The Praxiteles program is an interactive system for modeling and manipulating free-form, or sculptured, curves and surfaces. It provides functions to read, write, convert, generate, interrogate, and process curves and surfaces. The canonical form for all curves and surfaces stored in Praxiteles is the non-uniform rational B-spline, or NURBS. NURBS provide stable and versatile representations for a wide range of geometric shapes. Praxiteles can manipulate NURBS of arbitrary degree. The capabilities of Praxiteles fall into the following four broad categories:

1. Input/Output and Conversion

   2D and 3D lists and grids of points, space curves, surfaces (both untrimmed and trimmed), and surface curves in the IGES Version 5.2 data exchange format. High accuracy conversion between monomial basis parametric curves and surfaces and NURBS curves and surfaces.

2. Geometry Creation

   Creation of point sets, curve and surface fitting by approximation and interpolation, curves on surfaces, offset curves and surfaces, curve extraction from surfaces, faceted surfaces based on Delaunay triangulation, alpha-shape and alpha-hull extraction, and lofted, ruled, and blending surfaces.

3. Interrogation and Inspection

   Wireframe, shaded image, and color-coded curvature contour maps. Curve and surface evaluation. Surface isophotes, reflection lines, geodesics, and lines of principal curvature. Minimum distances between point sets and surfaces, unconstrained and constrained localization for automated inspection, and gross hydrodynamic feature extraction and feature deviation for blade-like surfaces.

4. Geometry Processing

   Approximation with degree elevation or lowering, conversion of surface curves to space curves, knot vector editing, curve and surface subdivision, and fairing to remove undesirable shape oscillations.