Find the intersection of a line with a plane: Difference between revisions

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 =={{header|REXX}}==
+===version 1===
 This program does NOT handle the case when the line is parallel to or within the plane.
 <lang rexx>/* REXX */
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 Say 'Intersection: P('||x','y','z')'</lang>
 {{out}}
 <pre>0*x + 0*y + 1*z = 5
 Intersection: P(0,-5,5)</pre>
+===version 2===
+handle the case that the line is parallel to the plane or lies withi it.
+<br>Beautification of plane and line definitions is yet tbd.
+<lang rexx>/*REXX*/
+Parse Value '1 2 3' With n.1 n.2 n.3
+Parse Value '3 3 3' With p.1 p.2 p.3
+Parse Value '0 2 4' With a.1 a.2 a.3
+Parse Value '3 2 1' With v.1 v.2 v.3
+a=n.1
+b=n.2
+c=n.3
+d=n.1*p.1+n.2*p.2+n.3*p.3  /* Parameter form of the plane */
+pd=''
+If a<>0 Then pd=a'*x'
+If b<>0 Then pd=pd '+' b'*y'
+If c<>0 Then pd=pd '+' c'*z'
+Say 'Plane''s definition:' pd '=' d
+ip=0
+Do i=1 To 3
+  ip=ip+n.i*v.i
+  dd=n.1*a.1+n.2*a.2+n.3*a.3
+  End
+If ip=0 Then Do
+  If dd=d Then
+    Say 'Line is part of the plane'
+  Else
+    Say 'Line is parallel to the plane'
+  Exit
+  End
+t=(d-(a*a.1+b*a.2+c*a.3))/(a*v.1+b*v.2+c*v.3)
+x=a.1+t*v.1
+y=a.2+t*v.2
+z=a.3+t*v.3
+ld='x='a.1; If v.1<>0 Then ld=ld'+t*'v.1
+ld=ld '; y='a.2; If v.2<>0 Then ld=ld'+t*'v.2
+ld=ld '; z='a.3; If v.3<>0 Then ld=ld'+t*'v.3
+Say 'Line definition:' ld
+Say 'Intersection: P('||x','y','z')'</lang>
+{{out}}
+<pre>Plane's definition: 1*x + 2*y + 3*z = 18
+Line definition: x=0+t*3 ; y=2+t*2 ; z=4+t*1
+Intersection: P(0.6,2.4,4.2)</pre>
 =={{header|Sidef}}==