Geometry Type Declarations

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 the``PointOnCurve``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``and``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):

  1. Trim
  2. Parametric transformation (an affine function)
  3. 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.
  • CoefAand``CoefB``are real numbers that define the affine function (the parametric transformation).
  • CartesianTransformationis a spatial transformation.

Topics