Find the intersection point of a plane and ray

Question

Given a ray with a point and a vector and a plane with a point and a normal vector to the plane. You have to find the intersection point of the plane and the ray..

So your job if you choose to accept is to write a shortest function that will do the job.

RULES:
The submission must be a complete program
And that's all

INPUT FORMAT:
x y z rx ry rz //gives the ray point and the ray vectors
x y z px py pz //gives the point on the plane and the vector normal to plane

OUTPUT FORMAT:
(x,y,z) //intersection point

Test Case:
2 3 4 0.577 0.577 0.577
7 1 3 1 0 0
(7,8,9)

The shortest codes in bytes win.

References: https://www.siggraph.org/education/materials/HyperGraph/raytrace/rayplane_intersection.htm thanks orlp for the reference

Answer 1

Mathematica, 20 bytes

Takes 4 lists as input. The dot product operator . has precedence over multiplication and division, so no more parentheses are needed.

#+#2(#3-#).#4/#2.#4&

Readable version:

x + v (r - x).n / v.n

where the arguments in order are x (ray point), v (ray direction), r (plane point), n (plane normal).

Answer 2

Perl, 107 bytes

Tested for all test cases (i.e. not tested at all) Run with each input number on its own line on STDIN

perl -M5.010 plane.pl
0
1
0
0
0
1
3
3
1
0
0
1
^D

plane.pl:

#!/usr/bin/perl
$$_=<>for a..l;say$a+($t=($j*($g-$a)+$k*($h-$b)+$l*($i-$c))/($j*$d+$k*$e+$l*$f))*$d,$",$b+$t*$e,$",$c+$t*$f

This kind of problem is absolutely not a good match for perlgolf. Perl lacks vector operations and uses too many $s

Answer 3

Haskell, 137 157/102 bytes

Follows both input and output pattern. Program reads input from stdin. 157 bytes.

z=zipWith
main=do
[(p,r),(l,n)]<-map(splitAt 3.map read.words).lines<$>getContents
print$(\[a,b,c]->(a,b,c))$z(+)p$map(*(sum(z(*)n(z(-)l p))/sum(z(*)n r)))r

With an input file that has format [[x,y,z],[rx,ry,rz],[x,y,z],[px,py,pz]] and output of format [x,y,z] (102 bytes):

z=zipWith
main=do
[p,r,l,n]<-read<$>getContents
print$z(+)p$map(*(sum(z(*)n(z(-)l p))/sum(z(*)n r)))r

Answer 4

R, 88 bytes

x=scan()
v=scan()
r=scan()
n=scan()
C=cat
C("(");C(x+v*sum((r-x)*n)/sum(v*n),sep=", ");C(")")

Adapted from the Mathematica answer. Takes the following values from stdin, x (ray point), v (ray direction), r (plane point), n (plane normal). Outputs (7, 8, 9) for the test case.

Answer 5

JavaScript (ES6), 157 bytes

This could probably be shorter. The test case is subject to rounding errors, but otherwise it respects the challenge.

P=prompt;[a,b,c,d,e,f,g,h,i,j,k,l]=(P()+' '+P()).split` `.map(e=>+e);alert('('+(a+(t=(j*(g-a)+k*(h-b)+l*(i-c))/(j*d+k*e+l*f))*d)+','+(b+t*e)+','+(c+t*f)+')')

Answer 6

JavaScript (ES6), 93 bytes

(a,b,c,A,B,C,x,y,z,X,Y,Z)=>`(${t=X*(x-a)+Y*(y-b)+Z*(z-c)/(X*A+Y*B+Z*C),[a+t*A,b+t*B,c+t*C]})`

f=
(a,b,c,A,B,C,x,y,z,X,Y,Z)=>`(${t=X*(x-a)+Y*(y-b)+Z*(z-c)/(X*A+Y*B+Z*C),[a+t*A,b+t*B,c+t*C]})`

console.log(f(2, 3, 4, 0.577350269, 0.577350269, 0.577350269, 7, 1, 3, 1, 0, 0))