity per unit area The effect cancels out – see more, but less intense, or see less but more intense diffuse component proportional to cos θ between light and surface normal N L θ Diffuse λ = kd IpλOλ cos θ = kd IpλOλ(N•L) Itotal = A1 IΔ1 = A2 IΔ2 Itotal Itotal A1 A2

Specular Component

The specular highlight is a region of high intensity moves along the surface depending on viewer position highly concentrated – falls off quickly with viewing angle

Specular Component

The specular highlight is a region of high intensity moves along the surface depending on viewer position highly concentrated – falls off quickly with viewing angle Phong model for specular reflection specular highlight depends on angle between reflect ray R and the gaze V N L α R V θ θ N L α R V θ θ same ray in each case left viewer will see less reflection right viewer will see less reflection since reflected ray diverges more since closer to reflected ray

Specular Component

The specular highlight is a region of high intensity moves along the surface depending on viewer position highly concentrated – falls off quickly with viewing angle Phong model for specular reflection specular highlight depends on angle between reflect ray R and the gaze V N L R V N L R V highest perceived intensity when R = V varies with viewer position

Specular Component

The specular highlight is a region of high intensity moves along the surface depending on viewer position highly concentrated – falls off quickly with viewing angle Phong model for specular reflection specular highlight depends on angle between reflect ray R and the gaze V N L α R V θ θ Specular λ = ks IpλOλ cosn α = ks IpλOλ(R•V)n n – specular reflection exponent high n, more focused (smaller) highlight

Specular Component

Calculating R, assuming L, N unit N L R θ θ

Specular Component

Calculating R, assuming L, N unit N L R θ θ N' L R θ θ S S Shrink N to level L, N', R N' = N * ( |L| * cos θ ) = N * cos θ

Specular Component

Calculating R, assuming L, N unit We have R = N’ + S S = N’ – L N L R θ θ N' L R θ θ S S Shrink N to level L, N', R N' = N * ( |L| * cos θ ) = N * cos θ

Specular Component

Calculating R, assuming L, N unit We have R = N’ + S S = N’ – L Therefore R = N’ + S = N' + (N' - L) = 2N' – L = 2N cos θ – L R = 2N(N•L) – L N L R θ θ N' L R θ θ S S Shrink N to level L, N', R N' = N * ( |L| * cos θ ) = N * cos θ

Specular Component

Calculating R, assuming L, N unit We have R = N’ + S S = N’ – L Therefore R = N’ + S = N' + (N' - L) = 2N' – L = 2N cos θ – L R = 2N(N•L) – L Now can compute Specularλ = ks IpλOλ(R•V)n N L R θ θ N' L R θ θ S S Shrink N to level L, N', R N' = N * ( |L| * cos θ ) = N * cos θ

Summary

The color, I, observed on the object will be the sum total of the interactions of all light sources and the material properties of the object I = Ambient + Diffuse + Specular + Transparent Iλ = ka IaλOλ + kd IpλOλ(N•L) + ks IpλOλ(R•V)n + Transparent Ia – the intensity of the ambient light Ip – the intensity of the point light source O – the intrinsic color of the object ka, kd, ks – ambient, diffuse, specular coefficients this is done for each color channel λ = (R, G, B)

• nly if N • L > 0

Algorithm

For each pixel P in the canvas: shoot a ray V from the eye E to P find intersection point Q with object find surface normal N at intersection point Q find the directions (unit vectors): L (Q to light) R (reflected ray L) V (Q to eye) Itotal = Ambient + Diffuse + Specular set pixel P to Itotal

• nly if N • L > 0

(x,y,0) (ex,ey,ez)

X L V N R

(lx,ly,lz)

Ray-Sphere Intersection

Sphere equation (x – cx)2 + (y – cy) 2 + (z – cz) 2 - R2 = 0 Ray equation p = source + t*direction px = sx + t*dx py = sy + t*dy pz = sz + t*dz Common point (px – cx) 2 + (py – cy) 2 + (pz – cz) 2 - R2 = 0 (sx + t*dx – cx) 2 + (sy + t*dy – cy) 2 + (sz + t*dz – cz) 2 - R2 = 0 t = ? could have 0, 1, or 2 solutions which one should we pick

Sphere Surface Normal

C P N N is of unit length and has the same direction as CP ray

Scene Specification

camera { location <0, 0, 80> screen_size 60 density 300 } light_ambient { rgb <0.2, 0.1, 0.1> } light_source { <-100, 125, 150>, rgb <1.0, 1.0, 1.0> } sphere { <10, 0, -20>, 35 color { rgb <0.0, 1.0, 0.0> } finish { ambient 0.2 diffuse 0.4 specular 0.8 phong_size 90 transparent 0.9 index 1.33 } }

(0,0,80) (-100,125,150) (10,0,-20) 60 60 300 -- #rays per row/column

• f the screen

image source: http://en.wikipedia.org/wiki/File:Ray_trace_diagram.svg

Scene Specification

camera { camera { location <0, 0, 80> location <0, 0, 80> screen_size 60 screen_size 60 density 300 density 40 } }

window is 60x60 but 300 rays so we need 300 x 300 Canvas windows is 60x60 but 40 rays so we need 40 x 40 Canvas ∆w = fit 40 into 60 ∆w = fit 300 into 60

• 30

+30

• 30

+30

• 30
• 30

+30 +30 window (-30,+30) is (0,0) in canvas window (+30,-30) is (300,300) in canvas window (-30,+30) is (00) in canvas window (+30,-30) is (40,40) in canvas

Single Object Multiple Light Sources

For each pixel P in the image: shoot a ray from the eye E to P find intersection point Q with object find surface normal N at intersection point Q for each light source S: find the directions: L (Q to S) R (reflected ray L) V (Q to eye) compute intensity for S: IS = Diffuse + Specular Itotal = Ambient + Sum IS (all visible light sources) set pixel (x, y) to Itotal

• nly if N • L > 0

X

Multiple Objects and Shadows

For each pixel P in the image: shoot a ray from the eye E to P find intersection point Q with closest object find surface normal N at intersection point Q for each light source S visible from Q: find the directions: L (Q to S) R (reflected ray L) V (Q to eye) compute intensity for S: IS = Diffuse + Specular Itotal = Ambient + Sum IS (all visible light sources) set pixel (x, y) to Itotal

• nly if N • L > 0

X

and not blocked by other object

Multiple Lights, Objects and Shadows

Shadows and multiple lights are handled by checking whether each light source illuminates the hit point directly I = Ambient + Diffuse + Specular Iλ = ksIaλOλ + ∑Si [ksIpiλOλ(N•L) + ksIpiλOλ(R•V)n ] Si = 1 if point light Ipi illuminates intersection point 0 if point light Ipi does not illuminate:

• another object blocks the light path
• this object blocks the light path N • L < 0