Computer Graphics (Fall 2003)

COMS 4160, Lecture 17: Ray Tracing Ravi Ramamoorthi

http://www.cs.columbia.edu/~cs4160

The Internet Ray Tracing Competition: http://www.irtc.org

Image courtesy Paul Heckbert 1983

Effects needed for Realism

• Shadows• Reflections (Mirrors)• Transparency • Interreflections• Detail (Textures etc.)• Complex Illumination• Realistic Materials• And many more

Turner Whitted 1980

Ray Tracing: History

• Appel 68• Whitted 80 [recursive ray tracing] (picture)

– Landmark in computer graphics

• Lots of work on various geometric primitives• Lots of work on accelerations• Current Research

– Real-Time raytracing (historically, slow technique)

– Ray tracing architecture

The Pinhole Camera

Image plane Pinhole

Illustration courtesy Greg Humphries

Ray Casting

Ray Tracing

• Shoot rays through pixels into the world

• For each pixel,– Find closest intersection in scene– Evaluate illumination model to color pixel

Comparison to Scan-Line

• Per-pixel evaluation, per-pixel rays (not scan-convert each object). On face of it, costly

• More complex shading, lighting effects possible

Ray paths

• LR*E

• Arbitrary paths: realism

• Trace from light or eye?– Most light rays don’t hit

eye

– Importance sampling

• Eye Ray tracing– Primary Rays

– Shadow Rays

– Reflected/Transmitted Rays

Appel 68

Recursive Ray Tracing

For each pixel– Trace Primary Ray, find intersection– Trace Shadow Ray(s) to light(s)

• Color = Visible ? Illumination Model : 0 ;

– Trace Reflected Ray• Color += reflectivity * Color of reflected ray

Shadow Rays

• How much light is reaching point P?• Fire a shadow ray towards each light in the scene• Numerical problems?

AB

S

P

Problems with Recursion

• Reflection rays may be traced forever

• Generally, set maximum recursion depth

• Same for transmitted rays (take refraction into account)

Ray/Object Intersections

• Heart of Ray Tracer– One of the main initial research areas

– Optimized routines for wide variety of primitives

• Various types of info– Shadow rays: Intersection/No Intersection

– Primary rays: Point of intersection, material, normals

– Texture coordinates

• Work out examples– Triangle, sphere, general implicit surface

More on Intersections

• Basic Algorithm– Test each object for intersection– Sort objects to find closest one– Trace shadow ray. If unblocked, compute

illumination

• Issues– Precision: self shadowing – Aliasing, Supersampling– Stochastic, Jittered sampling

Precision• Floating point calculations are imprecise!• Often, a ray’s origin is supposed to be on a

surface, but this might happen:

• Typical hack is to only allow t values above some small threshold, like .0000001

Comparisons

• Scan Conversion vs. Ray tracing– Ray tracing is (has been) much much slower

• Is this still true if number of objects large? Fractals?

• Acceleration structures (next), but still very slow usually

– Realism in imagery• Reflections, Refractions, soft shadows, complex lighting,

shading trivial in ray tracing. In scan conversion?

– Future?• Currently OpenGL uses scan conversion

• Real-Time raytracing? (already possible)

• Ray Tracing architecture (research at Stanford)

Acceleration

• Testing each object for each ray is slow– Fewer Rays

• Adaptive sampling [HW] , depth control

– Generalized Rays• Beam tracing, cone tracing, pencil tracing etc.

– Faster Intersections• Optimized Ray-Object Intersections

• Fewer Intersections

Acceleration Structures

• Reducing number of intersections– Bounding Volume hierarchy– If no intersection with bounding box, needn’t

check objects

• Grids– Uniform, Hierarchical

• Spatial Hierarchies– Oct-trees, kd trees, BSP trees

Acceleration Structures