Analysis of the performance of each approach

During the course of writing this article I decided to create a demo which illustrated the different topics in action. As I was researching the best way to implement the various heightfield algorithms I came upon some contradictions. Some people said you should normalize the surface normals before using them in any vertex normal calculation, some said it didn't matter. Also, many said the best way to compute the vertex normal was to average the surface normals, and others said just add up the surface normals and then normalize the resulting vector. Finally, there's the question of which algorithm looks best and performs best between Mean Weighed Equally and Mean Weighted by Angle. This section will attempt to compare and contrast the differences between the various methods.

It should be understood that the performance analysis I give below is based upon only have a single heightfield in the scene, with no other objects, which is animating on a Sine curve every frame. Actual performance in real-time situations could be both better and worse than those given below based upon whether your terrain is static or dynamic, and what else you have going on in your scenes. The information provided below is strictly for the purpose of comparing computational complexity of the different algorithms.

Img. High resolution terrain rendered without and with surface normals

MWE, Non-Normalized Surface Normals vs. Normalized Surfaces (Averaged Vertex Normals)
From a visual perspective I found that normalizing the surface does result in both darker looking terrain as well as smoother curves. Additionally, at relatively low resolutions there is no observable performance penalty for normalizing the surface normals. At very high resolutions, however, I found that normalizing the surfaces could lower the frame rate by as much as 6% (318 fps – 300 fps). The larger my resolution the more obvious the difference between normalized and non-normalized surface normals. With that being said, I found that normalizing the vertex normals with MWE can eliminate the need to normalize the surface normals.

Img. High resolution terrain rendered with averaging and normalizing of vertex normals with surface normals normalized. Very little difference.

MWE, Normalizing vs. Averaging of Vertex Normals
From a visual perspective, normalizing the vertex normals only really matters when the surfaces are not normalized. In either event normalizing the vertex normals has the effect of making the terrain look a bit lighter and spreads out the shadows. This difference however is most noticeable when viewed with the surface normals not normalized. Especially at higher resolutions if the surface normals were not normalized the vertex normals must be normalized. As with normalizing the surface normals, there is almost no noticeable performance penalty at lower resolutions for normalizing the vertex normals. At higher resolutions however, normalizing the vertex normals can drop the frame rate by an additional 6%. Given that normalizing both the surface and vertex normals incurs a 6% stackable framerate loss, and given the relatively little benefit gained from normalizing the vertex normals when the surface normals are averaged, my advice is to just normalize the surface normals and average the vertex normals. This will be doubly true when we get to MWA.

MWA, Non-Normalized Surface Normals vs. Normalized Surfaces (Averaged Vertex Normals)
Whereas normalizing the surfaces was optional for MWE, it is essential for MWA. When I render the weighted vertex normals without first normalizing the surfaces I get strange artifacts in the triangles which are perfectly flat. They either show up entirely black or entirely white. On the positive side, the amount of computation required to compute the angles far outweighs that which is required for normalizing the vectors. Always normalize the surface normals when using weighted vertex normals.

Img. High resolution terrain rendered with weighted surface normals and either normalized or averaged vertex normals.

MWA, Normalizing vs. Averaging of Vertex Normals (Normalized Surfaces)
This switch is probably the most interesting of all the other variables thus far. At lower resolutions the increased light caused by normalizing the vertex normals as opposed to averaging can make the terrain look more attractive. On the other hand, as the resolution of the terrain increases the extra light makes the terrain look unrealistic. A high resolution terrain with surface normals normalized and vertex normals averaged was the most realistic looking terrain I have yet to see. At the highest resolution the ripples in my terrain made it look like fine satin. The only downside is that the computation time for the weighted normals is quite extensive. In my experiences weighting the normals dropped my framerate from about 80% (1000 fps – 200 fps). The thing to keep in mind is that I was updating the height values and recomputing the normals every frame. In reality, there is likely to be very little run-time updating of weighted terrain normals. For that reason, weighted normals should still be considered a very viable solution when seeking very attractive and believable terrain.

Future research