RayTracing in one LINQ statement

by Miguel de Icaza

Through Don Syme's blog I read about Luke Hoban moving from the C# team at Microsoft to the F# team, I did not know about Luke's blog until now, it is a fantastic collection of cool C# 3 nuggets.

One of the things that impressed me the most is a recent sample he posted.

Luke implements a RayTracer in one line LINQ code. This test is insane (and sadly, our C# compiler is not yet able to handle that kind of complexity yet for LINQ statements). I reproduce it here (directly copy-pasted from Luke's blog):

var pixelsQuery =
  from y in Enumerable.Range(0, screenHeight)
  let recenterY = -(y - (screenHeight / 2.0)) / (2.0 * screenHeight)
  select from x in Enumerable.Range(0, screenWidth)
    let recenterX = (x - (screenWidth / 2.0)) / (2.0 * screenWidth)
    let point = Vector.Norm(Vector.Plus(scene.Camera.Forward, 
Vector.Plus(Vector.Times(recenterX, scene.Camera.Right), Vector.Times(recenterY, scene.Camera.Up)))) let ray = new Ray { Start = scene.Camera.Pos, Dir = point } let computeTraceRay = (Func<Func<TraceRayArgs, Color>, Func<TraceRayArgs, Color>>) (f => traceRayArgs => (from isect in from thing in traceRayArgs.Scene.Things select thing.Intersect(traceRayArgs.Ray) where isect != null orderby isect.Dist let d = isect.Ray.Dir let pos = Vector.Plus(Vector.Times(isect.Dist, isect.Ray.Dir), isect.Ray.Start) let normal = isect.Thing.Normal(pos) let reflectDir = Vector.Minus(d, Vector.Times(2 * Vector.Dot(normal, d), normal)) let naturalColors =
from light in traceRayArgs.Scene.Lights let ldis = Vector.Minus(light.Pos, pos) let livec = Vector.Norm(ldis) let testRay = new Ray { Start = pos, Dir = livec } let testIsects = from inter in from thing in traceRayArgs.Scene.Things select thing.Intersect(testRay) where inter != null orderby inter.Dist select inter let testIsect = testIsects.FirstOrDefault() let neatIsect = testIsect == null ? 0 : testIsect.Dist let isInShadow = !((neatIsect > Vector.Mag(ldis)) || (neatIsect == 0)) where !isInShadow let illum = Vector.Dot(livec, normal) let lcolor = illum > 0 ? Color.Times(illum, light.Color) : Color.Make(0, 0, 0) let specular = Vector.Dot(livec, Vector.Norm(reflectDir)) let scolor = specular > 0 ? Color.Times(Math.Pow(specular, isect.Thing.Surface.Roughness), light.Color) : Color.Make(0, 0, 0) select Color.Plus( Color.Times(isect.Thing.Surface.Diffuse(pos), lcolor), Color.Times(isect.Thing.Surface.Specular(pos), scolor)) let reflectPos = Vector.Plus(pos, Vector.Times(.001, reflectDir)) let reflectColor =
traceRayArgs.Depth >= MaxDepth ? Color.Make(.5, .5, .5) : Color.Times(isect.Thing.Surface.Reflect(reflectPos), f(new TraceRayArgs(new Ray { Start = reflectPos, Dir = reflectDir }, traceRayArgs.Scene,
traceRayArgs.Depth + 1))) select naturalColors.Aggregate(reflectColor, (color, natColor) => Color.Plus(color, natColor)))
.DefaultIfEmpty(Color.Background).First()) let traceRay = Y(computeTraceRay) select new { X = x, Y = y, Color = traceRay(new TraceRayArgs(ray, scene, 0)) }; foreach (var row in pixelsQuery) foreach (var pixel in row) setPixel(pixel.X, pixel.Y, pixel.Color.ToDrawingColor());

Although the above is pretty impressive, you might want to read about Luke's history of writing ray tracers as test cases for a new language (I write the factorial function, Luke writes Ray Tracers). His original sample from April goes into the details of how to define the scene, the materials and the objects and is useful to understand the above LINQ statement.

The full source code (includes the support definitions for defining the Scene and materials) is available here.

The original code (not LINQ-ified) is available here.

Posted on 16 Nov 2007