Check When a Point is Inside a Mesh

How To Check When Point is Inside a Mesh

This mesh method takes a Vector3 point and checks if it inside the mesh.

Design Outline

  1. Check if point inside or outside of bounding box, when inside continue with following checks;
  2. Cast a ray from the point in the positive and negative x directions;
  3. When there is a hit, move forward from hit point a very small amount along ray direction and recast ray from new point;
  4. Count hits, when zero or an odd number of hits then point is inside mesh and for a even number of hits > 0 non zero then point is outside of mesh.

Design Method

  1. Check bounding box;
var boundInfo = this.getBoundingInfo();
var max = boundInfo.maximum;
var min = boundInfo.minimum;
if(point.x < min.x || point.x > max.x) {
return false;
}
if(point.y < min.y || point.y > max.y) {
return false;
}
if(point.z < min.z || point.z > max.z) {
return false;
}
  1. Use the diameter of the mesh's bounding sphere as the distance to cast the ray
var diameter = 2 * boundInfo.boundingSphere.radius;
ray = new BABYLON.Ray(point, direction, diameter);
  1. Set hit count to zero, while hits occurring increment hit count
var hitCount = 0;
var pickInfo = ray.intersectsMesh(this);
while (pickInfo.hit) {
hitCount++;
pickInfo.pickedPoint.addToRef(direction.scale(0.00000001), point); //move point a small amout in ray direction
ray.origin = point;
pickInfo = ray.intersectsMesh(this);
}
  1. Count hits.
if((hitCount % 2) === 1) {
var pointFound = true;
}
else if ((hitCount % 2) === 0 && hitCount > 0) {
var pointFound = true;
}
return pointFound;

The Whole Function

Returns true if point is inside mesh, false otherwise.

BABYLON.Mesh.prototype.pointIsInside = function (point) {
var boundInfo = this.getBoundingInfo();
var max = boundInfo.maximum;
var min = boundInfo.minimum;
var diameter = 2 * boundInfo.boundingSphere.radius;
if(point.x < min.x || point.x > max.x) {
return false;
}
if(point.y < min.y || point.y > max.y) {
return false;
}
if(point.z < min.z || point.z > max.z) {
return false;
}
var pointFound = false;
var d = 0;
var hitCount = 0;
var gap = 0;
var distance = 0;
var ray = new BABYLON.Ray(BABYLON.Vector3.Zero(), BABYLON.Axis.X, diameter);;
var pickInfo;
var direction = point.clone();
var refPoint = point.clone();
hitCount = 0;
ray.origin = refPoint;
ray.direction = direction;
ray.distance = diameter;
pickInfo = ray.intersectsMesh(this);
while (pickInfo.hit) {
hitCount++;
pickInfo.pickedPoint.addToRef(direction.scale(0.00000001), refPoint);
ray.origin = refPoint;
pickInfo = ray.intersectsMesh(this);
}
if((hitCount % 2) === 1) {
pointFound = true;
}
return pointFound;
};

Playground Example

Generate random points in a volume around a twelve pointed star mesh. Place a sphere at each point and turn it red when inside the star.

Twelve Pointed Star

Further reading

Create Points Inside A Mesh
Helpful code snippet for creating points inside of a mesh in Babylon.js.
Draw Points on a Mesh Surface
Helpful code snippet for drawing points on a mesh surface in Babylon.js.