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Triangle/Ray Intersection

version 1.7 (309 KB) by Jaroslaw Tuszynski
Fast vectorized triangle/ray intersection algorithm


Updated 18 May 2018

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Ray/triangle intersection using the algorithm proposed by Möller and
Trumbore (1997), implemented as highly vectorized MATLAB code.
The algorithm can work with one and two sided surfaces, as well as, with
infinite lines, rays (lines bounded on one side) and segments (lines bounded on
both sides).
Input (all arrays in in Nx3, where N is number of vertices or rays):
orig : ray's origin
dir : ray's direction
vert0, vert1, vert2: vertices of the triangle
Intersect - boolean array of length N
t - distance from the ray origin to the intersection point in |dir|
u,v - barycentric coordinates of the intersection point units
xcoor - carthesian coordinates of the intersection point
In addition PointInsideVolume is 3D equivalent to 2D inpolygon function and can test if
array of points is inside or outside any volume defined by the surface grid.

Cite As

Jaroslaw Tuszynski (2021). Triangle/Ray Intersection (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (34)

Francesco Sturla

Hi! does anyone know a code that overcomes the limit discussed above (total number of triangles different than total ray number)?

Berk Bural

It doesn't work when total triangle number in mesh is different than total ray number. Therefore it has limited usage.


Emile Talon

Hi, I am trying to use this code in order to obtain thickness information of my 3D object.
I select a triangle on my mesh, and then place the origin of the ray along the normal to the baricentrum of my selected triangle.
The ray is then going to intersect my mesh first in the defined triangle and then in a second one.
How could I get the second triangle as an output of the function? And therefore the distance between this two traingles (and so the thickness of my object).
Any help would be really appreciated.

Yasaman Moghadamnia

Works perfectly for a ray! What sort of modification would you suggest for a line segment?

Bernard Beitz

There seems to be some confusion about the many-to-many case. If you have n rays and triangles, the function will test the k-th ray against the k-th triangle, but it will not test the k-th ray against every n triangles. So there are n intersection tests, not n^2. That's why you need to have as many rays as triangles in the many-to-many case. The one-to-many case is just treated as a special case of many-to-many where all n rays/triangles happen to be the identical.


Ludovic Breton

Hi, I too have the same question about the many rays/many faces. It doesn't seem to work, or maybe am I using it the wrong way. I'm trying to find whether the rays intersect a triangle on a segment going from the origin to each of the triangles in the scene.
Here's the code :
%% cube definition


%% Computation
origin=[2 3 2];
[intersect, t,u,v,xcoord] = TriangleRayIntersection(origin, direction, p0, p1, p2, 'lineType', 'segment','planeType','two sided','fullReturn', true);

%% we draw the figure
patch('Faces',Faces,'Vertices', Vertices,'FaceColor','m','FaceAlpha',0.8)

text(CG(:,1)+.2*N(:,1)/norm(N(:,1)), CG(:,2)+.2*N(:,2)/norm(N(:,2)), CG(:,3)+.2*N(:,3)/norm(N(:,3)), num2str((1:12)'));

By changing the scalar (e.g. 1 or 0.99) in front of "direction" I get either only ones or zeros for the value of intersect.

Jun W

Hi, in your first example Line 86-100 in 'TriangleRayIntersection_tutorial.m', you get 4 intersections, but 43 distances 't'. Aren't we supposed to get only 4 distances for the 4 intersections?

John Huss

I also agree with the previous comments. I can't get the many faces/many rays version to work. I have a complex stl surface consisting of approximately 25,000 triangles and a set of 400 rays that all start inside the model and go outwards. It says only 13 of them intersect, which is not correct. Any tips? I might try to loop through all rays one at a time instead.

Stuart Scollay

Hi, thanks for the code. I want to second Andre's comment. I too am having trouble getting the many rays, many faces implementation working.

Andre Paixao

Hi, Jaroslaw. Thanks for this very useful tool! I'm trying to find the intersection of many (M) rays in many faces of closed triangular meshes made of N>400000 vertices (with M<N).
The tool works great if I search for one ray at a time in a for loop, though it takes quite a while to go through all my rays.
To make it faster, I've been trying to run many rays at once but the function returns empty all the time (no intersections detected), which is weird. And yes, I'm using repmat to clone the rays until M=N and all the input are in Nx3 format.
However, it works well If I consider the rays passing through the centre of each triangle, as in your example.
I see comments from other users also struggling with the many rays-many faces option.
Can you help? Thks

Philip Kunz

Fabricio Castro

Jaroslaw Tuszynski

Reply to jack' green: I think you should be able to find much simpler codes to do 2D case. Or just write one to do line/line intersection for ray intersection with each line segment and see if the intersection point is between each segment end points.

jack' green

Hi, Jaroslaw. Thanks for provding such a cool tool. It works well on my computer. Just wonder is it possible to apply it to a purely 2D (in-plane) case where the triangles all become segments?

Yanjun Han

many faces / many rays intersection, the return value 'flag'? Should it be a matrix but actual it is not.

Yanjun Han

Hello, Can anyone help me! Now I have a series of path points, and I want project them on a specified mesh surface along the specified direction, for example dir=(0,0,1). For every path point, I can iterate over all the triangular meshes to get the corresponding projection points,but this is too time-consuming. Can I use a faster method?
I want to get the projection point of all the points in the fixed direction on the triangular mesh surface. How can I use the 'many faces / many rays intersection' ?

Ander Biguri

Does the many rays-many faces case only work with Nfaces==Nrays? If so, is there any specific reason for implementing that specific case?

Yumin Sun

Actually for multiple faces and multiple rays, one should remember you need to repmat origin, if all origins are same.

Leonardo Colavitti


To do your program better I suggests
1) Add description about use option FullReturn. It shold be '1' but not 'true' for example.
2) Add in initialize default output string
If xcoor not initialized than if no intersections error appear with params count.

Jamie Heather

Nice vectorised implementation with handy options for choosing between ray/line/segments and handling numerical precision issues - thanks!

Jaroslaw Tuszynski

Reply to Murat: You might have to look into using "border" parameter. If it does not work can you construct a scenario that demonstrates the issue and email it to me


Hi, the code is working well but it sometimes cannot handle with large incident angles. When the incident angle is around 90, it ignores triangles. Could you correct it?

Ehsan golk


I'm having trouble with the many rays, many faces option. Lets say I have 11 faces and 5 rays. What resizing of the inputs needs to be done? Do I need to repmat all arrays to be of size 55x3?

Based on what I can tell it can handle:
- one ray, many faces
- many rays, one face
- many rays, many faces (but # of faces = # of rays)

But I think I am just missing something here.

Jaroslaw Tuszynski

Reply to Nick: In many rays and many triangle case you still test for intersection of prearranged pairs and the return value informs you which ray/triangle pair intersected


Very useful but when considering many rays and many triangles is there a way to find which ray has intersected which triangle?


Amilcar Torres

Excellent.. Really helpful!!!


Looks great. Downloaded and will try it later.

Jaroslaw Tuszynski

Re to Anton Semechko: This is a low level function which can be called with one ray and many faces, many faces and one ray or many faces and rays. It is quite simple to apply repmat function to the inputs.

Anton Semechko

why does the number of rays have to equal the number of faces? that's so inconvenient

MATLAB Release Compatibility
Created with R2017b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: Ray/Triangle Intersection

Inspired: in_polyhedron,

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