# Quadratic Bezier triangles as drawing primitives

@article{Bruijns1998QuadraticBT, title={Quadratic Bezier triangles as drawing primitives}, author={Jan Bruijns}, journal={Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware}, year={1998} }

Bezier Triangles As Drawing Primitives J. Bruijns, Philips Research Laboratories’ We propose to use quadratic Bezier triangles as additional drawing primitives: quadratic Bezier triangles require much less model data for faithful representation of curved surfaces than planar triangles. Therefore, they require less storage and/or transmission capacity. Furthermore, they allow automatic level-of-detail. Finally, they result in considerable savings in model-view transformations and lighting…

## Figures and Tables from this paper

## 13 Citations

### Shading By Fast Bi-Quadratic Normal Vector Interpolation

- Computer Science
- 2005

It is shown that Bezier triangles and curves can be used for reducing the cost of Biquadratic Phong shading by virtue of fast calculation of area coordinates at the edge points, and this shading algorithm becomes faster than all the known fast Bi-quadratic normal vector interpolation methods.

### A new model for 3D graphical rendering

- Computer Science
- 2006

A non linear model for geometrical structures in a 3D rendering engine is considered (the Lembo model) and the properties of the model are shown; an ecient algorithm is shown to solve the projection problem directly on the model equations.

### A new model for 3 D graphical rendering

- Computer Science
- 2006

A non linear model (the Lembo model) for geometrical structures in a 3D rendering engine is considered: firstly the properties of the model are shown; then an efficient algorithm is shown to solve the projection problem directly on the model equations.

### An Efficient Algorithm for Adaptive Segmentation and Tessellation with Pixel Precision

- Computer ScienceEurographics Italian Chapter Conference
- 2007

A new algorithm is proposed to get a representation of a curved surface with the precision of the image pixel, with principles common to every kind of surface, and how these principles can be applied to quadratic and cubic beziér triangles.

### Hardware implementation of the subdivision loop algorithm

- Computer ScienceProceedings. 28th Euromicro Conference
- 2002

A comparative analysis of two possible implementations of this hardware unit corresponding to two different alternatives for applying loop subdivision to triangle meshes: subdivision based on forward differencing and on meshing scheme.

### Virtual worlds modeling for Web deployment

- Computer Science2000 10th Mediterranean Electrotechnical Conference. Information Technology and Electrotechnology for the Mediterranean Countries. Proceedings. MeleCon 2000 (Cat. No.00CH37099)
- 2000

A design architecture for the graphics engine of a virtual reality system to be deployed over the Web and a prototype application for virtual worlds modeling is presented along with detailed discussion on technical and implementation issues.

### New models for high-quality surface reconstruction and rendering

- Computer Science, Mathematics
- 2011

The main contribution of this thesis is the development of the first efficient GPU-based reconstruction and visualization methods using trivariate splines, i.e., splines defined on tetrahedral partitions, which are very well-suited for real-time reconstruction and high-quality visualizations of surfaces from volume data.

### Adaptive quasi-interpolating quartic splines

- Computer Science, MathematicsComputing
- 2009

An adaptive quasi-interpolating quartic spline construction for regularly sampled surface data based on a uniform quasi-Interpolating scheme, employing quartic triangular patches with C1-continuity and optimal approximation order.

### Watertight tessellation using forward differencing

- Computer ScienceHWWS '01
- 2001

An algorithm and hardware for the tessellation of polynomial surfaces that produces a bit-for-bit consistent triangle mesh across multiple independently tessellingated patches with continuous level-of-detail is described.

### 35 Work in Progress Framewordk for Real . Time Sumulations Anders Backman 41 Surface Construction with Near Last Square Acceleration based on Vertex Normals on Tringular Meshes Tony Barrera

- Computer Science
- 2002

This work presents an alternative implementation of dynamic image based rendering that allows for a very inexpensive process of creating dynamic image-based renderings of digitally recorded photo realistic, real-life objects.

## References

SHOWING 1-10 OF 20 REFERENCES

### Interactive Display of Large NURBS Models

- Computer ScienceIEEE Trans. Vis. Comput. Graph.
- 1996

These algorithms work well in practice and, on high-end graphics systems, are able to display models described using thousands of Bezier surfaces at interactive frame rates.

### Curves and surfaces for computer-aided geometric design - a practical guide, 4th Edition

- Computer ScienceComputer science and scientific computing
- 1997

The fourth edition has been thoroughly updated and revised to include a new chapter on recursive subdivision, as well as new sections on triangulations and scattered data interpolants, and the disk in the back of the book has been updated to include all of the programs, as the data sets from the text.

### A scan line algorithm for computer display of curved surfaces

- Computer ScienceSIGGRAPH '78
- 1978

The method described here extends polygon based techniques to produce an excellent approximation of bi-cubic parametric surfaces in scan line order to produce shaded images of curved surfaces.

### Real-time rendering of trimmed surfaces

- Computer ScienceSIGGRAPH '89
- 1989

Rational tensor product surfaces, (Bézier, NURBS, Hermite, polynomial, etc.) are rendered in real-time by uniform faceting and can be balanced for optimal implementation on different hardware platforms.

### Fast Dynamic Tessellation of Trimmed NURBS Surfaced 1

- Computer ScienceComput. Graph. Forum
- 1994

This paper presents a technique that uses graphical compilation to enable fast dynamic tessellation of trimmed NURBS surfaces under highly varying transforms.

### Shading bicubic patches

- Computer ScienceSIGGRAPH
- 1987

Two new methods are presented for deriving bicUBic approximations to the shading parameters over a bicubic patch, suitable for both hardware and software implementations.

### Adaptive forward differencing for rendering curves and surfaces

- MathematicsSIGGRAPH
- 1987

An adaptive forward differencing algorithm is presented for rapid rendering of cubic curves and bicubic surfaces and involves a simple linear transformation on the coefficients of the curve which can be accomplished with shifts and adds.

### An adaptive subdivision algorithm for crack prevention in the display of parametric surfaces

- Computer Science
- 1990

An algorithm is presented for rendering parametric spline patches using adaptive subdivision to allow large approximating polygons whenever their use does not result in visible errors in patch boundanes or 10 lighting anomalies.

### Rendering cubic curves and surfaces with integer adaptive forward differencing

- MathematicsSIGGRAPH '89
- 1989

An error analysis of forward differencing is provided which is useful as a guide for integer AFD implementation, and the proposed technique using 32 bit integer values is capable of rendering curves having more than 4K forward steps with an accumulated error of less than one pixel and no overflow problems.