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# Real-Time Rendering of Trimmed Surfaces PowerPoint PPT Presentation

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:

Real-Time Rendering of Trimmed Surfaces

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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:

• 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.

### 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

### 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

### 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

### 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 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 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

### 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

### 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