New Improvements

Video Atelier's new version of Geometrica lets users perform a wider range of geometrical operations and analysis using Mathematica's list processing, symbolic, and functional programming facilities.

New in Geometrica05

Geometrica05 represents a significant step in elaborating an encyclopedia of geometry and expanding the functions for exact drawing.

• The variables of shape and position are systematically distinguished. This way, it is possible to get an object such as a sphere using the simple syntax Sphere[].
• The treatment of conics and quadrics is fully unified using the algebraic representation of quadrics. Intersections and tests are thus greatly simplified. New constructs (pole, polar, conjugate directions, and others) and metric notions (areas and volumes) are now available.
• General volumes are introduced using parametric points depending on three variables.
• CAD applications have been expanded with new and faster Bezier functions for curves and surfaces and with special objects such as helix, helicoid, and staircases.
• Graphics have also been improved with, in particular, an automatic painting of surfaces.

Features added in Geometrica02

Geometrica02 introduced two major innovations with respect to Geometrica97: the functions had been reorganized to express more clearly the three ways of defining a geometrical object (Cartesian, Euclidean, and parametric) and 3D geometry was introduced.

• In Cartesian or analytical geometry, a point is defined by two or three coordinates and curves and surfaces by their equation which is a unique relation between the coordinates of the points which compose the curve or the surface. Such a definition is noted with the capital letter C at the beginning of the function every time a confusion with another definition may occur. This is the case for CPoint, CLine, CConic or CPlane which denote a Cartesian point, line, conic or plane.
• In Euclidean or synthetic geometry, the point is a primitive and there is a variety of ways of defining geometrical objects. This great variety is very helpful in practical applications and is unified by theorems. Basic functions specifically related to Euclidean geometry start with a capital E such as ELine or ECircle. This way, any confusion with other definitions related to the same object is avoided.
• Parametric or explicit definitions are well adapted for the representation of geometrical objects and for elements of objects such as bound points, segments, arcs or limited surfaces. It is however not unique. The parametric representation chosen in Geometrica is given by the function Pointer. The capital P in PPoint or PRange denotes the parametric definition. A curve or a surface in Geometrica is an object of head PPoint depending on one or two parameters in intervals defined by the option PRange.