Future research / other areas of interest

In addition to the topics I have covered in this article, I was asked to cover two additional areas of interest. Unfortunately, I did not have time to fully explore these topics. I list them here so the reader is aware of them and can do their own research if interested.

Smoothing Groups
Smoothing groups are most familiar to users of applications such as 3D Studio Max and other Modeling Packages. Smoothing groups are essentially sub-sections of vertices with shading which does not obey the same lighting rules as their surrounding vertices. This is useful in the case of a cylinder, for example. The cylindrical section of a cylinder is smooth and should thus have a smooth shading algorithm applied to it. The top however, or rather the transition from smooth edge to top, should not necessarily be a smooth transition. The user expects that the ring separating the edge and top is a hard edge and should thus not have averaged normals at those vertices. Smoothing groups allows you to do this by duplicating vertices and then setting different normals for one set of vertices than the other.

In the case of heightfields, smoothing groups could be useful at the peaks of tall mountains or at the edges of cliffs and drop offs. Either of the algorithms above would cause a smooth curve down the steep drop. In reality, there are often sudden drops in which there is not a smooth curve. Smoothing groups can then be used to give your terrain more realistic edges.

Computation of Normals from Parametric Equations
Another option is the computation of normals from some parametric equation. The best example of this would be a sphere. Normally a sphere is represented by an array of triangles which approximate the surface of a sphere. To compute the normal of any of those vertices one could use the usual method of crossing edges of a triangle. On the other hand, mathematically the normal to any point on the surface of a sphere is just the direction vector from the center of the sphere to that point on the surface. With this in mind, it is possible to compute a faster and/or more accurate surface normal on a sphere by using the mathematical definition of a sphere than computing normals via cross-product.

The application of this on a heightfield is less obvious. I can envision this only being useful when your terrain is procedurally generated from a well known function. In the demo I provided the positions of all the vertices are computed from a Sine function. In this example, it should be possible, knowing that the height of my vertices range from 0 to 1 as a function of 0 to 360 degrees, to compute the normal at each of the vertices based on the angle between 0 and 360 of that particular vertex. This will be left up to the reader to implement.

Conclusion

During the past two weeks I have had the opportunity to write a demo which explores the implementation of lighting normals of a heightfield while at the same time being able to make empirical observations about the usefulness and performance of each of the different popular algorithms. This article contains all that I have discovered about computing normals for lighting of a heightfield and I hope that it has been both informative and helpful. Based on my findings I will implement my heightfields using normalized, weighted surfaces, and averaged - not normalized, vertex normals whenever possible. For those that are part of the GameDev.net community I hope to see you on the forums and I look forward to your feedback regarding this article. Feel free to send your code corrections and/or comments directly to me via PM.

Appendix A: Demo Description, Links, and Key bindings

The screen shots, performance comparisons, code snippets, etc. of this article were all based upon information gathered from the attached demo. The demo was an opportunity for me to test various types of functionality and to determine the visual and performance impacts of those features. Because of that, the demo has a limited amount of functionality.

Links:
Source Code
Win32 Binary Executable

Keyboard Bindings:
Arrows Keys: Increase/Decrease the resolution of the heightfield
1: Toggle on/off wireframe display
2: Toggle on/off calculation of surface and vertex normals
3: Toggle Smooth vs. Flat shading
4: Toggle on/off normalization of surface normals
5: Toggle normalizing vs. averaging of vertex normals
6: Toggle on/off weighting of vertex normals by angle
0: Toggle on/off display of debug normals
9: Toggle on/off animation of heightfield

References

• "A Comparison of Algorithms for Vertex Normal Computation", Shuangshuang Jin, Robert R. Lewis, David West, 2003, Washington State University