Cropping mesh triangles at a given level

I'm trying to slice a mesh off at "sealevel". I can remove tris that are completely below sealevel, but I'm not sure how to alter tris that have one or two verts that cross the sealevel boundary so that they chop at sealevel, as in the picture below.

Any help on this would be gratefully received :) My maths is just failing me.

 // get this object's position
 float height = transform.position.y;
             
 // get the mesh parts
 Vector3[] verts = mesh.vertices;
 List tris = new List(mesh.triangles);
             
 // empty the mesh
 mesh.Clear();
             
 // remove tris
 int count = tris.Count / 3;
 for(int i = count-1; i >= 0; i--)
 {
    Vector3 v1 = verts[tris[i*3 + 0]];
    Vector3 v2 = verts[tris[i*3 + 1]];
    Vector3 v3 = verts[tris[i*3 + 2]];
                 
    // remove tris that are completely below sealevel
    if(v1.y + height <= sealevel && v2.y + height <= sealevel && v3.y + height <= sealevel)
    {
         tris.RemoveRange(i*3,3);
         continue;
    }
 }