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Real-Time Rendering of Trimmed Surfaces. SIGGRAPH 89 Alyn Rockwook, Kurt Heaton, Tom Davis (SGI). Introduction. Modern graphics systems have hardware support for polygon rendering:

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Real time rendering of trimmed surfaces

Real-Time Rendering of Trimmed Surfaces


Alyn Rockwook, Kurt Heaton,Tom Davis (SGI)


  • Modern graphics systems have hardware support for polygon rendering:

    • hundreds of thousands or even millions of polygons per second (including transformations, clipping, lighting, smooth shading, and z-buffering)

  • We need efficient methods to convert free-form surfaces to polygons.


  • Goals:

    • real-time performance

    • high quality images

    • portability

  • Previous work:

    • does not take advantage of hardware support

    • does not account for trimming

    • exhibits too many unwanted visual artifacts


  • Reminders:

    • object space is the 3D coordinate system in which the surface is defined

    • image space is to where the viewing transformations map the object space

    • screen space is the 2D coordinate system by projecting image space on the xy-plane

    • parameter space is the rectangle of (u,v) coordinates


  • Definition:

    • a region is monotone with respect to an axis if any line perpendicular to that axis has a convex intersection with the region

The method
The method

  • 7 main steps:

    • 1. convert to Bezier:

      • surfaces are converted to Bezier patches

      • trimming regions are loops of Bezier or piecewise linear curves

    • 2. calculate step sizes:

      • in parameter space, for each curve and surface, to guarantee the size of facets in screen space will not exceed a user specified tolerance

The method1
The method

  • 3. find extrema

    • find the points on the trimming curves where the tangents are parallel to the u or v axes

  • 4. divide into uv-monotone regions

    • each region is defined by a closed loop of curves

  • 5. cove and tile

    • each uv-monotone region is uniformly tessellated into a grid of rectangles connected by triangles to points evaluated along the curves

The method2
The method

  • 6. evaluate surface functions

    • polygons in (u,v) space are transformed to facets in object space

    • surface normals are calculated

  • 7. render facets

    • each facet is transformed to screen space, clipped, lighted, smooth shaded, and z-buffered using standard 3D graphics hardware


  • Met the goals:

    • 15,000 triangles per second (1989)

    • same image quality as the polygon hardware supports

    • the IRIS-4D GTX implementation was ported to a Personal IRIS in only two days


  • More good things:

    • patches can be processed in parallel

    • tile size smaller than a user specified tolerance (tradeoff image quality/rendering speed)

    • different size tiles without cracking

    • modular architecture:

      • steps with well defined interfaces

      • we can select the best way to implement each step

      • easier to develop and to maintain