CS 348B - Computer Graphics: Image Synthesis Techniques

Homework 2 - Height Field Intersection

Assigned Thursday, April 8.   Due Tuesday, April 20.


For this assignment, you will improve pbrt's support for rendering terrain - landscapes and seascapes. To see examples of what is possible with higher resolution terrains, take a look at the entry on rendering ocean scenes from the 348B Rendering Competition in 2001. 

This kind of terrain is often represented as an elevation map, or what we will call a height field: a table indicating the height of a surface above each point of a uniform 2D grid. In other words, we are tabulating the values of a height function z(x,y) in a 2D array. 

The default pbrt implementation (see /pbrtsrc/shapes/heightfield.cpp) converts the height field to a triangle mesh.  

Height fields have a very orderly structure, which is ignored in simply turning them into triangle meshes. Your assignment is to apply techniques like those used for acceleration structures to develop a fast intersection routine for height fields. An efficient solution will be substantially faster than the default implementation.

Step 0

You must have pbrt installed correctly, as in homework 1. 

Step 1

Copy /usr/class/cs348b/files/hw2 to your working directory.

Run 'pbrt hw2.lrt sea1.lrt land1.lrt'.  When you list multiple scene files like this, pbrt simply concatenates them as input.  This command generates a fill hw2.exr, which you can convert to a tiff (exrtotiff hw2.exr hw2.tiff) and a jpg (convert -quality 95 hw2.tiff hw2.jpg) as in homework 1. 

The height fields used for the land and water are fairly low in resolution -- just 64x64.  Furthermore, the surface facets are accentuated by the fact that the normal vectors of the surface are not interpolated for shading. 

Step 2 (Main Assignment)

You will write a fast height field intersection routine, which will allow you to render much finer terrains, and more quickly. 

You should do this by enhancing the core pbrt file, pbrtsrc/shapes/heightfield.cpp.  Specifically:

You should put some thought into how to do this efficiently. The lectures on acceleration structures like grids and kd-trees should suggest good approaches. Note that the height field data is already basically in the form of a 2D uniform grid - this should be helpful for whatever method you decide to implement.

Of course, your method should be robust - be sure it can work from a variety of viewpoints (and for a variety of different height fields).

Step 3

Once you've got the base intersection routines working, add the following additional features:

Misc Data

There is a 1000x1000 sea terrain in /usr/class/cs348b/files/terrain/sea1000.lrt.  This might take a while to render with the default implementation!

There are also a number of other sky textures to choose from in the /usr/class/cs348b/textures directory.


Create a web page with the following pieces of information and email it to cs348b-spr0304-staff@lists.stanford.edu.  Please be as clear and as concise as possible, as there are 30+ students and only one TA!

Implementation documentation

  1. Include a paragraph describing how you implemented Steps 2 and 3.  Highlight anything you did that was unorthodox, particularly important, or that you enjoyed discovering.  
  2. Include an html link to  your code.


  1. Include and label the following pictures:
  2. Also include:


  1. Q: I don't understand what this assignment is about.  Doesn't pbrt already store the height field in an acceleration structure?
    A: The default pbrt implementation does store the tessellated height field in a 3D K-d tree.  This default implementation is actually highly optimized.  However, you can provide a useful specialized implementation for height fields by exploiting the structure of the height field.  For instance, a common approach is to traverse a 2D grid, building the height field triangles in that cell when you need to.  This can save a lot of memory for larger height fields.  Another approach would be to use a 2D K-d tree. These specializations are possible because of the structure of the height field, and are simpler and often more efficient than more general 3D versions.  Choose an acceleration structure that interests you and explore it in this simpler 2D space. 
  2. Q: How do I compile pbrt with optimizations?
    A: Type 'make clean' to delete existing object files and executables.  Type 'make OPT=-O2' (there's a dash before the capital O).  That builds the system with optimization.
  3. Q: How do I time my code for the timing results on my web page?
    A: On Linux, you can use commands such as: 'time pbrt hw2-view1.lrt'.  After rendering is complete, the time command will print out a line, where the first token is the total time executed in user mode, in seconds.
  4. Q: I can't get my intersection routine faster than the default implementation!
    A:  It may be challenging to get your intersection routine as fast as the default version in pbrt, because pbrt has been quite carefully optimized with a 3D K-d tree.  It  is not a requirement for the assignment that your code run as fast as the default implementation (your routine is still practically useful because it probably uses less memory than the default).  Nevertheless, it is possible to get your specialized height field intersection as fast or faster than pbrt, and you can get extra credit if you succeed in doing so.
  5. Q: I can't seem to eliminate some black reflected regions in the foreground of the image when rendering with sea1000.lrt.  Is that okay?
    A: You may get some black regions where the water is reflecting far away from the forward direction.  The sky background doesn't actually cover the entire hemisphere, and the water will appear black where the correct reflection direction misses the sky geometry (a cylinder).  This doesn't happen in sea1.lrt, but it does in the foreground of sea1000.lrt where the water is more bumpy.  However, if you are getting black speckles on the crests of your waves in the distance, then this is likely an artifact of your Phong interpolation scheme; this is something you should eliminate.
  6. Q: There doesn't seem to be a heightfield project in the Windows build system!
    A:  That's correct.  However, Eilene Hao has kindly created and shared a heightfield VS project that you can add to the pbrt VS solution.  It's available at /usr/class/cs348b/files/heightfield.vcproj.  
  7. Q: Exactly what time on April 20 is the assignment due?  It doesn't say!
    A: Please send us the write-up for your URL by the end of the day (11:59 pm).
  8. Q: I'm having trouble setting a gdb breakpoint in my heightfield plugin code.  What's the best way to do this?
    A: The main difficulty is that plugin code is loaded dynamically by pbrt.  
    Greg recommends:  (1) Load up the executable and put a breakpoint in MakeShape(). Then step OVER the code that loads the DLL. Then you can put breakpoints in your code. (2) Use printf.

    Matt adds:  (1) Best thing to do is set a breakpoint in Scene::Render, then step into the accelerator and then into your intersection code. At that point, you should be able to set other breakpoints in your module. (2) If you want to debug your constructor, set a breakpoint in pbrtShape(), which eventually calls your constructor.)



This homework will be graded according to the following system:

0 - Little or no work was done
* - Significant effort was put into the assignment, but not everything works correctly.
** - The algorithm you implemented was functionally complete; it passed all of our tests.
*** - (Extra credit)  You demonstrate that your intersection routines are as fast as the original (optimized) pbrt implementation.

You will get one grace day for this assignment, which you may save and use on homework 2 or 3 (but not on the final project).

Copyright © 2004 Pat Hanrahan