Modules  
Curve Type Declarations  
Surface Type Declarations  
Geometric Mathematical Operator Type Declarations  
Detailed Description
 Version
 2.0
In general, each curve and surface has a parametric function that describes its minimal natural definition.

Curves have a parametric function that takes a single argument,
Parameter
), which is a real number. The result of thePointOnCurve
function is a 3D cartesian point represented by three real numbers.PointOnCurve = F(Parameter)
For example, the following parametric function provides the minimal natural definition of a circle on the Z=0 plane, centered in (0,0,0), and having the radius:
R
.X = Radius * cos(Parameter), Y = R * sin(Parameter), Z = 0

Surfaces have a parametric function that takes two arguments,
Parameter_U
andParameter_V
, which are real numbers. The result of the function (PointOnSurface
) is a 3D cartesian point represented by three real numbers.PointOnSurface = F(Parameter_U, Parameter_V)
For example, the following parametric function provides the minimal natural definition of the Z=0 plane:
X = Parameter_U, Y = Parameter_V, Z = 0
To represent other circles and planes, the following items are sequentially applied to each curve and surface (except for NURBS curves and NURBS surfaces):
 Trim
 Parametric transformation (an affine function)
 Cartesian transformation
For example, the following equation shows the application of these modifications:
PointOnCurve = CartesianTransformation( F(CoefA * Parameter + CoefB) )
Where the equation components have the following characteristics:
Parameter
value is bounded by two real numbers as follows:IntervalMin <= Parameter <= IntervalMax
.CoefA
andCoefB
are real numbers that define the affine function (the parametric transformation).CartesianTransformation
is a spatial transformation.