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 ``
  1. Trim
  2. Parametric transformation (an affine function)
  3. Cartesian transformation

To represent other circles and planes, the following items are sequentially applied to each curve and surface (except for NURBS curves and NURBS surfaces):

For example, the following equation shows the application of these modifications:

``PointOnCurve = CartesianTransformation( F(CoefA * Parameter + CoefB) ) ``

  • Parameter value is bounded by two real numbers as follows: IntervalMin <= Parameter <= IntervalMax.
  • CoefA and CoefB are real numbers that define the affine function (the parametric transformation).
  • CartesianTransformation is a spatial transformation.

Where the equation components have the following characteristics:

Topics