Date: Thu, 28 Mar 2024 13:15:41 +0000 (UTC)
Message-ID: <1172858340.7460.1711631741395@ip-10-0-0-233.us-west-2.compute.internal>
Subject: Exported From Confluence
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Introduction
Subdivision surfaces are the most common way to model complex smooth geo=
metry in RenderMan, and for good reasons: they guarantee the smoothness of =
a model and they impose very few topological constraints on the modeler.
A common way to approach a subdivision surface is to imagine a polygon m=
esh (the control mesh) that undergoes a local averagi=
ng (or smoothing) at every vertex, creating a new set of vertices that have=
a smoother appearance than the original mesh. One application of this aver=
aging operator everywhere on a mesh is a single subdivision step. If we could take an infinite number of subdivision steps, eventuall=
y we will converge to a limit surface, which has a se=
t of guaranteed smoothness properties depending on the type of subdivision =
being used.
Two levels of subdivision
Like most other types of geometry, a subdivision mesh is described by it=
s control mesh. Unlike NURBS, the control mesh is not confined to be rectan=
gular, so in this respect, the control mesh is very similar to the polygona=
l surface. But where polygonal surfaces require large numbers of points to =
appear smooth, a subdivision mesh's limit surface is guaranteed to be =
smooth - meaning that polygonal artifacts or faceting are never present, no=
matter how the surface animates, or how closely it is viewed.
Unlike many other renderers, RenderMan's implementation of subdivision s=
urfaces does not apply a fixed number of subdivision steps to a polygonal m=
esh. Instead, it adaptively tessellates into micropolygons whose size is&nb=
sp;by default computed in terms of pixel=
s on the screen. Moreover, e=
ven if the micropolygons are large due to the micropolygon length setting, =
their vertices are computed directly from the limit surface for the highest=
accuracy.
Comparison with Polyg=
ons
A common question to consider when modeling assets is: should a polygona=
l asset be rendered as-is, or should be it converted to a subdivision surfa=
ce? If the asset is not smooth in nature (i.e. simple geometry with hard si=
lhouettes), then polygons are probably all that is needed. If the asset is =
meant to be a smooth surface, then the tradeoffs become more complicated:=
p>
- The number of polygons that may be needed to represent a smooth surface=
may be significantly higher (and require more memory) than the equivalent =
subdivision mesh. In such cases, it is obvious that the subdivision mesh is=
the better representation.
- However, polygons are usually considerably cheaper if the renderer does=
n't need to perform any subdivision. The renderer needs to retain extra mem=
ory on a subdivision surface in order to be able to perform subdivision. If=
the asset is significantly over-modeled, to begin with, it may be the case=
that the limit surface may not differ significantly from the control mesh,=
and the extra memory needed to perform the subdivision was wasted. In that=
case, the polygonal representation may suffice (i.e. it may be considered =
"smooth enough"). Note that the renderer tries very hard to mitigate cases =
where subdivision meshes are over-modeled by converting their underlying re=
presentation to what is essentially a polygonal representation upfront in a=
"pre-tessellation" step, saving memory by discarding the subdivision data.=
- Subdivision meshes have the ability to perform watertight dicing in ord=
er to close potential holes or cracks caused by displacement. In RenderMan,=
polygons cannot do this because they don't retain enough data.
- Subdivision meshes have some topological constraints; in particular, fa=
ces cannot have holes, and they cannot represent non-manifold surfaces (sur=
faces where an edge may be incident to more than two faces - imagine two cu=
bes sharing a single edge). In practice, this is usually not a significant =
problem.
Features
Subdivision Schemes
RenderMan's implementation of subdivision meshes includes two subdivisio=
n schemes:
- Catmull-Clark=
subdivision surfaces are the industry standard. It is a quadr=
ilateral-based subdivision scheme, and works best with control meshes that =
are comprised mostly of quads - any non-quad geometry is immediately conver=
ted to quadrilaterals on the very first subdivision step. They generally go=
od for most situations and have no special concerns when it comes to textur=
e filtering.
- Loop subdivision surf=
aces (Not Supported in XPU) is a triangle-based scheme, which is optimi=
zed for control meshes that are entirely triangles: they tend to require le=
ss memory than Catmull-Clark scheme. However, due to the nature of triangle=
s, derivatives can be discontinuous from face to face, which may lead to te=
xturing artifacts that require extra effort to solve.
<=
/li>
- Bilinear subdivision surfaces simply render high level 4-sided faces to bilinear patches, a=
nd subdivides all n-sided faces to n blps. Like other SubdivisionMeshes it supports all=
hierarchical edits, is guaranteed to be watertight, and can be used in con=
junction with PTex.
Sharp Creases and Cor=
ners
Not all geometry is smooth everywhere. In cases where a sharp feature ne=
eds to be preserved, an edge or vertex can be tagged as a crease or a corner. This means that near that feature, no =
actual subdivision will be applied, and the resulting limit surface will be=
unchanged from the control mesh.
Semi-sharp Creas=
es and Corners
When approximating a smooth surface with polygons, it is common to apply=
a fillet operator onto a sharp edge in order to convert it into a rounded =
edge. Unfortunately, fillets tend to create many more polygons. This proble=
m is somewhat mitigated by conversion of the polygon mesh into a subdivisio=
n surface: now, the smoothness of the surface is guaranteed; however, the s=
ize of the rounded edge is still determined by the size of the faces adjace=
nt to the edge, and it may still prove necessary to introduce new faces int=
o the model to control the size of the edge curve.
To mitigate this problem, RenderMan's implementation of subdivision surf=
aces allow for edge and vertices to be tagged as semi-sharp creases and corners, respectively. Tagging an edge as a semi-sharp c=
rease means that the resulting limit surface near the edge will be somewher=
e in between where it would have been if it had been tagged as a fully shar=
p crease (i.e. the control mesh) and where it would normally have ended up =
as a fully smooth surface. The example below shows the subdivision mesh res=
ulting from a cube control hull, with various crease strengths applied.
Watertight Dicing
A benefit of using subdivision meshes over polygon meshes is that the to=
pological data needed to perform subdivision is also useful for guaranteein=
g that the surface will remain watertight, no matter what happens in the di=
splacement. In particular, if the faces immediately adjacent to a shared ed=
ge compute a different displacement result, on a polygon mesh a crack will =
likely appear as the faces pull apart. While this seems like an obvious thi=
ng to avoid, in practice it may not be easy to do so particularly when usin=
g a complicated texture asset derived from PTex or a UDIM based workflow. I=
f a subdivision mesh is used instead of a polygon mesh, with watertight dic=
ing enabled, the renderer can ensure that no cracks will appear at face bou=
ndaries.
Boundary Interpolation=
In order to provide the smoothest possible limit surface, the averaging =
behavior of a subdivision surface is such that the limit surface "pulls awa=
y" from the boundaries of the control mesh by default. This can be undesira=
ble when dealing with non-closed meshes, especially those that need to conn=
ect seamlessly with other adjoining meshes. As a convenience, RenderMan pro=
vides boundary interpolation rules that allow this behavio=
r to be overridden, allowing the surface to continue all the way to the bou=
ndary of the control mesh. Different rules allow for smooth or sharp corners (vertices that have exactly two incident edges). Th=
e example below shows the boundary interpolation rules applied to a simple =
9 face control mesh.
Subdivision mesh, no boundary interpolation
Subdivision mesh, boundary interpolate: edges and corners
Subdivision mesh, boundary interpolation: edges only
This idea of boundary interpolation can also be extended to the interpol=
ation rules applied when dealing with data over the surface, most notably t=
exture coordinates (in this context, RenderMan uses the term faceva=
rying boundary interpolation). When dealing with the seams between=
disjoint UV regions, the renderer can use several different rules, trading=
off the smoothness of the subdivided result away from the seams against th=
e desire to interpolate the seams exactly. Note that no matter what rule is=
chosen, the UV texture map editor must also abide by the same rules, other=
wise undesirable texturing artifacts will result. The following image =
demonstrates the different rules applied to a 4x4 grid of quads segmented i=
nto three UV regions.
The "interpolateboundary" tag control=
s how interpolation boundary face edges are interpolated. This tag has one =
optional integer argument and zero floating-point arguments. If the integer=
argument is not specified it is assumed to have a value of 1. A value of 0=
specifies that no boundary interpolation behavior should occur (the defaul=
t behavior when this tag is not specified). A value of 1 indicates that all=
the boundary edge-chains are sharp creases and that boundary vertices with=
exactly two incident edges are sharp corners. A value of 2 indicates that =
all the boundary edge-chains are sharp creases; boundary vertices are not a=
ffected.
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