|Curve Type Declarations|
|Surface Type Declarations|
|Geometric Mathematical Operator Type Declarations|
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 the
PointOnCurvefunction 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:
X = Radius * cos(Parameter), Y = R * sin(Parameter), Z = 0
Surfaces have a parametric function that takes two arguments,
Parameter_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):
- 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:
Parametervalue is bounded by two real numbers as follows:
IntervalMin <= Parameter <= IntervalMax.
CoefBare real numbers that define the affine function (the parametric transformation).
CartesianTransformationis a spatial transformation.