Geometry Type Declarations

Detailed Description

group a3d_geometry_types

In general, each curve and surface has a parametric function that describes its minimal natural definition.

Version

2.0

  • 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:

  • 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.