Arc Spline Curves
Arc Spline Curves are Free-form 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 n-1 splines, one per each adjacent pair of
points. Each spline has two properties: double Curvature and a 3D Normal
vector.
Plane of i-th spline is calculated as plane with i-th
normal vector passing through i-th data point. Only direction
orthogonal to the segment between ends of the spline, which are the i-th and i+1-th
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 i-th 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
interface.
To create an Arc Spline Curve:
1. call to
Create(2) of
IDIObjectGenerator interface with
parameter eType set to eObjTypeArcSplineCurve member of
EObjectType enumeration.
2. Cast or query
IArcSpline3DCurve from IUnknown
returned from the above call.
2. Use ICurveFreeForm
queried from
ArcSpline3DCurve to define set of data
points
3. Use IArray3D
obtained with
IArcSpline3DCurve.GetSplineNormals
to access array of normals one per spline plane
4. Use IArrayNum
obtained with
IArcSpline3DCurve.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
from IArcSpline3DCurve.
Obtained IFrame
interface gives access (via query) to IFrameEx,
which has ToLocal and ToGlobal
methods.
IArcSpline3DCurve.GetSpline method gives access to
IArc
interface implemented by a single spline in the curve. The interface along with
IArcEx
accessed from it allow more detailed local calculations. Results of the
calculations can be converted to/from 3D as described above.
See also: Pipes sample
See also:
Curves Overview, Native Curves
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