Lecture 8Lecture 8Advanced Rendering Advanced Rendering – Ray Tracing, Radiosity & – Ray Tracing, Radiosity &

NPRNPR

Lecture 8Lecture 8Advanced Rendering Advanced Rendering – Ray Tracing, Radiosity & – Ray Tracing, Radiosity &

NPRNPR

Ray Tracing

Y

X

Z

eye

screen

incident ray

worldcoordinates

scenemodel

nearestintersected

surface

refractedray

reflectedray

shadow“feeler”

ray

Slide Courtesy of Roger Crawfis, Ohio State

Ray-Tracing Pseudocode

• For each ray r from eye to pixel, color the pixel the value returned by ray_cast(r):

ray_cast(r){ s nearest_intersected_surface(r); p point_of_intersection(r, s); u reflect(r, s, p); v refract(r, s, p); c phong(p, s, r) + s.kreflect ray_cast(u) + s.krefract ray_cast(v); return(c);}

Slide Courtesy of Roger Crawfis, Ohio State

Pseudocode Explained• s nearest_intersected_surface(r);

– Use geometric searching to find the nearest surface s intersected by the ray r

• p point_of_intersection(r, s);– Compute p, the point of intersection of ray r

with surface s

• u reflect(r, s, p); v refract(r, s, p);– Compute the reflected ray u and the refracted

ray v using Snell’s Laws

Slide Courtesy of Roger Crawfis, Ohio State

Reflected and Refracted Rays

• Reflected and refracted rays are computed using Snell’s Law

surface1

N

v

u rreflected

rayincident

ray

surfacenormal

refractedray

1

2

1

2

2

1

2

1

sin

sin

Slide Courtesy of Roger Crawfis, Ohio State

Pseudocode Explained• phong(p, s, r)

– Evaluate the Phong reflection model for the ray r at point p on surface s, taking shadowing into account (see next slide)

• s.kreflect ray_cast(u)– Multiply the contribution from the reflected ray u by

the specular-reflection coefficient kreflect for surface s

• s.krefract ray_cast(v)– Multiply the contribution from the refracted ray v by

the specular-refraction coefficient krefract for surface s

Slide Courtesy of Roger Crawfis, Ohio State

About Those Calls to ray_cast()...

• The function ray_cast() calls itself recursively• There is a potential for infinite recursion

– Consider a “hall of mirrors”

• Solution: limit the depth of recursion– A typical limit is five calls deep– Note that the deeper the recursion, the less the

ray’s contribution to the image, so limiting the depth of recursion does not affect the final image much

Slide Courtesy of Roger Crawfis, Ohio State

Pros and Cons of Ray Tracing

• Advantages of ray tracing– All the advantages of the Phong model– Also handles shadows, reflection, and

refraction

• Disadvantages of ray tracing– Computational expense– No diffuse inter-reflection between surfaces– Not physically accurate

• Other techniques exist to handle these shortcomings, at even greater expense!

Slide Courtesy of Roger Crawfis, Ohio State

An Aside on Antialiasing

• Our simple ray tracer produces images with noticeable “jaggies”

• Jaggies and other unwanted artifacts can be eliminated by antialiasing:– Cast multiple rays through each image pixel– Color the pixel the average ray contribution– An easy solution, but it increases the number of

rays, and hence computation time, by an order of magnitude or more

Slide Courtesy of Roger Crawfis, Ohio State

Reflections• Mathematically, what does this

mean? What is thereflected

color?

Slide Courtesy of Roger Crawfis, Ohio State

Glossy Reflections• We need to integrate the color

over the reflected cone.• Weighted by the reflection

coefficient in that direction.

Slide Courtesy of Roger Crawfis, Ohio State

Translucency• Likewise, for blurred refractions,

we need to integrate around the refracted angle.

Slide Courtesy of Roger Crawfis, Ohio State

Translucency

Slide Courtesy of Roger Crawfis, Ohio State

Translucency

Slide Courtesy of Roger Crawfis, Ohio State

Shadows• Ray tracing casts shadow feelers to a

point light source. • Many light sources are illuminated over

a finite area.• The shadows between these are

substantially different. • Area light sources cast soft shadows

– Penumbra– Umbra

Soft Shadows

Slide Courtesy of Roger Crawfis, Ohio State

Soft Shadows

Umbra

Penumbra

Slide Courtesy of Roger Crawfis, Ohio State

Camera Models• Up to now, we have used a pinhole

camera model.• These has everything in focus

throughout the scene.• The eye and most cameras have a

larger lens or aperature.

Slide Courtesy of Roger Crawfis, Ohio State

Depth-of-Field

Motion Blur

Slide Courtesy of Roger Crawfis, Ohio State

Supersampling

1 sample per pixel 256 sample per pixel16 sample per pixel

Slide Courtesy of Roger Crawfis, Ohio State

More On Ray-Tracing• Already discussed recursive ray-tracing!• Improvements to ray-tracing!

– Area sampling variations to address aliasing• Cone tracing (only talk about this)• Beam tracing• Pencil tracing

• Distributed ray-tracing!

Area Subdivision (Warnock)

(mixed object/image space)

Clipping used to subdivide polygons that are across regions

Area Subdivision (Warnock)

1. Initialize the area to be the image plane

2. Four cases:1. No polygons in area: done2. One polygon in area: draw it3. Pixel sized area: draw closest polygon4. Front polygon covers area: draw it

Otherwise, subdivide and recurse

BSP (Binary Space Partition) Trees

Partition space into 2 half-spaces via a hyper-plane

a

b

cd

e

a

cb

e d

BSPNode* BSPCreate(polygonList pList) if(pList is empty) return NULL;

pick a polygon p from pList; split all polygons in pList by p and insert pieces into pList; polygonList coplanar = all polygons in pList coplanar to p; polygonList positive = all polygons in pList in p’s positive halfspace; polygonList negative = all polygons in pList in p’s negative halfspace;

BSPNode *b = new BSPNode; b->coplanar = coplanar; b->positive = BSPCreate(positive); b->negative = BSPCreate(negative);

return b;

BSP TreesCreating the BSP Tree

BSPRender(vertex eyePoint, BSPNode *b) if(b == NULL) return;

if(eyePoint is in positive half-space defined by b->coplanar) BSPRender(eyePoint,b->negative); draw all polygons in b->coplanar; BSPRender(eyePoint,b->positive); else BSPRender(eyePoint,b->positive); draw all polygons in b->coplanar; BSPRender(eyePoint,b->negative);

BSP TreesRendering the BSP Tree

BSP Trees

Advantages

view-independent tree

anti-aliasing (see later)

transparency

Disadvantages

many small polygons

over-rendering

hard to balance tree

PortalsSeparate environment into cellsPreprocess to find potentially visible polygons from any cell

PortalsTreat environment as a graphNodes = cells, Edges = portalsCell to cell visibility must go along edges

More spatial subdivision methods…

• Octree• Bounding volume (box, sphere)• Oriented Bounding Box