The Pisces Acronym
Understanding each term in the Pisces
acronym gives insight into the Pisces Project and its goals:
Pisces is also known as a Platform for Implicit Surface Computations
and the Exploration of Singularities.
- Pisces strives to provide a computational environment
for two categories of users. By far the most common user is
the researcher or educator who wants to use Pisces
to investigate implicitly-defined curves or surfaces that
arise in his or her own work. For this user, Pisces is a tool.
The other set of users includes researchers who are developing algorithms
that compute implicitly-defined objects. For them,
Pisces provides graphics, memory management, a suite of test functions,
and other algorithms with which to compare their results.
- Pisces computes curves and surfaces that are defined
as the set of points that satisfy a given equation. For example,
the set of points that satisfy the equation
is a circle with radius 1. We say that the circle
is defined implicitly by this equation.
- Surfaces and Curves
- Pisces has algorithms to compute one- and
two-dimensional objects, although these objects may exist in
an arbitrary-dimensional ambient space. For example, Pisces can
compute curves in the plane, curves in three-space, and so on.
Although it is possible to compute implicitly-defined objects of
dimension greater than two, these objects are currently very challenging
to visualize and understand.
- Pisces is an interactive tool. It is designed
to provide users with the tools to investigate implicitly-defined
structures and to experiment with a variety of methods for computing these
- When a curve or surface intersects itself, or when it
contains a "pinch point" (for example, a cusp), we say that the
surface has a singularity. Numerical algorithms designed to compute
typically have great difficulty in the neighborhood of a singularity.
A focus of the Pisces Project is to pay particular attention to
singularities and to develop algorithms that do not fail near singular
The Pisces Home Page
Comments to: email@example.com
Last modified: Mon Nov 27 14:16:32 1995
Copyright © 1995 by
The Geometry Center,
all rights reserved.