# Knowledgebase:3D Solid Construction Methods

A listing of various 3D solid construction methods sites in alphabetical order.

A Caltech course presented by Peter Schröder Denis Zorin on subdivision surfaces. Complete course notes and a few Java applets.

Marching Triangles is a surface based approach to implicit surface polygonisation. It provides: polygonisation of open surfaces; dynamic integration of new implicit surface regions; efficient representation and reduced computation cost.

Lecture notes from the SIGGRAPH '95 course by Andrew Witkin, David Baraff and Michael Kass. In PDF format.

ARANZ is an established developer of 3D scanning and modelling technology for applications as diverse as movie-making, geological modelling and medicine. ARANZ supplies both hardware and software solutions to industry.

This article explores the issues related to rendering realistic surfaces using standard texture-mapping hardware. Such hardware enables the rapid rendering of color-mapped surfaces with interpolated surface shading. By computing textures on the fly using new algorithms, this article extends the domain to bump mapping, Phong shading and reflection mapping in combination. The efficiency of the algorithms arises from a combination of caching data in parametric arrays and using tables for fast evaluation of shading functions. These tables are computed efficiently by making use of angular coherence.

In displacement mapping, the surface is actually modified, in contrast to bump mapping where only the surface normal is modified. This means that displacement mapped surfaces will show the effect even in silhouette. Page maintained by G. Scott Owen.

An article written by Paul Bourke detailing two (inefficient) methods of evenly distributing points on a sphere. They do however allow for an arbitrary number of points to be distributed unlike many other algorithms which only work for a restricted set of points. Includes C and C++ source code.

Function Representation in Geometric Modeling & Computer Graphics. The function representation (or F-rep) defines a geometric object by a single real continuous function of point coordinates as F(X) >= 0. F-rep is an attempt to step to a more general modeling scheme using real functions. Site maintained by A. Pasko.

Various illustrated articles by Paul Bourke covering miscellanous topics in geometry.

We present a technique for rendering displacement mapped geometry in a ray-tracing renderer. Displacement mapping is an important technique for adding detail to surface geometry in rendering systems. It allows complex geometric variation to be added to simpler geometry, without the cost in geometric complexity of completely describing the nuances of the geometry at modeling time and with the advantage that the detail can be added adaptively at rendering time. A paper (in PostScript format) by Matt Pharr and Pat Hanrahan from the 1996 Eurographics Workshop on Rendering.

The Animation Research Lab at the Graphics, Visualization & Useability Center at the Georgia Institute of Technology. Specifying the motion of animated characters in computer animations and virtual environments is a difficult problem. Here, in the animation group, we are exploring one possible solution to this problem: applying control algorithms to physically realistic models of the systems that we would like to animate.Here is the current evolution of this lab

This is a very comprehensive site that hosts graphics research papers. All may be downloaded free. Maintained by Paul Nettle.

L-systems are sets of rules and symbols (also known as "formal grammars") that model growth processes. This introductory article was written by David G. Green.

Research paper and images by A. J. Preetham, Peter Shirley & Brian Smits.

A data base of published papers on methods used in the 3D computer graphics industry,

A list of 48 pages concerning the frequent question ``How can I arrange N points evenly on a sphere?

*. Maintained by Anton Sherwood.*

An overview of subdivision surfaces and related research papers. Illustrations are provided. Authors include Tony DeRose, Tom Duchamp and Hugues Hoppe.

H. Prautzsch: Analysis of Ck-Subdivision surfaces at extraordinary points. Written in German.

This paper by Jamis Buck is intended to inform the reader of how the basic ray tracing algorithm works. It takes a very simplistic approach to the explanation, avoiding the mathematical perspective traditionally used by many books and papers on the subject. It is intended primarily to inform the curious, rather than to teach the ambitious.

A tessellation is any repeating pattern of interlocking shapes. This site gives students a comprehensive introduction to tessellations and explains the basic math that is used in creating them. This site is a service of the Oracle Education Foundation.

How to arrange the direction vectors of N luminous fluxes of equal intensity illuminating a target sphere with perfectly diffuse reflection. Author Hugo Pfoertner.

Over 400 computer science & engineering papers (in compressed PostScript) from Washington University, including 4 papers on subdivision surfaces.

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