mikeswoods / ndray

A raytracer written in Haskell

What is this is

This project is a continuation of a final project originally submitted for CIS 552: Advanced Programming at the University of Pennsylvania.

What is this is not

It is a simple raytracer and definitely NOT physically based in any way, shape or form (although this may change in the future). It was (and is) a learning experience and an excuse to play around with Haskell and computer graphics (as if one needs an excuse!).

TODO

• Cubic texture mapping support

• Sky sphere support -- right now, only static backgrounds are supported

• Textures should be made more extensible so that defining new textures does not mean adding another constructor to the BasicTexture data type. I envision having a BasicTexture type, ImageTexture type, NoiseTexture type, etc. and that there is a uniform way to retrieve a texel from each given a (u,v) coordinate. I can't figure out how to do this yet with just typeclasses -- need to look into type/data families, etc.

• Create some kind of mesh rendering options data type to control how meshes are rendered: enable/disable Phong shading, autoscaling, etc.

• Create or find a decent Perlin/Simplex noise implementation

• More procedural texture types: sinusoidal, noise-based, as well as more exotic ones like marble, wood, etc.

• Allow the Lua script to modify objects in-place. So instead of, say rotating a sphere like "sphere = RotateX(sphere, 30)", you could just do "RotateX(sphere, 30)". Maybe this is a good/bad idea? Need to think about it more.

• Split out KD-Tree implementation into a standalone package and submit to Hackage. Maybe do the same for the Tensor module as well?

Various notes

Affine Transformations

How to transform an object in an object's intersection test function

Given a 4x4 transformation matrix M:

1. Transform the intersection point with M

2. Transform the ray's origin and direction with inverse(M)

3. Transform the normal at the point of intersection with transpose(inverse(M))

Refractive indices for various materials

Taken from http://en.wikipedia.org/wiki/List_of_refractive_indices

• Vacuum n = 1.00
• Water: n = 1.31
• Glass: n = 1.49
• Diamond: n = 2.419

Resources I found useful

Below is a short list of resources I found online that have helped me along the way.

Bounding boxes

AABBs (axis-aligned bounding boxes)

• http://zeuxcg.org/2010/10/17/aabb-from-obb-with-component-wise-abs/
• http://www.gamedev.net/topic/495016-aabb-rotation/
• http://www.cs.unc.edu/~zhangh/technotes/bbox.pdf
• http://dev.theomader.com/transform-bounding-boxes/

Algorithm overview

• http://www.cs.utexas.edu/~fussell/courses/cs384g/lectures/lecture09-Ray_tracing.pdf
• http://www.mikejutan.com/raytracer/mikejutanA5Manual.pdf

Affine transformations

• http://stackoverflow.com/questions/18418855/raytracing-problems-with-transformations
• http://scratchapixel.com/lessons/3d-basic-lessons/lesson-4-geometry/transforming-normals/

Camera orientation

• http://stackoverflow.com/questions/13078243/ray-tracing-camera
• http://www.cse.ohio-state.edu/~parent/classes/681/Lectures/08.RTgeometryHO.pdf
• http://stackoverflow.com/a/5944402
• http://stackoverflow.com/a/13078758
• http://steveharveynz.wordpress.com/2012/12/20/ray-tracer-part-two-creating-the-camera/

Haskell-related

Unboxing vectors, etc.

• http://stackoverflow.com/a/10866718

Using the ST monad (needed for JuicyPixels)

• http://stackoverflow.com/questions/22594806/how-do-i-write-pixels-with-juicypixels-in-st-monad
• http://www.haskell.org/haskellwiki/Monad/ST

Lenses

• http://www.haskell.org/haskellwiki/LensBeginnersCheatsheet

Matrix / REPA stuff

• http://www.cse.chalmers.se/edu/course/DAT280_Parallel_Functional_Programming/Papers/tutorialWinner.pdf
• http://chimera.labs.oreilly.com/books/1230000000929/ch05.html##sec_par-repa-arrays
• http://stackoverflow.com/questions/10747079/what-are-the-key-differences-between-the-repa-2-and-3-apis
• http://negativeprobability.blogspot.com/2011/11/affine-transformations-and-their.html

Lua intergration with HsLua

• http://osa1.net/posts/2014-04-27-calling-haskell-lua.html

Math

Linear algebra

• http://stackoverflow.com/questions/2624422/efficient-4x4-matrix-inverse-affine-transform

Interpolation

• http://paulbourke.net/miscellaneous/interpolation/

Data structures

KD-Trees

• http://blog.frogslayer.com/kd-trees-for-faster-ray-tracing-with-triangles/

OBJ models

Format

• http://people.sc.fsu.edu/~jburkardt/data/obj/obj.html
• http://en.wikipedia.org/wiki/Wavefront_.obj_file

Example models

• http://people.sc.fsu.edu/~jburkardt/data/obj/obj.html

Intersection formulas

Plane

• http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_1_Introduction.shtml

Sphere

• http://wiki.cgsociety.org/index.php/Ray_Sphere_Intersection

Triangle

• http://en.wikipedia.org/wiki/M%C3%B6ller%E2%80%93Trumbore_intersection_algorithm

Lighting

Shading

• http://www.ccs.neu.edu/home/fell/CSU540/programs/RayTracingFormulas.htm
• http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_1_Introduction.shtml
• http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_2_Phong_Mirrors_and_Shadows.shtml

Attenuation

http://www.cs.cmu.edu/~jkh/462_s07/assts/assignment3/

Reflection

• http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_2_Phong_Mirrors_and_Shadows.shtml

Refraction

• http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_2_Phong_Mirrors_and_Shadows.shtml
• http://en.wikipedia.org/wiki/List_of_refractive_indices

UV Mapping / texture mapping

• http://bentonian.com/Lectures/AdvGraph1314/3.%20Ray%20tracing%20-%20color%20and%20texture.pdf (Cube, sphere, & torus mapping)
• http://en.wikipedia.org/wiki/UV_mapping
• http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_6_Textures_Cameras_and_Speed.shtml
• http://paulyg.f2s.com/uv.htm
• http://www.siggraph.org/education/materials/HyperGraph/mapping/surface0.htm (Good resource on mapping)

Other resources

General

• http://paulbourke.net -- This guy's site is great. It's full of 3D related info.

Textures

• http://paulbourke.net/texture_colour/