Introduction

Curves can be used to render large numbers of thin strands of geometry very efficiently, making this primitive particularly well-suited for modeling fur, hair, and blades of grass. This geometry type is an approximate representation, designed to render more efficiently in both time and memory compared 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) and round (tube-like) curves, and it is possible to choose from a variety of basis functions.

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• Bezier - A Bezier basis generates a 3D curve that passes through every third control vertex. The remaining control vertex positions 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 basis with curves that contain multiple segments (that is, more than 4 control points), some care should be taken to ensure that incoming and outcoming outgoing 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 changes direction.
• B-Spline - While a B-Spline basis function can be somewhat less intuitive to use in that it generates a curve that typically only approximately comes close to passing through the given control vertices, an advantage is that this basis function tends to yield very smooth curves. Discontinuities in the smoothness of the curve are possible if multiple control vertices are repeated consecutively (aka multiplicity).
• Catmull-Rom - This basis function generates a curve that is guaranteed to pass through every interior, non-endpoint control vertex, and it tends to generate smooth curves, although there can sometimes be unexpected "wobbles" in areas of high curvature with this basis function choice (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 curve that does not pass through the control vertices exactly, unlike the Catmull-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 cap.

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• 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 that will twist around so that their orientation always follows the user-specified normals (for both camera and other ray types). No-normal curves (always camera facing) are not supported. Flat curves are no appropriate for foliage or other "flat" surfaces where the  geometry is roughly rectangular and the desired silhouette is obtained with a cut-out texture. For these 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 greater fidelity (although not in all cases), and as a direct consequence round curves do tend to produce a more accurate reproduction of occlusion and shadowing for fur and hair compared to flat curves. User normals must not be present when using round curves; if user-specified normals are provided, they will take precedence over the round curve default and as a result the curve will be rendered as a twisting ribbon-like curve that follows the user-specified normals (e.g., a flat curve). Currently, round curves tend to exhibit 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.

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