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Curve Type Declarations | |
Surface 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 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):
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.