Date: Fri, 29 Mar 2024 12:46:28 +0000 (UTC)
Message-ID: <119155113.727.1711716388261@ip-10-0-0-233.us-west-2.compute.internal>
Subject: Exported From Confluence
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Introduction
Curves can be used to render large numbers of thin strands of geometry v=
ery efficiently, making this primitive particularly well-suited for modelin=
g fur, hair, and blades of grass. This geometry type is an approximate repr=
esentation, designed to render more efficiently in both time and memory com=
pared to an equivalent surface of circular cross section. The trade-off is =
that when viewing curve geometry up close, there can sometimes be geometric=
artifacts; these artifacts tend to not be perceptible as the curves become=
more distant from the camera. RenderMan supports both flat (ribbon-like) a=
nd round (tube-like) curves, and it is possible to choose from a variety of=
basis functions.
Parameters
Width
The width of a curve can vary over the length of the curve. It is possib=
le to specify a constant width that applies to all curve strands in the pri=
mitive, or widths can be specified to be different on a per-curve strand, p=
er-segment, or per-vertex basis.
|
|
Varying Width (tapered width ranges from 0.005 to 0.0 along the length of e=
ach curve)
|
Constant Width (constant width of 0.005 along length of each curve)
|
When specified per-segment or per-vertex, ne=
gative values for width can be used along curves: as the value of width is =
interpolated along the curve, the curve will taper to a sharp tip and the p=
ortion of curve with a negative width will disappear. This can be used to s=
lightly randomize the length of hair in a clump without changing control po=
ints or their animation/simulation.
Basis
Given a set of control points that the user supplies as vertices, which =
composes the hull of the curve, the basis function determines how the actua=
l rendered curve appears. For example, some basis functions, such as the Ca=
tmull-Rom basis, guarantee that the rendered curve will pass through all in=
terior, non-endpoint control vertices, whereas others, such as B-spline, ty=
pically do not pass exactly through any of the control vertices. Each basis=
function has different trade-offs in terms of smoothness, controllability =
and ease-of-use.
- Bezier - A Bezier basis generates a 3D curve that pass=
es through every third control vertex. The remaining control vertex positio=
ns are used to determine the incoming and outgoing tangent of the curve of =
the adjacent vertex that the curve does pass through. When using a Bezier b=
asis with curves that contain multiple segments (that is, more than 4 contr=
ol points), some care should be taken to ensure that incoming and outcoming=
tangents line up at vertices that are on the rendered curve, or there will=
be a discontinuity in the smoothness of the curve where it suddenly change=
s direction.
- B-Spline - While a B-Spline basis function can be some=
what less intuitive to use in that it generates a curve that typically only=
approximately comes close to passing through the given control vertices, a=
n advantage is that this basis function tends to yield very smooth curves. =
Discontinuities in the smoothness of the curve are possible if multiple con=
trol vertices are repeated consecutively (aka multiplicity).
- Catmull-Rom - This basis function generates a curve th=
at is guaranteed to pass through every interior, non-endpoint control verte=
x, and it tends to generate smooth curves, although there can sometimes be =
unexpected "wobbles" in areas of high curvature with this basis function ch=
oice (see images below for an example). Using a B-Spline basis instead can =
smooth out the wobbles, although a B-Spline basis typically produces a curv=
e that does not pass through the control vertices exactly, unlike the Catmu=
ll-Rom basis (for non-endpoint control vertices).
- Linear - Specifying linear curves yields straight line=
segments, continuous linear segments in a curve are joined with a round ca=
p.
The example below shows how different basis affects the shape of a curve=
given the exact same control vertices: while control vertices and the curv=
e hull is dawn in white, the curve is drawn in yellow.
It is common practice to use B-Spline and Catmull-Rom curves with multip=
licity at curves extremities to better control where the curve begins and e=
nds. Note that in order for such types of curve basis to end at the exact p=
osition of the first and last curve control vertex, these have to be repeat=
ed one more time Catmull-Rom and two more times for B-Splines.
=
B-Spline with multiplicity
Catmull-Rom with multiplicity
Mode
RenderMan supports both flat (ribbon-like) curves and round (tube-like) =
curves, demonstrated in the images below.
- Flat Curves - usually recommended for blades of grass =
or other geometry where the curve geometry is relatively more "ribbon-like"=
than tube-like in appearance. User-normals are specified for flat curves t=
hat will twist around so that their orientation always follows the user-spe=
cified normals (for both camera and other ray types). No-normal curves (alw=
ays camera facing) are not supported. Flat curves are no appropriate for fo=
liage or other "flat" surfaces where the geometry is roughly rectangu=
lar and the desired silhouette is obtained with a cut-out texture. For thes=
e it is much better end more efficient to use polygons instead.
- Round Curves - typically recommended for hair and=
fur since this usually represents the underlying hair geometry with greate=
r fidelity (although not in all cases), and as a direct consequence round c=
urves do tend to produce a more accurate reproduction of occlusion and shad=
owing for fur and hair compared to flat curves. User normals must not be pr=
esent when using round curves; if user-specified normals are provided, they=
will take precedence over the round curve default and as a result the curv=
e will be rendered as a twisting ribbon-like curve that follows the user-sp=
ecified normals (e.g., a flat curve). Currently, round curves tend to exhib=
it better time and memory performance compared to flat curves. It is highly=
dependent on the BxDF and shading model, but in some cases, the tube-like =
varying normal produced when using round curves can yield more interesting =
shading results.
Flat Curves with User-Specified Normals
Opacity
Like all geometry in RenderMan, if the BxDF attached to a curves primiti=
ve computes presence or opacity, this will control whether the curves are p=
resent on screen and to what percent. To improve raytracing performance, pr=
esence and opacity signals are always cached for curves. There is also an o=
ptimization implemented for round curves where if the opacity is specified =
in the "Os" primitive variable, then a more efficient code path is taken wh=
en computing shadowing which avoids the need to run any BxDFs or lookup int=
o the opacity cache.
Minimum Width
An option can be used to specify the minimum width for curves. When spec=
ified, this artificially widens curves so that they are at least as wide as=
the specified minimum width (measured in pixels), with a corresponding dec=
rease in presence. The effect is that the curve looks about the same when r=
endered, except that the high spatial frequency geometry is now band-limite=
d thus minimizing aliasing artifacts, which just means that fewer camera sa=
mples are needed in order to anti-alias the curve (and thus fewer rays need=
to be traced, resulting in faster performance). Useful values for minimum =
hair width range from 0.0 to 1.0.
Option "curve" "float minwidt=
h" [0] (default: 0)
=
curve:minwidth =3D 1.0 with 64 samples per p=
ixel  =
; &n=
bsp;  =
; curve:minwidth =3D 0.2 with 64 sample=
s per pixel
Notice in the example images above that the render with curve:minwidth=
=3D1.0 has converged after 2.5 minutes using only 64 samples-per-pixel, whe=
reas visual inspection reveals that the render with curve:minwidth=3D0.2 (a=
lso rendered using 64 samples-per-pixel) still has some areas with not-full=
y-converged aliasing artifacts after the same 2.5 minutes of rendering (whi=
ch do ultimately resolve with more samples). Minwidth is not a physical-bas=
ed control, you may notice the curve:minwidth=3D1.0 setting has introduced =
a perceptible amount of bias in the render (that is, it is slightly smoothe=
r in a few areas), although the introduced bias is not visually objectionab=
le, in some cases it considered desirable as it produces a softer look.
Best Practices
When rendering hair or fur, it is recommended that:
- Round curves should typically be enabled when appropriate. Doing so&nbs=
p;will ensure high quality hair shadowing in any lighting configurati=
on by intersecting against cylindrical hair geometry instead of flat ribbon=
s, resulting in significantly more realistic occlusion.
<=
/span>
- Many hair or fur strands should be packed into relatively few Cur=
ves primitives (e.g., 10,000 or more strands per Curves primitive), rather =
than rendering millions of Curves primitives that each are composed of just=
one or a few strands of hair.
- If a model is composed of several curves objects that substantial=
ly overlap in volume (e.g. fur coat and undercoat), the best performance is=
achieved when these objects shares the same values for transformation, vis=
ibility flags and group membership.
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