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Find the intersection of a line with a plane: Difference between revisions
Find the intersection of a line with a plane (view source)
Revision as of 20:45, 7 May 2022
, 2 years ago→{{header|Prolog}}: Adding Prolog
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</pre>
=={{header|Prolog}}==
{{trans|Picat}}
{{works with|GNU Prolog}}
{{works with|SWI Prolog}}
<lang Prolog>
:- initialization(main).
vector_plus(U, V, W) :-
U = p(X1, Y1, Z1),
V = p(X2, Y2, Z2),
X3 is X1 + X2,
Y3 is Y1 + Y2,
Z3 is Z1 + Z2,
W = p(X3, Y3, Z3).
vector_minus(U, V, W) :-
U = p(X1, Y1, Z1),
V = p(X2, Y2, Z2),
X3 is X1 - X2,
Y3 is Y1 - Y2,
Z3 is Z1 - Z2,
W = p(X3, Y3, Z3).
vector_times(U, S, V) :-
U = p(X1, Y1, Z1),
X2 is X1 * S,
Y2 is Y1 * S,
Z2 is Z1 * S,
V = p(X2, Y2, Z2).
vector_dot(U, V, S) :-
U = p(X1, Y1, Z1),
V = p(X2, Y2, Z2),
S is X1 * X2 + Y1 * Y2 + Z1 * Z2.
intersect_point(RayVector, RayPoint, PlaneNormal, PlanePoint, IntersectPoint) :-
vector_minus(RayPoint, PlanePoint, Diff),
vector_dot(Diff, PlaneNormal, Prod1),
vector_dot(RayVector, PlaneNormal, Prod2),
Prod3 is Prod1 / Prod2,
vector_times(RayVector, Prod3, Times),
vector_minus(RayPoint, Times, IntersectPoint).
main :-
RayVector = p(0.0, -1.0, -1.0),
RayPoint = p(0.0, 0.0, 10.0),
PlaneNormal = p(0.0, 0.0, 1.0),
PlanePoint = p(0.0, 0.0, 5.0),
intersect_point(RayVector, RayPoint, PlaneNormal, PlanePoint, p(X, Y, Z)),
format("The ray intersects the plane at (~f, ~f, ~f)\n", [X, Y, Z]).
</lang>
{{out}}
<pre>
The ray intersects the plane at (0.000000, -5.000000, 5.000000)
</pre>
=={{header|Python}}==
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