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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