Triangulation does not preserve original edges

[zzfoo]

In the above image, the two neighbor triangles (where the red arrow points) are not fully connected, while all other neighbor triangles are.

(please let me know if I didn't make myself clear.)

[zzfoo]

@mikelmaron @hjanetzek @zugaldia @incanus @springmeyer
sorry to disturb, but this issue is important to me. can any of you guys answers it for me? thanks in advance

[finscn]

This issue troubles me too.

[finscn]

@mikelmaron @hjanetzek @zugaldia @incanus @springmeyer @zzfoo

I changed pointInTriangle() to

// check if a point lies within a convex triangle
function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {
    return (cx - px) * (ay - py) - (ax - px) * (cy - py) > 0 &&
           (ax - px) * (by - py) - (bx - px) * (ay - py) > 0 &&
           (bx - px) * (cy - py) - (cx - px) * (by - py) > 0;
}

change >= to > .

It could solve this problem ， but I don't know whether it is the best way.

My test case :

var testPoints = [
    [
        [10, 10], [300, 10], [10, 300]
    ],
    [
        [50, 50], [100, 50], [50, 100]
    ],
    [
        [150, 50], [200, 50], [150, 100]
    ],
];

Just replace the testPoints in viz.js

.

[mourner]

Is this behavior causing any particular issues? It seems like a result I would expect.

[finscn]

@mourner

Current result of earcut is :

I would expect is :

I think the result of Polygon triangulation should be a mesh， One border could most belong to two triangles.

[finscn]

If one border shared to many triangles ， the triangulation will lost the value in the real-world（e.g. ： NavMesh Pathfinding , Mesh Transform )

NavMesh Pathfinding:

Mesh Transform:

Maybe earcut would not be used in those use case , but it's the base of Polygon triangulation,
I hope it could support this feature.

[finscn]

And , there is result of current version earcut :

You look the triangles below two rect holes ， they are correct，
But the triangles above two rect holes are wrong.

[finscn]

@mourner , there is a document about Triangulation :
https://www.geometrictools.com/Documentation/TriangulationByEarClipping.pdf
It said that :

The key point : "Each vertex shares exactly two edges. The only place where edges are allowed to intersect are at the vertices."

---

In the famous & classic book "Geometric Tools for Computer Graphics" ， there is similar claim :

The key point : "The edges are only allowed to intersect at the vertices. "

.

In fact, by definition, the result of current version earcut in my test case is not Triangulation at all.

.
I'm a Chinese guy , with bad english , I hope you could understand me.
If my words is impolite ， I hope you could forgive me . It's not because I'm impolite , just because my poor english , I don't know how to express my opinion in the right way.

And the most words above are translated by google.

.

[mourner]

I see the issue now — thanks for the explanation. I don't have immediate suggestions to fix this — this problem might stem from the original tactics from https://www.cosy.sbg.ac.at/~held/projects/triang/triang.html to deal with degenerate cases by filtering out collinear points at various stages of the algorithm. Needs investigation.

[finscn]

Thank you , @mourner .

And there is a better test case :

//  replace the testPoints in viz.js.
var testPoints = [
    [
        [10, 10],
        [300, 10],
        [300, 300],
        [10, 300]
    ],
    [
        [50, 50],
        [100, 50],
        [100, 100],
        [50, 100]
    ],

    [
        [150, 50],
        [200, 50],
        [200, 100],
        [150, 100]
    ],

    [
        [50, 150],
        [100, 150],
        [100, 200],
        [50, 200]
    ],

    [
        [150, 150],
        [200, 150],
        [200, 200],
        [150, 200]
    ],
];

My solution can't solve this bug in this test case, So I think this test case is more representative.

[finscn]

@mourner , I think the bug at eliminateHoles().

The node linkList that return value of eliminateHoles in my test case is this :

I think the correct one should be like this :

And , whatever , 10 ,11 ,12 will be in one line , the filterPoints will remove 11.