Taking LINQ to Objects to Extremes: A fully LINQified RayTracer

Taking LINQ to Objects to Extremes: A fully LINQified RayTracer

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Not too long ago I blogged about a C# raytracer which took advantage of a lot of C#3.0 language constructs.  However, you may have noticed that it did not actually use LINQ query expressions all that much.  Well, after discussing this with a coworker on the PLINQ team at lunch one day - I was convinced that it should be possible to express the logic of the raytracer in a LINQ to Objects query.  The result is below - a single 60-line LINQ query which captures the complete raytracing algorithm.

[DISCLAIMER:  I am by no means suggesting it's a good idea to write code like this.  Do so only at your own risk!  Just as you *could* write your entire application in one method body, or decide to replace all if statements with virtual method dispatches, doing what I show below is a clear abuse of this language construct.  But it's an interesting example to show that there is a lot of expresiveness available in C#3.0 query expressions.]

One Really Big Query Expression!

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());
Let Expressions

"let" query clauses allow you to introduce a variable into scope which can be used by the following query clauses.  Similar to local variables in a method body, this gives you a way to avoid evaluating a common expression multiple times by storing it in a variable.  This can be very useful even in much simpler queries.  Of course, in the query above - let is absolutely critical.

Recursion

A raytracer is inhenertly recursive - whenever a ray hits a reflective or transparent surface, new rays have to be cast.  Thus the query that expreses the raytracer needs to be recursive.  But the let clause doesn't support declaring recursive functions.  Not to let that stop us (as it really should!) - we can use the Y combinator to introduce recursion by hand.  Mads wrote a very detailed description of the recursive lambda expressions in C# recently - and the code example above uses my personal implementation of some of the same ideas he describes. 

Expression-based control structures

When you are trying to write things in a single query expression - you don't have the luxury of using any statements.  Since most of the C# control structures are  statement based (if, switch, for, while, etc.) - this can make things a little trickier.  One really valauble expression-based control structure is the ternary operator ( x ? y : z ).  This is used in a couple of places above to provide the necessary branching logic.  The rest of the control structuring is accomplished with LINQ Standard Query Operators - Select, SelectMany, Where, OrderBy, Aggregate and DefaultIfEmpty.  As functional programmers have shown for years, the expressiveness of these very general list processing operations is impressive.

Conclusion

In case you had any doubts - hopefully this convinces you that C#3.0 Query Expressions are really a very expressive language construct.  Of course - this expressiveness is probably best used in more moderation than shown here!

File iconLINQRayTracer.cs

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  • Dimchansky - Thanks for the comment on the performance difference between the query-based version and the original version.  As you point out, there is a fairly significant performance overhead for the version that uses one giant query.  I should have mentioned this as an additional reason to *not* recommend this extreme kind of code for a typical application.

    The culprit in terms of performance in this case is primarily the many "let" clauses.  These each incur a method call, a delegate invocation and an allocation of a "SelectIterator".  Since many of these are run in tight loops which are hit close to millions of times during a typical run, the additional cost is magnified significantly.

  • Welcome to the thirty-eighth Community Convergence. These posts are designed to keep you in touch with

  • Impressive! Regarding the comments on this article, one should really do something about the crap! But I guess you don't have the option to delete any of 'em, do you LukeH?

  • Uhh... Is that thingie what you call a BIG query?

    How about a 40KB-length, seven-level-nested one? :)

  • Last fall in Barcelona, Spain two PM's from the C# team gave talks on key parts of the new technology

  • Vi riporto un link ad un post che potete trovare anche nei link della StartPage di VisualStudio. Sono

  • 这里是LINQ to XML利用let暂时存放子节点的数据,再从查询let中的数据得到XML中子节点多个属性.

  • Do you have a version of the Ray Tracer distributed with the Parallel Extensions CTP where the code has more comments for people without 3D graphics experience?  The organization of the CTP version is superb(in comparison to the single file one), but without XML comments I found navigating it tiresome...  (I know teaching 3d programming was not the purpose of either, but I thought I'd ask.)  I've learned quite a bit from it already.

    Also, I haven't looked at the code for this one, but did you use Parallel Linq in it, the post didn't seem to imply it.  If not, why didn't you?

  • I'm finally getting into the groove with LINQ and lambda expressions, and am over the initial skepticism

  • An interesting question that someone asked of me recently, indicating perhaps that the information from

  • Pretty cool, fun reading through it all :P

    I was just wondering about the performance issue raised. I haven't read the other version of the code so I don't know if this improvement would be just for this mega-LINQ version or not. But I was looking at the section of the query that works out if an object is in shadow from the light and I think the query could be tweaked a bit.

    Couldn't you put in a where clause to filter out objects which intersect the ray from the light but are beyond the originally intersected object? Then you could remove the order by and use FirstOrDefault(), saving on intersecting all other objects in the scene once you found a shadow casting object.

    I guess depending on how many objects you have and how much shadow you have this may have varying levels of improvement.

  • Предыдущая серия: http://blogs.gotdotnet.ru/personal/bezzus/PermaLink.aspx?guid=2F2B4B66-809C-441B-BDE9-FA45D71445F3...

  • I have ported this raytracer to XQuery!  All the code explained line by line so you can understand what is going on.  It runs with XQSharp.

    More information can be found here:

    http://www.xqsharp.com/xqsharp/samples/raytracer/index.htm

  • Wow... this is the greatest piece of code written in a LONG time.  You need to get an award or something.

  • Hi , I am trying to implement the same RayTracer in VB.net.But it is unable to recognize isect variable.

    Can someone plz help.

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