14.14.8 Orthogonal projection in space:
projection
See Section
13.15.8
for projections in the plane.
The
projection
command creates a projection.
projection
takes one mandatory argument and one optional argument:
O
, a geometrix object.
Optionally,
P
, a point.
projection(
O
)
returns a new command which projects points onto
O
.
projection(
O
,
P
)
returns and draws the projection of
P
onto
O
.
Examples
Input:
P:=point(0,0,1);
p1:= projection(line(point(0,0,0), point(1,1,1)))
coordinates(p1(P))
Output:
⎡
⎢
⎢
⎣
1
3
,
1
3
,
1
3
⎤
⎥
⎥
⎦
which is the projection of (0,0,1) onto the line.
Input:
coordinates(projection(plane(point(1,0,0),point(0,0,0),point(1,1,1)),point(0,0,1)))
Output:
⎡
⎢
⎢
⎣
0,
1
2
,
1
2
⎤
⎥
⎥
⎦
which is the projection of the point (0,0,1) onto the plane.