CODEWITHSUNDEEP
c++mathgraphics3d
mhjlam
mhjlam

Reputation: 160

Finding left/right vertices to a point in a triangle in 3D

Given a triangle in 3D and a point on one of its edges, I want to find out which of the vertices of that edge is to the left of that point, and which is to the right.

Please see the image below:

In this image, vertices v2 and v3 are always positioned as shown. There is also a line segment between v3 and v2. The problem is with vertices v0 and v1, which may be given in a swapped order. I want to find out whether v0 is to the 'left' or 'right' of v3 so that I can enforce v0 to always be to its left and v1 to always be to its right.

Since this problem is in 3D I am not sure how to efficiently compute the relative positions of the vertices. Do I first reduce this to a 2-dimensional problem (and if so, how) or is there another way?

Upvotes: 1

Views: 1081

Answers (3)

Angew is no longer proud of SO
Angew is no longer proud of SO

Reputation: 171127

As clarified in the comments, "left" and "right" (or any other ordering of v0 and v1) depends on some reference. You mentioned you know the triangle's normal vector (call it N) - that can be used for such a reference.

Let's say that the normal vector points towards the viewer in your example image. Then, compute the vector product of v2 - v3 and v0 - v3. This will either point to the same half-space as the normal (meaning v0 is "to the left"), or to the opposite half-space (meaning v0 is "to the right").

Since N is normal to the triangle's plane, a vector v points to the same half-space if the angle between v and N is less than 90 degrees; in other words, if the dot product of v and N is positive.

These together give you the ordering criterion you need.

Upvotes: 1

Raxvan
Raxvan

Reputation: 6505

in 3d the "left" and "right" is dependent to the position of the observer (lets call this position P ). Imagine that you are viewing that triangle from the other side , then the left and right are reversed. So viewing from position P you need to determine if the vertices are clockwise or anti-clockwise.

To do that you can compute this:

N = normalize( cross( v0 - v2, v1 - v2 ) );
PV = normalzie( P - v2 );
if( dot( PV, N ) > 0.0 )
{
    //anticlockwise , so you are viewing the picture like in your drawing, then v0 is on the left of vector v3v2, and v1 is on the right
}
else
{
    //clockwise, v0 is on the right
}

Note that if dot product is almost/or 0 then P is on the same plane as your triangle.

Upvotes: 1

Abhishek Bansal
Abhishek Bansal

Reputation: 12715

Find the cross product of vectors v2-v3 and v1-v2. Deduce the direction from the direction of the product.

Whether the vector is pointing upwards from the plane or downward.

This is if I have correctly understood your definition of right and left.

Upvotes: 0

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