RealTime Rendering of Trimmed Surfaces

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Real-Time Rendering of Trimmed Surfaces

• SIGGRAPH 89
• Alyn Rockwook, Kurt Heaton,Tom Davis (SGI)

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Introduction

• 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.

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Introduction

• 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

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Introduction

• 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

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Introduction

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

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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

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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

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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

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Results

• 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

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Results

• 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