Arc Spline Curves
Arc Spline Curves are Freeform curves, which
instead of interpolation between data points are defined by pieces of arcs
(splines) connecting adjacent points. Each spline arc belongs to its own plane (plane
of the spline) passing through the two points and which has normal defined by the user.
When Arc Spline Curve has n data
points it also has n1 splines, one per each adjacent pair of
points. Each spline has two properties: double Curvature and a 3D Normal
vector.
Plane of ith spline is calculated as plane with ith
normal vector passing through ith data point. Only direction
orthogonal to the segment between ends of the spline, which are the ith and i+1th
data points, (called segment of the spline) is important in normal of the spline. That is why during object
initialization normals are adjusted to make directions orthogonal to the
segments and normalised (length modified to 1). Normal vector of a spline must not be parallel to
segment of the spline.
Note that
because each spline has its own plane the resulting curve does not have to be
flat or two dimensional.
When an arc has zero curvature and hence is a straight line there are many
planes which can contain the line. In this case normal for the spline does not
have to be defined.
The curve has parameterization by piecewise normalized natural parameter:
for a given parameter t it corresponds to point with
normalized natural
parameter tLoc = t  i on the ith arc,
where i = floor(t) is the integral part of t. t=2.5,
for example is parameter of the point in the middle of the third arc.
Arc Spline Curves implement
IArcSpline3DCurve_DG
interface.
To create an Arc Spline Curve:
1. Call to IObjectGenerator_DG.Create<IArcSpline3DCurve_DG>() to obtain
IArcSpline3DCurve_DG.
2. Use ICurveFreeForm_DG
queried from IArcSpline3DCurve_DG to define set of data points
3. Use IPointArray_DG
obtained with
IArcSpline3DCurve_DG.GetSplineNormals
to access array of normals one per spline plane
4. Use IArrayDouble_DG
obtained with
IArcSpline3DCurve_DG.GetCurvatureArray
to modify curvature of arcs. By
default, curvature is zero, which represents a straight line.
Spline frames
Each plane of spline has distinctive frame
(frame of the spline) associated
with it: Origin of the frame is located at the first end of the spline arc. x
axis belongs to the plane and directed towards the second end of the spline arc.
y axis belongs to the plane too and defined as orthogonal to x. direction
of z axis coincides with normal of the plane.
Spline frames described above are useful for conversion between two
dimensional coordinates of arcs in spline planes and 3D coordinates. The frames
can be accessed by querying
IFrameArray_DG
from IArcSpline3DCurve_DG.
The obtained IFrame_DG
interfaces have ToLocal and ToGlobal
methods.
IArcSpline3DCurve_DG.GetSpline method gives access to
IArc_DG
interface implemented by a single spline in the curve. The interface allows more detailed local calculations. Results of the
calculations can be converted to/from 3D as described above.
See also:
Curves Overview, Native Curves
