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4.4.5.4 Geometric Functions
$FGLNXPL Intersection point of line and plane
$FGLSXSP Intersection point of line segment and sphere
$FGPLPT3 Plane constructed from 3 points
Virtual Machine Reference, Model Customization
Simulation Macro Functions, Geometric Functions
Geometric functions accept and return sequences that define the canonical form of geometrical
entities. The canonical forms currently in use are:
� Point: {x,y,z} coordinates of the point
� Line: {x,y,z,i,j,k} point on line and direction vector of the infinite line
� Plane: {d,i,j,k} distance from origin and normal vector
It is important to note that geometric functions work with sequences and not arrays. The input
arguments to geometric functions can be constructed using the $FSEQ function or the { }
sequence operators. For example, the following are equivalent:
P1=$FSEQ(1,2,3)
P1={1,2,3}
Geometric functions will return a value of $NULL if the geometric entity cannot be created.
The $FGLNXPL Function
result=$FGLNXPL(line,plane)
This function returns an {x,y,z} sequence defining the point at the intersection of an infinite line
and plane. A value of $NULL is returned if the line does not intersect the plane.
The $FGLSXSP Function
result=$FGLSXSP(point1,point2,point3,radius)
This function returns a sequence defining the point(s) of intersection between a line segment and
sphere. The line segment is defined by the start and ending points: point1 and point2. The sphere
is defined by its center point3 and radius. The return sequence has a length of 2, 5 or 8, with
values as follows:
1 Number of intersection points: 0, 1 or 2
2 Segment location with respect to sphere:
–1: Segment is entirely inside the sphere
0: Segment intersects the sphere
1: Segment is entirely outside the sphere
3:5 First intersection point
6:8 Second intersection point (furthest from start of line segment)
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