**Extending the radiosity method to include specularly reflecting and translucent materials**

Holly E. Rushmeier, Kenneth E. Torrance

Pages: 1-27

DOI: 10.1145/77635.77636

An extension of the radiosity method is presented that rigorously accounts for the presence of a small number of specularly reflecting surfaces in an otherwise diffuse scene, and for the presence of a small number of specular or ideal diffuse...

**Performing geometric transformations by program transformation**

Robin A. Nicholl, Tina M. Nicholl

Pages: 28-40

DOI: 10.1145/77635.77637

Problems in geometry often possess symmetry properties that may be exploited in order to develop solutions. Algorithms based on these symmetry properties will frequently use geometric transformations to transform one case into another...

**Knot insertion for Beta-spline curves and surfaces**

Barry Joe

Pages: 41-65

DOI: 10.1145/77635.77638

Discrete Beta-splines arise when a Beta-spline curve is subdivided; that is, extra knots are inserted so that the curve is expressed in terms of a larger number of control vertices and Beta-splines. Their properties and an algorithm for their...

**Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms**

Herbert Edelsbrunner, Ernst Peter Mücke

Pages: 66-104

DOI: 10.1145/77635.77639

This paper describes a general-purpose programming technique, called Simulation of Simplicity, that can be used to cope with degenerate input data for geometric algorithms. It relieves the programmer from the task of providing a consistent...

**The implementation of an algorithm to find the convex hull of a set of three-dimensional points**

A. M. Day

Pages: 105-132

DOI: 10.1145/77635.77640

A detailed description of the implementation of a three-dimensional convex hull algorithm is given. The problems experienced in the production and testing of a correct and robust implementation of a geometric algorithm are discussed. Attention...

**Multidimensional icons**

Tyson R. Henry, Scott E. Hudson

Pages: 133-137

DOI: 10.1145/77635.77641

Background: Direct manipulation interfaces, such as the Macintosh desktop, often represent objects with icons [l, 41. For example, text files are represented by icons. Selection of the icon invokes an editor to view the file it represents, thus...

**A two-dimensional view controller**

Andrew S. Glassner

Pages: 138-141

DOI: 10.1145/77635.77642

Description: Many two-dimensional graphics programs provide a user with a rectangular screen window for viewing a two-dimensional image. Common examples of this underlying “world” image include text, line, or shaded pictures, and...