Maximum Smoothing Angle
The Smoothing Threshold Concept
The Maximum Smoothing Angle (MSA) is of fundamental importance in getting LightWave Objects to render and animate well, particularly when Bones are involved. The MSA appears as a variable data field in several menus and unless an appropriate figure is inserted, strange and unsatisfactory results can be obtained. Unfortunately, all explanations of the MSA which I have read in LightWave manuals and in articles written by LightWave professionals, are confusing. This is not helped when one finds quite contradictory information given in NewTek's own documentation. After looking at the topic from a practical perspective, I believe a simpler way of dealing with the MSA has been found. I've called it the Smoothing Threshold.
The MSA affects the ability of the smoothing algorithm to build a smoother/flatter boundary between connected Polygons. The mechanism only works on Polygons sharing a common edge and two Points along that edge. Smoothing also affects the ability of Layout's Surface functions to render a smooth looking boundary that would otherwise appear angular. This ability is known as Phong Shading. The MSA in Modeler pops up within the Subdiv (Subdivide/Smooth) command in the Polygon menu. When you wish to apply the
Subdivide/Smooth command, you are given the option of using a more appropriate
MSA than the 89.5degrees default, assuming you actually know a more appropriate value! This is where a clear understanding of the MSA principle is needed. Unfortunately, the conventional approach requires a degree of lateral thinking and can make an interesting Modeler task into a chore.
NewTek's version 5 definition of the MSA describes how it ....determines the maximum angle between any two adjacent polygons that will be rendered smoothly. Any angle greater than this value will be rendered with the edges between the polygons showing. So, the MSA is the maximum angle between adjoining polygons that can be smoothed. Well no, actually, it's not. That interpretation suggests only very angular seams can be smoothed, when the opposite is the case. So, understanding how it, 'determines the maximum angle', is the clue to understanding the problem. A more accurate definition of the MSA is:
The maximum angle subtended by the projected Normals of adjoining Polygons, up to which the seam will be smoothed.
A Normal is a line drawn at right angles to the surface of the Polygon.
It may be located anywhere within the surface, though LightWave places it at the geometric
centre of the Polygon. When you select a polygon or group of polygons, LightWave
automatically draws in the Normals. Normals are automatic features and cannot be manipulated
in any way. They provide a visual indication of the direction a polygon faces.
Double-sided polygons show two normals.
So, if the Normals meet the criterion, then the Polygons will be Smoothed. Confusing isn't it! The best thing here is a diagram. The following shows two pairs of adjoining polygons seen 'edge on' so their seam angle and their Normals can be clearly visualised. The polygons may be single- or double-sided, the principle is unaffected.
In this diagram, the first pair of Polygons (P1 and P2) are inclined at an acute angle (A) to each other. Conversely, Polygons P3 and P4 are obtuse (B). This arrangement has been made to illustrate the relevance of the default MSA setting of 89.5degrees. An important point to note about these diagrams is that angles A and B are related to SA1 and SA2 as follows:
A = 180 - SA1
B = 180 - SA2
The proof of this relationship is a simple exercise in trigonometry and will not be considered further here. The rule to remember is that the opposite angles of any quadrilateral add up to 180degrees. So, what we need to determine is which seam will be smoothed under the default setting.
In the first pair of Polygons, SA1 is obtuse and therefore larger than the default setting of 89.5degrees Accordingly, S1 will not be smoothed. Remember, the MSA is the Maximum angle that will be smoothed. In the second case, N3 and N4 subtend an acute angle, therefore they will be smoothed. It becomes clear that the default MSA of 89.5degrees is to allow any Polygon inclination which is just obtuse (at least 0.5degree so) to be smoothed over by the Subdivide/Smooth command. It will also be rendered smooth by
Phong Shading. Conversely, acutely inclined Polygons are not smoothed at the default setting.
This explanation of the MSA is fine in theory, but what setting should one use in practice? It's rather difficult to visualise intersecting Normals in a complex Object mesh! This is where the Smoothing Threshold idea can be of practical help when using Modeler. Think of the Smoothing Threshold as the complementary angle to the MSA. The Smoothing Threshold is the Minimum angle at which smoothing will occur. It's analogous to A and B in the diagrams. Under default conditions, you can see that the MSA and the Smoothing Threshold are each about 90degrees. However, when you examine an Object closely, you will see it contains Polygons are at various angles. Some may be larger than the
Threshold and others will be smaller. Those which are larger will be smoothed out. So if you decided to reduce the Threshold considerably, say to 30degrees, a lot more seams will get smoothed. However, you might find many seams which should be kept sharp will become rounded. Conversely, raising the Threshold to say 120degrees will enforce considerably more restraint in the smoothing process. Subdividing without extravagant Smoothing is usually the objective of the Subdiv command. Unfortunately, there's no such button as the Threshold Limit control! So, after assessing an appropriate Threshold from the general character of the Object, you have to express it in terms of the dreaded MSA. It's easy enough. Just subtract your estimated Threshold from 180degrees and use the result in the MSA setting. The following Tutorials (*) will show you how the Smoothing Threshold setting affects the results you get from
Subdivide/Smooth command in Modeler.
(*) In the WaveGuide manual.
After making a brief reference to the significance of the Normals, NewTek go on to conclude:
A default MSA of 89.5degrees assures that any surfaces at right angles (90degrees) or greater to each other will not be smoothed (!) (My exclamation mark)
In mid-2001, NewTek's release of LightWave v6.5 and subsequently v7 for the PC and Mac platforms, included a new approach to the Maximum Smoothing Angle. They've called it the 'Smooth Threshold'. Now this may be purely coincidental, but it's inclusion in their first upgrade since the publication of WaveGuide looks suspiciously like plagerism. Having said that, NewTek's description of the smoothing principle is no more lucid than it was in version 3.5!