Ray Tracing

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Ray Tracing
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Illumination models realism

• Weve been using the Phong lighting model for
  illumination.
• Is it realistic?
• Empirical specular term for highlights
• Ambient term for indirect illumination
• No illumination away from light give shadow-like
  effect, but
• No cast shadows
• No surface interreflection
• No refraction through transparent or translucent
  objects including caustics

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Global illumination

• Global illumination techniques strive to include
  all of these physical phenomena.
• In practice, they often do not.
• Path tracing simulate light optics
• Reflections/refractions (glossy objects,
  caustics)
• Lens effects
• Radiosity simulate light transfer
• Diffuse-diffuse reflections (color bleeding)
• Typically very expensive not interactive.

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Forward vs Backward mapping

• Weve been studying the traditional graphics
  pipeline.
• Commonly referred to as forward mapping objects
  are transformed into image space to determine
  pixel coverage.
• Ray tracing, a special case of path tracing,
  transforms pixels into object space to determine
  object contribution backward mapping.

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Ray tracing

• To determine the color of a given pixel
• Create a ray from the eye, through the pixel, and
  into the world
• Intersect the ray with all objects in the scene
• Determine the visible surface
• Directly displaying the first intersection is
  commonly referred to as ray casting.
• As well see later, calling visibility ray
  tracing ray casting misses the point of what
  full ray tracing does different.

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Visibility determination
Screen
Eyepoint
Scene
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Lighting model

• Once weve determined which object we can see
  along a particular ray, we have to determine
  color.
• Assume we had triangles in the scene we could
  determine an intersection be first determining if
  the ray intersects the plane of the triangle,
  then where, then if where is inside.
• We can now easily determine
• Surface normal
• View direction
• Light direction
• Texture coordinates
• So we can apply whatever light model we want
  Phong for instance.

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Shadows

• Or we can take our first step toward a full ray
  tracing algorithm
• We could trace a shadow-ray from the point of
  intersection toward the light and determine if
  some other object blocks the light source.

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Inter-object reflections

• We could trace a ray off reflective surfaces and
  determine if they hit objects if they do we
  compute the lighting equations for the secondary
  ray and determine the contribution of this
  reflection at the first intersection

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Refraction

• Transparent and translucent objects refract
  (bend) the light that passes through them. We
  could compute refracted rays and trace them as
  well.
• We can calculate the angle from the indices of
  refraction of the two materials which interface
  at the ray-object intersection.

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Recursive ray tracing

• Full recursive ray tracing (as suggested by
  Whitted) does all of these at every intersection.

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The good the bad

• Good
• Transparency
• Reflections
• Shadows
• Conceptually simple / pretty easy to write no
  clipping, no projections, no scan conversion
• Bad
• Intersection tests are expensive
• Intersection tests are expensive
• Intersection tests are expensive
• Typical framebuffer ? 1 million pixels
• Typical scene 1 million polygons

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Ray-object intersections

• In general, we parameterize the ray and find the
  parameter value where the ray intersects the
  object.
• Doing this for all objects, we keep the smallest
  non-negative parameter value thats the
  intersection with the first object along the ray.
• From the intersection point, we can compute
  whatever surface properties we need.
• How should we represent a ray?
• So how do we compute intersections?

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Ray representation

• Whats a ray?
• It has an origin and a direction.
• Any point on the ray is just origin
  tdirection
• So our intersection test just need to solve for t.

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Ray-triangle intersection

• Triangles are the most common model
  representation
• Lowest common denominator
• Can use hardware to accelerate
• Basic approach
• Find plane equation (from vertex coordinates)
• Find intersection between ray and plane
• Does triangle contain intersection point?
• We can interpolate surface properties for this
  intersection from the vertices, but only if we
  need to separate this calculation from the
  intersection test.

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Constructive Solid Geometry

• Use Boolean operations to combine simple
  primitives into complex objects.
• CSG models are typically represented as trees,
  Boolean operators make the nodes and geometric
  primitives make up the leaves.
• A common modeling concept for any
• kind of rendering, but its especially
• easy to determine what the resulting
• surface is for ray tracing.

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Shadow rays area lights

• We can sample instead
• Add up contribution from shadow rays reaching the
  area light.
• Trade-off instead of on very expensive test, we
  have several potentially expensive tests.

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Shadow rays translucent shadowing

• Translucent objects should cast colored shadows.
• We can fake the colored shadows
• Find all intersections along the ray.
• If an object is translucent, attenuate the light
  accordingly.
• Only give up if we hit an opaque object or too
  many translucent objects.
• Whats wrong with this hack?

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Lens effects

• Typically, the camera model is that of a pin-hole
  camera.
• We can easily insert a lens into the optical path
  and get the expected effects.

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What bounding volume?

• Spheres
• Cheap intersection test
• Typically a poor fit
• Hard to cluster optimally see poor fit
• Axis-aligned bounding boxes (AABBs)
• Ray-box test we had before reasonably cheap
• Easier to get good fits than spheres
• Trivial clustering
• Oriented bounding boxes (OBBs)
• Medium intersection test
• Very good fit (provably, asymptotically better
  than AABB)
• Medium clustering difficulty

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Spatial partitioning

• Classification of space into non-overlapping
  portions
• Uniform-grid
• Octree
• k-D tree
• BSP-tree

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Stochastic ray tracing
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What cant ray tracing do?
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What cant ray tracing do?
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Radiosity can capture that

• Radiosity models the transport of light between
  surfaces.
• Part of full the radiosity solution is computing
  reflection between every pairing of surfaces.
• If you really have time to kill, you could use
  the BRDF to drive stochastic sampling in a path
  tracer to get diffuse-diffuse reflections.
• It would probably actually be slower than the
  radiosity solution for less accurate results, but
  in the limit it would converge to the right
  thing.