Collision detection - why not working properly?

PeasyCam library is required.

I'm trying to detect a point-triangle collision using this tutorial: http://www.jeffreythompson.org/collision-detection/tri-point.php . But my sketch is 3d, so I translating a 3d coorinates in 2d using screenX() and screenY(). The problem is that when my mouse is inside of triangle, sometimes the resulting "hit" color is blinking and I have "no hit" message. Can't understand why the collision is not working properly, it must be "hit" all the time my mouse is inside of thiangle. Any suggestions? Thanks.

import peasy.*;
PeasyCam jcam;

ArrayList <Point> points = new ArrayList <Point>();
ArrayList <Triangle> triangles = new ArrayList <Triangle>();

void setup()
{
  size(800, 800, P3D);
  smooth();
  jcam = new PeasyCam(this, 200);

  color tempColore=color(255, 255, 255);

  PVector v1= new PVector(0, 0, 0);
  Point pt1 = new Point(v1, tempColore);
  points.add(pt1);

  PVector v2= new PVector(100, 0, 0);
  Point pt2 = new Point(v2, tempColore);
  points.add(pt2);

  PVector v3= new PVector(0, 100, 0);
  Point pt3 = new Point(v3, tempColore);
  points.add(pt3);

  PVector v4= new PVector(100, 0, 0);
  Point pt4 = new Point(v4, tempColore);
  points.add(pt4);

  PVector v5= new PVector(100, 100, 0);
  Point pt5 = new Point(v5, tempColore);
  points.add(pt5);

  PVector v6= new PVector(0, 100, 0);
  Point pt6 = new Point(v6, tempColore);
  points.add(pt6);


  //triangles initialize
  for (int i=0; i<points.size(); i=i+3)
  {
    Triangle tr = new Triangle(points.get(i).pos, points.get(i+1).pos, points.get(i+2).pos);
    triangles.add(tr);
  }

}

boolean triPoint(float x1, float y1, float x2, float y2, float x3, float y3,float mx, float my)
  {
    // get the area of the triangle
    float areaOrig = abs( (x2-x1)*(y3-y1) - (x3-x1)*(y2-y1) );

    // get the area of 3 triangles made between the point
    // and the corners of the triangle
    float area1 =    abs( (x1-mx)*(y2-my) - (x2-mx)*(y1-my) );
    float area2 =    abs( (x2-mx)*(y3-my) - (x3-mx)*(y2-my) );
    float area3 =    abs( (x3-mx)*(y1-my) - (x1-mx)*(y3-my) );

    // if the sum of the three areas equals the original,
    // we're inside the triangle!
    if (area1 + area2 + area3 == areaOrig)
    {
      return true;
    }
    return false;
  }


void draw()
{
  background(150);

  for (int i = triangles.size ()-1; i >= 0; i--)
  {
    color tempColore=0;

    float ax = screenX(triangles.get(i).A.x,triangles.get(i).A.y);
    float ay = screenY(triangles.get(i).A.x,triangles.get(i).A.y);
    float bx = screenX(triangles.get(i).B.x,triangles.get(i).B.y);
    float by = screenY(triangles.get(i).B.x,triangles.get(i).B.y);
    float cx = screenX(triangles.get(i).C.x,triangles.get(i).C.y);
    float cy = screenY(triangles.get(i).C.x,triangles.get(i).C.y);
    float mx = mouseX;
    float my = mouseY;

    boolean hit = triPoint(ax,ay,bx,by,cx,cy,mx,my);

    if(hit==true)
    {
      tempColore = #A57066;
      println("hit");
    }
    else
    {
      tempColore = #CEBE9A;
      println("no hit");
    }
    triangles.get(i).display(tempColore);
  }


  for (int i = points.size ()-1; i >= 0; i--)
  {
    points.get(i).display();
  }

}


class Point
{
  PVector pos;
  color colore;


  Point(PVector posIn, color coloreIn)
  {
    pos = posIn;
    colore=coloreIn;
  }

  void display()
  {
    colorMode(RGB);
    noStroke();
    fill(colore);
    pushMatrix();
    translate(pos.x,pos.y,pos.z);
    box(1);
    popMatrix();
  }
}


class Triangle
{
  PVector A, B, C;
  color colore;

  Triangle (PVector Ain, PVector Bin, PVector Cin)
  {
    A=Ain;
    B=Bin;
    C=Cin;
  }

  void display(color coloreIn)
  {
    colore = coloreIn;
    fill(colore);
    beginShape(TRIANGLE);
    stroke(255,20);
    strokeWeight(2);
    vertex(A.x,A.y,A.z);
    vertex(B.x,B.y,B.z);
    vertex(C.x,C.y,C.z);
    endShape();
  }
}