Find the intersection of a line with a plane: Difference between revisions
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<pre>intersection at [ 0 -5 5]</pre> |
<pre>intersection at [ 0 -5 5]</pre> |
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=={{header|Sidef}}== |
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{{trans|Perl 6}} |
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<lang ruby>struct Line { |
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P0, # point |
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u⃗, # ray |
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} |
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struct Plane { |
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V0, # point |
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n⃗, # normal |
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} |
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func dot_prod(a, b) { a »*« b -> sum } |
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func line_plane_intersection(𝑳, 𝑷) { |
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var cos = dot_prod(𝑷.n⃗, 𝑳.u⃗) -> |
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|| return 'Vectors are orthogonal' |
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var 𝑊 = (𝑳.P0 »-« 𝑷.V0) |
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var S𝐼 = -(dot_prod(𝑷.n⃗, 𝑊) / cos) |
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𝑊 »+« (𝑳.u⃗ »*» S𝐼) »+« 𝑷.V0 |
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} |
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say ('Intersection at point: ', line_plane_intersection( |
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Line(P0: [0,0,10], u⃗: [0,-1,-1]), |
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Plane(V0: [0,0, 5], n⃗: [0, 0, 1]), |
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))</lang> |
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{{out}} |
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<pre> |
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Intersection at point: [0, -5, 5] |
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</pre> |
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=={{header|zkl}}== |
=={{header|zkl}}== |
Revision as of 18:19, 14 January 2017
Finding the intersection of an infinite ray with a plane in 3D is an important topic in collision detection.
- Task
Find the point of intersection for the infinite ray with direction (0,-1,-1) passing through position (0, 0, 10) with the infinite plane with a normal vector of (0, 0, 1) and which passes through [0, 0, 5].
Perl 6
<lang perl6>class Line {
has $.P0; # point has $.u⃗; # ray
} class Plane {
has $.V0; # point has $.n⃗; # normal
}
sub infix:<∙> ( @a, @b where +@a == +@b ) { [+] @a «*» @b } # dot product
sub line-plane-intersection ($𝑳, $𝑷) {
my $cos = $𝑷.n⃗ ∙ $𝑳.u⃗; # cosine between normal & ray return 'Vectors are orthoganol; no intersection or line within plane' if $cos == 0; my $𝑊 = $𝑳.P0 «-» $𝑷.V0; # difference between P0 and V0 my $S𝐼 = -($𝑷.n⃗ ∙ $𝑊) / $cos; # line segment where it intersets the plane $𝑊 «+» $S𝐼 «*» $𝑳.u⃗ «+» $𝑷.V0; # point where line intersects the plane }
say 'Intersection at point: ', line-plane-intersection(
Line.new( :P0(0,0,10), :u⃗(0,-1,-1) ), Plane.new( :V0(0,0, 5), :n⃗(0, 0, 1) ) );</lang>
- Output:
Intersection at point: (0 -5 5)
Python
Based on the approach at geomalgorithms.com[1]
<lang python>#!/bin/python from __future__ import print_function import numpy as np
def LinePlaneCollision(planeNormal, planePoint, rayDirection, rayPoint, epsilon=1e-6):
ndotu = planeNormal.dot(rayDirection) if abs(ndotu) < epsilon: raise RuntimeError("no intersection or line is within plane")
w = rayPoint - planePoint si = -planeNormal.dot(w) / ndotu Psi = w + si * rayDirection + planePoint return Psi
if __name__=="__main__":
#Define plane
planeNormal = np.array([0, 0, 1])
planePoint = np.array([0, 0, 5]) #Any point on the plane
#Define ray rayDirection = np.array([0, -1, -1]) rayPoint = np.array([0, 0, 10]) #Any point along the ray
Psi = LinePlaneCollision(planeNormal, planePoint, rayDirection, rayPoint) print ("intersection at", Psi)</lang>
- Output:
intersection at [ 0 -5 5]
Sidef
<lang ruby>struct Line {
P0, # point u⃗, # ray
}
struct Plane {
V0, # point n⃗, # normal
}
func dot_prod(a, b) { a »*« b -> sum }
func line_plane_intersection(𝑳, 𝑷) {
var cos = dot_prod(𝑷.n⃗, 𝑳.u⃗) -> || return 'Vectors are orthogonal' var 𝑊 = (𝑳.P0 »-« 𝑷.V0) var S𝐼 = -(dot_prod(𝑷.n⃗, 𝑊) / cos) 𝑊 »+« (𝑳.u⃗ »*» S𝐼) »+« 𝑷.V0
}
say ('Intersection at point: ', line_plane_intersection(
Line(P0: [0,0,10], u⃗: [0,-1,-1]), Plane(V0: [0,0, 5], n⃗: [0, 0, 1]),
))</lang>
- Output:
Intersection at point: [0, -5, 5]
zkl
<lang zkl>class Line { fcn init(pxyz, ray_xyz) { var pt=pxyz, ray=ray_xyz; } } class Plane{ fcn init(pxyz, normal_xyz){ var pt=pxyz, normal=normal_xyz; } }
fcn dotP(a,b){ a.zipWith('*,b).sum(0.0); } # dot product --> x fcn linePlaneIntersection(line,plane){
cos:=dotP(plane.normal,line.ray); # cosine between normal & ray _assert_((not cos.closeTo(0,1e-6)), "Vectors are orthoganol; no intersection or line within plane"); w:=line.pt.zipWith('-,plane.pt); # difference between P0 and V0 si:=-dotP(plane.normal,w)/cos; # line segment where it intersets the plane # point where line intersects the plane: //w.zipWith('+,line.ray.apply('*,si)).zipWith('+,plane.pt); // or w.zipWith('wrap(w,r,pt){ w + r*si + pt },line.ray,plane.pt);
}</lang> <lang zkl>println("Intersection at point: ", linePlaneIntersection(
Line( T(0.0, 0.0, 10.0), T(0.0, -1.0, -1.0) ), Plane(T(0.0, 0.0, 5.0), T(0.0, 0.0, 1.0) ))
);</lang>
- Output:
Intersection at point: L(0,-5,5)