Ray Tracing Outline - inst.eecs.berkeley.edu

Ray Tracing Outline For each pixel { Shoot ray r from eye to center of pixel with trace( r ) } function trace( r ) For each object { Find object with closest intersection, x. } If x exists { For each light source { For all other objects { Check for intersection of ray from light to x. } If no intersection { Calculate direct illumination with Phong model. } Accumulate calculated color. }

Calculate reflection ray r, and recurse calling trace( r ) Accumulate reflected colors, and return. } } Leverage C++ Using C++ will make complicated code very simple. Take advantage of it! Abstract base class Object. Subclasses for spheres, triangles, etc. Store objects as array of pointers, and iterate with virtual Intersect function. Common information (Kd, Ks, Ka) Each actual object type will have its own intersection function. Data Structures

Sphere: center, radius Ellipsoid: Just sphere with 4x4 tranformation applied to it. Triangle: vertices, normal Ray: start, direction Input files: Can use parser from As3 Need: camera information, object information Objects should at least have Ks, Kd, color, location, but the assignment is open-ended. E.g., can have Ka if you want, or not. Can have texture map information. Intersections Parametric ray equation: r(t)=p+td t>=0 Implicit sphere equation: f(p)=||p-c||-r=0

p is any point on spheres surface, c is the center, r is the radius. Intersection (with an implicit equation) is just root finding. Explicit triangle equation: t(u,v)=(1-u-v)v0+uv1+vv2 Barycentric Solve linear system of equations. Intersections (More) Ellipsoids (from www-courses.cs.uiuc.edu/~cs419/rayintersection.ppt) Ellipsoid Intersection d o Let T be a 4x4 transformation that

distorts a sphere into the ellipsoid Ellipsoid is implicit surface of f(T-1x) f(T-1r(t)) = f(T-1(o + t d)) = f(T-1o + t T-1d) Ellipsoid::Intersect(Ray Ellipsoid::Intersect(Rayr)r){{ Ray RayTir Tir==(Ti (Ti**r.o, r.o,Ti Ti**r.d); r.d); return returnSphere::Intersect(Tir); Sphere::Intersect(Tir); }}

Hit point needs to be in world coords t same in both coordinates x=o+td These eqns should be flipped f(T-1x)=0 x T T-1 T-1d T-1o f(x) = 0 T-1x

Local Illumination (a quick reminder) Phong illumination model (not to be confused with Phong shading) For each light: Speeding things up BSP trees with bounding boxes Intersections take up most of the time. If create BSP structure, then can check for intersection from front to back from a given starting ray location. Octrees Figure out which cells it intersects, and check for intersections only with objects inside those cells

More features Here are some suggestions: Transparency with refraction Anti-aliasing Lens effects / depth of field Super quadrics Programmable shading Texture, bump, and/or displacement mapping

Spot lights and/or area lights Other interesting features Tips Make sure you test your code early and often. Ray tracers are hard to debug. Dont try to implement everything at once. E.g., start with only spheres, 1 light source, and a constant local illumination value to test your intersection code. Take advantage of the newsgroup. This assignment is open-ended. However, we strongly suggest using C++. Very strongly. Start now! You dont know what silly problems youll encounter. Plus, youll get really into it and want to add lots of extra features.