CS 563: Advanced Computer Graphics

Assignment 1: Heightfield Intersection

Due: February 20, 2007

Description

This assignment was adapted from CS 348B, Stanford University, Spring 2005 For this assignment, you will improve pbrt's support for rendering terrain in scenes like landscapes and seascapes. Terrain is often represented as an elevation map, or what we will call a heightfield: a 2D table indicating the height of a surface above each point of a uniform grid. In other words, a heightfield is tabulated form of a height function z(x,y) stored in a 2D array.

pbrt has no native support for rendering directly from heightfield data. Instead, it converts heightfields into triangle meshes by connecting adjacent height values in the array. This approach is general but relatively inefficient; by converting to triangles we lose the orderly structure of the heightfield, which can be exploited to render more efficiently. Your assignment is to apply techniques similar to those used for grid-based acceleration structures to develop a fast intersection routine for heightfields.

Step 1

Click here to download a zip file containing several pbrt scene files, heightfield data, and textures. The UNIX version of pbrt should build the heightfield shape plugin by default. If you're using windows, copy the heightfield.vcproj file to pbrt/win32/Projects/ and add the project file in the pbrt solution. After you have built the heightfield plugin, run pbrt on scenes: hftest.pbrt and landsea-0.pbrt, and you should see output images (hftest.exr and landsea-0.exr) that look like this:

Step 2

Your assignment is to write a fast heightfield intersection algorithm, which will allow you to render higher resolution terrains more quickly than the current implementation. You should do this by modifying the existing 'pbrt/shapes/heightfield.cpp' file; you do not need to change other pbrt files. Specifically, you need to:

• Add and implement Intersect() and IntersectP() functions, which will allow the renderer to intersect a ray directly with the heightfield.
• Change CanIntersect to return true, so that pbrt uses your functions instead of the Refine method to convert to a triangle mesh.

Your implementation of Intersect() and IntersectP() will likely use an acceleration structure like a uniform grid or kd-tree. If you choose to use an acceleration structure, you should start by searching for a paper that describes a fast method for marching rays through uniform grids. Also feel free to peruse the pbrt source for examples, but make sure you understand any code that you borrow.

Step 3

Once you have the fast intersection routines working, add the following additional features:

• Compute the u and v coordinates so that you can texture map heightfields. You can test this by rendering the texture.pbrt scene, which maps the land heightfield with a colored grid texture.
• Perform Phong interpolation of the normals across each heightfield triangle. See the text book for information about Phong interpolation.

Here are some example images of what you should see after completing the steps above:

Suggestions

• Make sure you understand how pbrt deals with transformations (e.g. object-to-world)
• You should understand the GetShadingGeometry() function and how it's used by the integrator to shade an intersection point. You will need to implement this as a member function in the heightfield class (for Step 3).
• It will probably be difficult for your algorithm to out perform pbrt, which uses a highly optimize 3D kd-tree to render triangle meshes. However, you should try to make your code as fast as possible.

Submission

Write a web page and mail the URL to me.. The page should contain the following:

• A brief description of the algorithm(s) you implemented in steps 2 and 3.
• A link to your modified heightfield.cpp file
• Two renderings of landsea-0.pbrt: one with Phong interpolated normals and one without.
• Renderings of scene files landsea-0.pbrt, landsea-1.pbrt, landsea-2.pbrt, and texture.pbrt, with Phong interpolation if you have it. Below each image include the time it took to render using your implementation vs. the original version of heightfield.cpp.
• A rendering of landsea-big.pbrt, which contains a 1000x1000 sea heightfield. This should be a good stress test for your algorithm.

FAQ

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: On Unix systems, 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.  On Windows, build the system under "Release" mode.    


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 hw1-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 landsea-big.pbrt.  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 landsea-big.pbrt 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.

Grading

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 rendering does not work fully
** - The intersection routine was functionally complete, but step 3 doesn't work at all.
*** - Intersection and texture mapping worked, but normal interpolation didn't.
**** - Intersection and normal interpolation worked, but texture mapping didn't.
***** - All requirements satisfied, and the implementation is faster than the original

Note that only ONE star is available for intersection routines that aren't functional from all viewpoints, regardless of texture mapping and/or normal interpolation.