I am currently attempting to make a navigation mesh for our 2D top down game, which is a multiplayer game using Node.js as the server communication. At the moment, I have implemented A* over an obstacle hardnessmap, which is awfully slow and laggy at times when we test our game on Heroku. I have been trying to find an algorithm to automatically generate the navmesh after map creation, instead of me having to do this manually. I am currently attempting to use Delaunay's Triangulation Divide and Conquer algorithm, but I am running into some issues. I have already asked a question on StackOverflow and am not getting many suggestions and help from it, so I figured I would come here. Is there another algorithm that might be better to use for the navmesh generation in comparison to Deluanay's Triangulation? My current implementation seems extremely buggy during the merge step and I cannot find the error. I have checked over the code countless times, comparing it to the description of the algorithm from http://www.geom.uiuc.edu/~samuelp/del_project.html.
My current code is this:
class MapNode
{
constructor(x, y)
{
this.position = new Vector(x, y);
this.neighbors = [];
}
distance(n)
{
return this.position.distance(n.position);
}
inNeighbor(n)
{
for (let i = 0; i < this.neighbors.length; i++)
{
if (this.neighbors[i] === n)
return true;
}
return false;
}
addNeighbor(n)
{
this.neighbors = this.neighbors.filter((node) => node != n);
this.neighbors.push(n);
}
addNeighbors(arr)
{
let self = this;
arr.forEach((n) => self.neighbors.push(n));
}
removeNeighbor(n)
{
this.neighbors = this.neighbors.filter((neighbor) => neighbor != n);
}
}
class Triangle
{
constructor(p1, p2, p3)
{
this.p1 = p1;
this.p2 = p2;
this.p3 = p3;
this.neighbors = [];
}
addNeighbors(n)
{
this.neighbors.push(n);
}
}
function genSubMat(matrix, ignoreCol)
{
let r = [];
for (let i = 0; i < matrix.length - 1; i++)
{
r.push([]);
for (let j = 0; j < matrix[0].length; j++)
{
if (j != ignoreCol)
r[i].push(matrix[i + 1][j]);
}
}
return r;
}
function determinantSqMat(matrix)
{
if (matrix.length != matrix[0].length) return false;
if (matrix.length === 2) return matrix[0][0] * matrix[1][1] - matrix[1][0] * matrix[0][1];
let det = 0;
for (let i = 0; i < matrix.length; i++)
{
let r = genSubMat(matrix, i);
let tmp = matrix[0][i] * determinantSqMat(r);
if (i % 2 == 0)
det += tmp;
else
det -= tmp;
}
return -det;
}
// if d is in the circle formed by points a, b, and c, return > 0
// d is on circle, return 0
// d is outside of circle, return < 0
function inCircle(a, b, c, d)
{
let arr = [a, b, c, d];
let mat = [
[],
[],
[],
[]
];
for (let i = 0; i < arr.length; i++)
{
mat[i][0] = 1;
mat[i][1] = arr[i].position.x;
mat[i][2] = arr[i].position.y;
mat[i][3] = arr[i].position.x * arr[i].position.x + arr[i].position.y * arr[i].position.y;
}
return determinantSqMat(mat);
}
function walkable(from, to, hardnessMap)
{
let diff = new Vector(to.x - from.x, to.y - from.y);
if (Math.abs(diff.x) > Math.abs(diff.y)) diff.scale(Math.abs(1 / diff.x));
else diff.scale(Math.abs(1 / diff.y));
let current = new Vector(from.x + diff.x, from.y + diff.y);
while (Math.round(current.x) != to.x || Math.round(current.y) != to.y)
{
if (hardnessMap[Math.floor(current.y)][Math.floor(current.x)] === 1)
return false;
current.x += diff.x;
current.y += diff.y;
}
return true;
}
function getLowest(nodes)
{
let lowest = nodes[0];
for (let i = 1; i < nodes.length; i++)
{
if (nodes[i].position.y < lowest.position.y)
lowest = nodes[i];
}
return lowest;
}
// returns the angle between 2 vectors, if cw is true, then return clockwise angle between,
// else return the ccw angle between. b is the "hinge" point
function angleBetween(a, b, c, cw)
{
let ba = new Vector(a.position.x - b.position.x, a.position.y - b.position.y);
let bc = new Vector(c.position.x - b.position.x, c.position.y - b.position.y);
let v0 = new Vector(0, 1);
let angleBA = v0.angleBetween(ba) * 180 / Math.PI;
if (angleBA < 0) angleBA += 360;
let angleBC = v0.angleBetween(bc) * 180 / Math.PI;
if (angleBC < 0) angleBC += 360;
let smallest = Math.min(angleBA, angleBC);
let largest = Math.max(angleBA, angleBC);
let angle = largest - smallest;
return (cw) ? angle : 360 - angle;
}
function sortSmallestAngle(a, b, list, cw)
{
list.sort((m, n) =>
{
let vab = new Vector(a.position.x - b.position.x, a.position.y - b.position.y);
let vmb = new Vector(m.position.x - b.position.x, m.position.y - b.position.y);
let vnb = new Vector(n.position.x - b.position.x, n.position.y - b.position.y);
if (cw)
return vab.angleBetween(vmb, cw) - vab.angleBetween(vnb, cw);
else
return vab.angleBetween(vnb, cw) - vab.angleBetween(vmb, cw);
});
}
// a is in list, b is in the other list
function getPotential(a, b, list, cw)
{
sortSmallestAngle(b, a, list, cw);
for (let i = 0; i < list.length - 1; i++)
{
let angle = angleBetween(b, a, list[i], cw);
if (angle > 180) return false;
else if (inCircle(a, b, list[i], list[i + 1]) <= 0)
return list[i];
else
{
a.removeNeighbor(list[i]);
list[i].removeNeighbor(a);
}
}
let potential = list[list.length - 1];
if (potential)
{
let angle = angleBetween(a, b, potential, cw);
if (angle > 180) return false;
return potential;
}
return false;
}
function merge(leftNodes, rightNodes, leftBase, rightBase, hardnessMap)
{
leftBase.addNeighbor(rightBase);
rightBase.addNeighbor(leftBase);
let newLeft = leftNodes.filter((n) => n != leftBase);
let newRight = rightNodes.filter((n) => n != rightBase);
let potentialLeft = getPotential(leftBase, rightBase, newLeft, false);
let potentialRight = getPotential(rightBase, leftBase, newRight, true);
if (!potentialLeft && !potentialRight) return;
else if (potentialLeft && !potentialRight)
merge(newLeft, newRight, potentialLeft, rightBase, hardnessMap);
else if (potentialRight && !potentialLeft)
merge(newLeft, newRight, leftBase, potentialRight, hardnessMap);
else
{
if (inCircle(leftBase, rightBase, potentialLeft, potentialRight) <= 0)
merge(newLeft, newRight, potentialLeft, rightBase, hardnessMap);
if (inCircle(leftBase, rightBase, potentialRight, potentialLeft) <= 0)
merge(newLeft, newRight, leftBase, potentialRight, hardnessMap);
}
}
// divide and conquer algorithm
function delaunay(nodes, hardnessMap)
{
if (nodes.length <= 3)
{
for (let i = 0; i < nodes.length; i++)
for (let j = 0; j < nodes.length; j++)
if (i != j)
nodes[i].addNeighbor(nodes[j]);
return nodes;
}
else
{
nodes.sort((a, b) =>
{
let tmp = a.position.x - b.position.x;
if (tmp === 0) return b.position.y - a.position.y;
return tmp;
});
let l = nodes.length;
let leftNodes;
let rightNodes;
if (l === 4)
{
leftNodes = delaunay(nodes.slice(0, 3), hardnessMap);
rightNodes = delaunay(nodes.slice(3, 4), hardnessMap);
}
else
{
leftNodes = delaunay(nodes.slice(0, Math.floor(nodes.length / 2)), hardnessMap);
rightNodes = delaunay(nodes.slice(Math.floor(nodes.length / 2), nodes.length), hardnessMap);
}
let leftBase = getLowest(leftNodes);
let rightBase = getLowest(rightNodes);
merge(leftNodes, rightNodes, leftBase, rightBase, hardnessMap);
console.log("=============================MergeComplete================================");
return nodes;
}
}
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