cur_conic - Geometric procedure

Creates a curve


Description

Creates a rational cubic parametric segmented curve that interpolates two or more positions and tangents. cur_conic does not care about the length of tangents, only the direction. For every segment a Midpoint or P-value must also be specified. A Midpoint is just any intermediate position while a P-value is a scalar float that controls the "fullness" of the segment.

If tangents are chosen in such a way that they intersect and form a nice triangle with the segment chord as baseline then the resulting segment becomes a classical plane conic segment (quadric rational). If the tangents are chosen in such a way that inflexion or twist is forced the resulting segment becomes a cubic rational generalized (3D-) conic.

A type parameter is used to control whether to project positions and tangents onto the XY-plane of the active coordinate system or not before creating the curve.

Syntax

cur_conic(id, type, p1, tp1, MP, p2, tp2,MPn,pn,tpn:attributes);

REF	id;
STRING	type*4;
VECTOR	p1;
VECTOR	tp1;
VECTOR/FLOAT	MP;
VECTOR	p2;
VECTOR	tp2;
VECTOR/FLOAT	MPn;
VECTOR	pn;
VECTOR	tpn;

Principal parameters

id	- Local identity
type	- The string "FREE" or "PROJ"
p1	- First position (beginning of first segment)
tp1	- First tangent position
MP	- Midpoint or P-value for first segment
p2	- Second position (end of first segment)
tp2	- Second tangent position

Optional parameters

MPn	- Additional Midpoints or P-values, one per additional segment
pn	- Additional positions, one per additional segment
tpn	- Additional tangent positions, one per additional segment

Attributes

PEN	- Pen or colour number
LEVEL	- Level number
BLANK	- Visible(0) or invisible(1)
CFONT	- Solid(0), dashed(1) or centerline(2)
CDASHL	- Dashlength
WIDTH	- Linewidth

Example

cur_conic(#1,"PROJ", vec(0, 0), vec(1, 1), 0.4,
vec(5, 0), vec(6, -1), vec(8, -1),
vec(10, 0), vec(11, 1));

Creates a conic curve with two segments. First segment has a P-value of 0.4 and second segment is defined by a Midpoint position = (8,-1).

Comments

A true 3D spacecurve can only be defined in a 3D module with type set to "FREE". In a 2D module or with type set to "PROJ" a planar curve with torsion = 0 is always created even if defining positions are not in the same plane.

cur_conic is intended for curves with relatively few defining positions, maximum = 50. To interpolate large number of positions use cur_conarr.

P-values should be positive values in the range 0 <= P < 0.85. A value of zero gives a straight line segment and the cooresponding tangent positions are left without notice. Watch out for kinks !