// Cloned by Brendan on 28 Oct 2019 from World "Complex World" by Starter user
// Please leave this clone trail here.
/**
// MCM Foundations of AI
// Stucent Name: Brendan Bonner
// Code Submission for A* assignment
// Description: AB Starter World with addtional functions whenever the logicalMoveEnemy() function is called.
// The A* function uses a standalone grid made up of objects containg the A data elements, includeing the hueristic,
// distance, whether diagonal avaiable or not and the parent.
// The sets are managed by a sorted array containing the open set, while the closed set is based on a flag
// in the A* array.
// The visuals and the sound have been replaced by blue boxes and a click that gets slightly louder and faster
// when the enemy and agent are close to each other.
**/
// ==== Starter World ===============================================================================================
// (c) Ancient Brain Ltd. All rights reserved.
// This code is only for use on the Ancient Brain site.
// This code may be freely copied and edited by anyone on the Ancient Brain site.
// This code may not be copied, re-published or used on any other website.
// To include a run of this code on another website, see the "Embed code" links provided on the Ancient Brain site.
// ==================================================================================================================
// =============================================================================================
// More complex starter World
// 3d-effect Maze World (really a 2-D problem)
// Movement is on a semi-visible grid of squares
//
// This more complex World shows:
// - Skybox
// - Internal maze (randomly drawn each time)
// - Enemy actively chases agent
// - Music/audio
// - 2D world (clone this and set show3d = false)
// - User keyboard control (clone this and comment out Mind actions to see)
// =============================================================================================
// =============================================================================================
// Scoring:
// Bad steps = steps where enemy is within one step of agent.
// Good steps = steps where enemy is further away.
// Score = good steps as percentage of all steps.
//
// There are situations where agent is trapped and cannot move.
// If this happens, you score zero.
// =============================================================================================
// ===================================================================================================================
// === Start of tweaker's box ========================================================================================
// ===================================================================================================================
// The easiest things to modify are in this box.
// You should be able to change things in this box without being a JavaScript programmer.
// Go ahead and change some of these. What's the worst that could happen?
AB.clockTick = 100; // Speed of run: Step every n milliseconds. Default 100.
AB.maxSteps = 1000; // Length of run: Maximum length of run in steps. Default 1000.
AB.screenshotStep = 50; // Take screenshot on this step. (All resources should have finished loading.) Default 50.
//---- global constants: -------------------------------------------------------
const show3d = true; // Switch between 3d and 2d view (both using Three.js)
const TEXTURE_WALL = '/uploads/brendanb/box_tron1.jpg';
const TEXTURE_MAZE = '/uploads/brendanb/box_tron1.jpg';
const TEXTURE_AGENT = '/uploads/brendanb/pacload.png';
const TEXTURE_ENEMY = '/uploads/starter/ghost.3.png';
//const TEXTURE_ENEMY = '/uploads/brendan/1570456293.png';
const gridsize = 20; // number of squares along side of world NB: Pacman was 28
const NOBOXES = Math.trunc((gridsize * gridsize) / 10);
// density of maze - number of internal boxes
// (bug) use trunc or can get a non-integer
const squaresize = 20; // size of square in pixels
const MAXPOS = gridsize * squaresize; // length of one side in pixels
const SKYCOLOR = 0xddffdd; // a number, not a string
const startRadiusConst = MAXPOS * 0.8; // distance from centre to start the camera at
const maxRadiusConst = MAXPOS * 10; // maximum distance from camera we will render things
//--- change ABWorld defaults: -------------------------------
ABHandler.MAXCAMERAPOS = maxRadiusConst;
ABHandler.GROUNDZERO = true; // "ground" exists at altitude zero
//--- skybox: -------------------------------
// skybox is a collection of 6 files
// x,y,z positive and negative faces have to be in certain order in the array
// https://threejs.org/docs/#api/en/loaders/CubeTextureLoader
const SKYBOX_ARRAY = [
"/uploads/brendanb/radial_gradient_blue.png",
"/uploads/brendanb/radial_gradient_blue.png",
"/uploads/brendanb/radial_gradient_lightblue.png",
"/uploads/brendanb/radial_gradient_darkblue.png",
"/uploads/brendanb/radial_gradient_blue.png",
"/uploads/brendanb/radial_gradient_blue.png",
];
//--- Mind can pick one of these actions -----------------
const ACTION_LEFT = 0;
const ACTION_RIGHT = 1;
const ACTION_UP = 2;
const ACTION_DOWN = 3;
const ACTION_STAYSTILL = 4;
// in initial view, (smaller-larger) on i axis is aligned with (left-right)
// in initial view, (smaller-larger) on j axis is aligned with (away from you - towards you)
// contents of a grid square
const GRID_BLANK = 0;
const GRID_WALL = 1;
const GRID_MAZE = 2;
const GRID_ENEMY = 10; // added information if grid contains the actors, rather than checking globals
const GRID_AGENT = 20; // added information if grid contains the actors, rather than checking globals
var BOXHEIGHT; // 3d or 2d box height
var GRID = new Array(gridsize); // can query GRID about whether squares are occupied, will in fact be initialised as a 2D array
var theagent, theenemy;
var wall_texture, agent_texture, enemy_texture, maze_texture;
// enemy and agent position on squares
var ei, ej, ai, aj;
// added new class to make it easier to pass coordinates
class coordinates {
constructor(i, j) {
this.i = i;
this.j = j;
}
}
var start = new coordinates();
var target = new coordinates();
var badsteps;
var goodsteps;
const MAX_OPENSET = gridsize * gridsize;
// diagonal option enabled significantly increases performance of the enemy bot
// and allows access to shorter routes
var diagonal = true;
// if you want to see A* in action
const PROOF = true;
var proofArray = [];
function loadResources() // asynchronous file loads - call initScene() when all finished
{
var loader1 = new THREE.TextureLoader();
var loader2 = new THREE.TextureLoader();
var loader3 = new THREE.TextureLoader();
var loader4 = new THREE.TextureLoader();
loader1.load(TEXTURE_WALL, function (thetexture) {
thetexture.minFilter = THREE.LinearFilter;
wall_texture = thetexture;
if (asynchFinished()) initScene(); // if all file loads have returned
});
loader2.load(TEXTURE_AGENT, function (thetexture) {
thetexture.minFilter = THREE.LinearFilter;
agent_texture = thetexture;
if (asynchFinished()) initScene();
});
loader3.load(TEXTURE_ENEMY, function (thetexture) {
thetexture.minFilter = THREE.LinearFilter;
enemy_texture = thetexture;
if (asynchFinished()) initScene();
});
loader4.load(TEXTURE_MAZE, function (thetexture) {
thetexture.minFilter = THREE.LinearFilter;
maze_texture = thetexture;
if (asynchFinished()) initScene();
});
}
function asynchFinished() // all file loads returned
{
if (wall_texture && agent_texture && enemy_texture && maze_texture) return true;
else return false;
}
//--- grid system -------------------------------------------------------------------------------
// my numbering is 0 to gridsize-1
function occupied(i, j) // is this square occupied
{
// Added check to ensure that occupied square is in grid.
if (i <= gridsize && j <= gridsize &&
i >= 0 && j >= 0) {
switch (GRID[i][j]) {
case GRID_WALL:
case GRID_MAZE:
case GRID_ENEMY:
case GRID_AGENT:
return true;
default:
return false;
}
}
// off the grid
return true;
}
function iswall(i, j) // is this square occupied
{
switch (GRID[i][j]) {
case GRID_WALL:
case GRID_MAZE:
return true;
default:
return false;
}
}
// translate my (i,j) grid coordinates to three.js (x,y,z) coordinates
// logically, coordinates are: y=0, x and z all positive (no negative)
// logically my dimensions are all positive 0 to MAXPOS
// to centre everything on origin, subtract (MAXPOS/2) from all dimensions
function translate(i, j) {
var v = new THREE.Vector3();
v.y = -squaresize;
v.x = (i * squaresize) - (MAXPOS / 2);
v.z = (j * squaresize) - (MAXPOS / 2);
return v;
}
function initScene() // all file loads have returned
{
var i, j, shape, thecube;
// set up GRID as 2D array
for (i = 0; i < gridsize; i++)
GRID[i] = new Array(gridsize);
// set up walls
for (i = 0; i < gridsize; i++)
for (j = 0; j < gridsize; j++)
if ((i === 0) || (i == gridsize - 1) || (j === 0) || (j == gridsize - 1)) {
GRID[i][j] = GRID_WALL;
shape = new THREE.BoxGeometry(squaresize, BOXHEIGHT, squaresize);
thecube = new THREE.Mesh(shape);
thecube.material = new THREE.MeshBasicMaterial({
map: wall_texture
});
thecube.position.copy(translate(i, j)); // translate my (i,j) grid coordinates to three.js (x,y,z) coordinates
ABWorld.scene.add(thecube);
}
else
GRID[i][j] = GRID_BLANK;
// set up maze
for (var c = 1; c <= NOBOXES; c++) {
i = AB.randomIntAtoB(1, gridsize - 2); // inner squares are 1 to gridsize-2
j = AB.randomIntAtoB(1, gridsize - 2);
GRID[i][j] = GRID_MAZE;
shape = new THREE.BoxGeometry(squaresize, BOXHEIGHT, squaresize);
thecube = new THREE.Mesh(shape);
thecube.material = new THREE.MeshBasicMaterial({
map: maze_texture
});
thecube.position.copy(translate(i, j)); // translate my (i,j) grid coordinates to three.js (x,y,z) coordinates
ABWorld.scene.add(thecube);
}
// set up enemy
// start in random location
do {
i = AB.randomIntAtoB(1, gridsize - 2);
j = AB.randomIntAtoB(1, gridsize - 2);
}
while (occupied(i, j)); // search for empty square
ei = i;
ej = j;
// shape = new THREE.BoxGeometry ( squaresize, BOXHEIGHT, squaresize );
shape = new THREE.SphereGeometry(squaresize / 2, BOXHEIGHT / 2, squaresize / 2);
theenemy = new THREE.Mesh(shape);
theenemy.material = new THREE.MeshBasicMaterial({
map: enemy_texture
});
ABWorld.scene.add(theenemy);
drawEnemy();
// set up agent
// start in random location
do {
i = AB.randomIntAtoB(1, gridsize - 2);
j = AB.randomIntAtoB(1, gridsize - 2);
}
while (occupied(i, j)); // search for empty square
ai = i;
aj = j;
shape = new THREE.SphereGeometry(squaresize / 2, BOXHEIGHT / 2, squaresize / 2);
theagent = new THREE.Mesh(shape);
theagent.material = new THREE.MeshBasicMaterial({
map: agent_texture
});
ABWorld.scene.add(theagent);
drawAgent();
GRID[ai][aj] = GRID_AGENT;
GRID[ei][ej] = GRID_ENEMY;
// finally skybox
// setting up skybox is simple
// just pass it array of 6 URLs and it does the asych load
ABWorld.scene.background = new THREE.CubeTextureLoader().load(SKYBOX_ARRAY, function () {
ABWorld.render();
AB.removeLoading();
AB.runReady = true; // start the run loop
});
}
// --- draw moving objects -----------------------------------
function drawEnemy() // given ei, ej, draw it
{
theenemy.position.copy(translate(ei, ej)); // translate my (i,j) grid coordinates to three.js (x,y,z) coordinates
ABWorld.lookat.copy(theenemy.position); // if camera moving, look back at where the enemy is
}
function drawAgent() // given ai, aj, draw it
{
theagent.position.copy(translate(ai, aj)); // translate my (i,j) grid coordinates to three.js (x,y,z) coordinates
ABWorld.follow.copy(theagent.position); // follow vector = agent position (for camera following agent)
}
// A* Support Functions
// This is the set of new A* functions, the first is to create a spot location data type
// this contains the location, A* paramenters, as well as pointer array to the neighbours
function gridSpot(i, j) {
// Location
this.i = i;
this.j = j;
// f, g, and h values for A*
this.f = 0;
this.g = 0;
this.h = 0;
// Neighbors
this.neighbors = [];
// Where did I come from?
this.parent = undefined;
this.closed = false; // are we in closed set
// Figure out who my neighbors are
this.addNeighbors = function () {
var i = this.i;
var j = this.j;
if (i < gridsize - 1) this.neighbors.push(aStarGrid[i + 1][j]);
if (i > 0) this.neighbors.push(aStarGrid[i - 1][j]);
if (j < gridsize - 1) this.neighbors.push(aStarGrid[i][j + 1]);
if (j > 0) this.neighbors.push(aStarGrid[i][j - 1]);
if (diagonal)
// diagonals are also neighbours:
{
if (i > 0 && j > 0) this.neighbors.push(aStarGrid[i - 1][j - 1]);
if (i < gridsize - 1 && j > 0) this.neighbors.push(aStarGrid[i + 1][j - 1]);
if (i > 0 && j < gridsize - 1) this.neighbors.push(aStarGrid[i - 1][j + 1]);
if (i < gridsize - 1 && j < gridsize - 1) this.neighbors.push(aStarGrid[i + 1][j + 1]);
}
};
}
// Create Global A* Grid Array
var aStarGrid = [];
// initialise a astar grid in parallel to main "GRID"
function aStarInit() {
var i, j;
// create the aStarGrid
for (i = 0; i < gridsize; i++) {
aStarGrid[i] = [];
for (j = 0; j < gridsize; j++) {
aStarGrid[i][j] = new gridSpot(i, j);
// console.log("A* Initialise: " + i + ", " + j);
}
}
for (i = 0; i < gridsize; i++) {
for (j = 0; j < gridsize; j++) {
aStarGrid[i][j].addNeighbors();
}
}
console.info("A* Initialise: Complete");
}
// A* function that returns the next position in the as a coordinate (i,j)
function aStar(grid, start, target) {
// Initialize both open and closed list
var openSet = [];
var child;
var completed = false;
var targetNode = aStarGrid[target.i][target.j]; // define the target
var startNode = aStarGrid[start.i][start.j]; // define the target
var currentNode;
var nextMove = new coordinates(start.i, start.j);
// Push the start node onto the openlist to start the analysis
openSet.push(startNode); // push startnode onto Openset
// clearup previous search - need to be more efficient with memory
console.info("cleaning up previous results");
for (i = 0; i < gridsize; i++) {
for (j = 0; j < gridsize; j++) {
currentNode = aStarGrid[i][j];
currentNode.f = currentNode.h = currentNode.g = 0;
currentNode.closed = false;
currentNode.parent = null;
}
}
// loop through all of the a* openlist or until target or error found
while ((openSet.length > 0) && !completed) {
if (openSet.length > MAX_OPENSET) {
// Prevent Memory Issues when debugging OpenSet
console.error("there is a problem with the openset, bail out!");
completed = true;
return nextMove;
}
// Sort the list based on the f value
openSet.sort((a, b) => (a.f > b.f) ? 1 : -1); //sort set by f
currentNode = openSet.shift(); // shift the first entry of OpenSet
currentNode.closed = true; // quick check for closed
console.info("Current: " + currentNode.i + ", " + currentNode.j + " - (O/C) is " + openSet.length);
if (currentNode == targetNode) {
// Proof array
if (PROOF){
proofArray.push(targetNode);
}
// Found Target - now backtrack to get next node
while (currentNode.parent != startNode) {
// if we require proof, push store path
if (PROOF){
proofArray.push(currentNode);
}
// backtrack to return the next move
currentNode = currentNode.parent;
}
completed = true;
// Proof array
if (PROOF){
proofArray.push(startNode);
}
} else {
// if we are not at target, build openSet
for (n = 0; n < currentNode.neighbors.length; n++) {
// for each of the neighbours, calculate the children
child = currentNode.neighbors[n];
// check if in closedSet or occupied
if (child.closed) {
// move to next child
} else if (iswall(child.i, child.j)) {
// closedSet.push(child);
child.closed = true;
} else {
// calculate values and add to openSet
if ((child.i == currentNode.i) || (child.j == currentNode.j))
child.g = currentNode.g + 10; // if not diagonal, use 10 as metric
else
child.g = currentNode.g + 14; // rougly the square path if diagonal
child.h = aStarHeuristics(child, targetNode);
child.f = child.g + child.h;
child.parent = currentNode;
if (openSet.indexOf(child) < 0) {
// if not in openSet
openSet.push(child);
}
} // check if closedSet
} // loop through neighbours
} //check if we have reached target
}
nextMove.i = currentNode.i;
nextMove.j = currentNode.j;
console.info("returning form a*: ");
return nextMove;
// end of openSet, and not completed.
}
function aStarHeuristics(start, end) {
if (diagonal)
return (Math.pow(start.i - end.i, 2) + Math.pow((start.j - end.j), 2));
else
return (Math.abs(start.i - start.i) + Math.abs(start.j - end.j));
}
// --- take actions -----------------------------------
function moveLogicalEnemy() {
// move towards agent
// put some randomness in so it won't get stuck with barriers
var i, j;
start.i = ei;
start.j = ej;
target.i = ai;
target.j = aj;
// call the a* algorithm to provide the best path between targets (GRID not necessary, as globals used)
bestPath = aStar(GRID, start, target);
// Only Move if the space is empty
if (!occupied(bestPath.i, bestPath.j)) {
GRID[ei][ej] = GRID_BLANK; // Store Agents Position
// move enemy to new position
ei = bestPath.i;
ej = bestPath.j;
GRID[ei][ej] = GRID_ENEMY;
}
console.info("enemy moving to : " + ei + "," + ej)
}
function moveLogicalAgent(a) // this is called by the infrastructure that gets action a from the Mind
{
var i = ai;
var j = aj;
// depending on the agent move, spin the sphere
switch (a) {
case ACTION_LEFT:
i--;
theagent.rotation.y = 0;
break;
case ACTION_RIGHT:
i++;
theagent.rotation.y = -1;
break;
case ACTION_UP:
j++;
theagent.rotation.y = -2;
break;
case ACTION_DOWN:
j--;
theagent.rotation.y = 2;
break;
default:
break;
}
if (!occupied(i, j)) {
GRID[ai][aj] = GRID_BLANK; // Clear Agents Previous Position
ai = i;
aj = j;
GRID[ai][aj] = GRID_AGENT; // Store Agents Position
}
}
// --- key handling --------------------------------------------------------------------------------------
// This is hard to see while the Mind is also moving the agent:
// AB.mind.getAction() and AB.world.takeAction() are constantly running in a loop at the same time
// have to turn off Mind actions to really see user key control
// we will handle these keys:
var OURKEYS = [37, 38, 39, 40];
function ourKeys(event) {
return (OURKEYS.includes(event.keyCode));
}
function keyHandler(event) {
if (!AB.runReady) return true; // not ready yet
// if not one of our special keys, send it to default key handling:
if (!ourKeys(event)) return true;
// else handle key and prevent default handling:
if (event.keyCode == 37) moveLogicalAgent(ACTION_LEFT);
if (event.keyCode == 38) moveLogicalAgent(ACTION_DOWN);
if (event.keyCode == 39) moveLogicalAgent(ACTION_RIGHT);
if (event.keyCode == 40) moveLogicalAgent(ACTION_UP);
// when the World is embedded in an iframe in a page, we want arrow key events handled by World and not passed up to parent
event.stopPropagation();
event.preventDefault();
return false;
}
// --- score: -----------------------------------
function badstep() // is the enemy within one square of the agent
{
if ((Math.abs(ei - ai) < 2) && (Math.abs(ej - aj) < 2)) return true;
else return false;
}
function agentBlocked() // agent is blocked on all sides, run over
{
return (occupied(ai - 1, aj) &&
occupied(ai + 1, aj) &&
occupied(ai, aj + 1) &&
occupied(ai, aj - 1));
}
function updateStatusBefore(a)
// this is called before anyone has moved on this step, agent has just proposed an action
// update status to show old state and proposed move
{
var x = AB.world.getState();
AB.msg("Step: " + AB.step + "<br>x = (" + x.toString() + ")");
// <br>a = (" + a + ")<br>");
}
function updateStatusAfter() // agent and enemy have moved, can calculate score
{
// new state after both have moved
var y = AB.world.getState();
var score = (goodsteps / AB.step) * 100;
//AB.msg("y = (" + y.toString() + ") <br>" +
AB.msg(" Bad steps: " + badsteps +
" Good steps: " + goodsteps +
" Score: " + score.toFixed(2) + "% ", 2);
}
function playSound() // is the enemy within one square of the agent
{
// load click sound & based on distance, speed up and change volume
var sound = new Audio('/uploads/brendanb/click.ogg');
var soundRate = 1 + (((Math.abs(ei - ai)) + Math.abs((ej - aj))) / (gridsize));
console.log("PlaybackRate: " + soundRate);
sound.playbackRate = soundRate;
sound.volume = 1 / soundRate;
if (Math.abs(ei - ai) + Math.abs(ej - aj) < 2) {
sound.playbackRate = soundRate * 2;
sound.play();
}
sound.play();
}
// Debugging using AB was not the friendliest, so created function to debug using node.js
// prints a 2D text grid containing elements
function consoleGrid() {
var gridString = "";
for (var i = gridsize - 1; i >= 0; i--) {
gridString = "";
for (var j = 0; j < gridsize; j++) {
switch (GRID[i][j]) {
case GRID_WALL:
gridString = gridString + ".";
break;
case GRID_MAZE:
gridString = gridString + "+";
break;
case GRID_AGENT:
gridString = gridString + "A";
break;
case GRID_ENEMY:
gridString = gridString + "E";
break;
default:
gridString = gridString + " ";
break;
}
}
console.log(gridString);
}
start.i = ei;
start.j = ej;
target.i = ai;
target.j = aj;
// console.log("Heuristic: " + aStarHeuristics(start, target));
}
AB.world.newRun = function () {
AB.loadingScreen();
AB.runReady = false;
badsteps = 0;
goodsteps = 0;
aStarInit();
if (show3d) {
BOXHEIGHT = squaresize;
ABWorld.init3d(startRadiusConst, maxRadiusConst, SKYCOLOR);
} else {
BOXHEIGHT = 1;
ABWorld.init2d(startRadiusConst, maxRadiusConst, SKYCOLOR);
}
loadResources(); // aynch file loads
// calls initScene() when it returns
// Initiailise A* Array
document.onkeydown = keyHandler;
};
AB.world.getState = function () {
var x = [ai, aj, ei, ej];
return (x);
};
var enemyAngle = 0;
var cameraAngle;
AB.world.takeAction = function (a) {
updateStatusBefore(a); // show status line before moves
console.info("-: Agent: " + ai + "," + aj + " Enemy: " + ei + "," + ej);
moveLogicalAgent(a);
if ((AB.step % 2) === 0) { // slow the enemy down to every nth step
playSound();
moveLogicalEnemy();
}
console.info("+: Agent: " + ai + "," + aj + " Enemy: " + ei + "," + ej);
// consoleGrid();
if (badstep()) badsteps++;
else goodsteps++;
// Spin the enemy around every turn
enemyAngle += 0.2;
theenemy.rotation.y = enemyAngle;
// theagent.rotation.y -= 0.2;
drawAgent();
drawEnemy();
updateStatusAfter(); // show status line after moves
// enemy will agressively pin agen to wall, if score reaches 10%, generally pointless (and
// and exponentially increasing time to claim run over
if (agentBlocked() || ((goodsteps / AB.step) < 0.10)) // if agent blocked in, run over
{
AB.abortRun = true;
goodsteps = 0; // you score zero as far as database is concerned
// musicPause();
// soundAlarm();
}
// Proof array
if (PROOF){
drawProof();
}
};
AB.world.endRun = function () {
// musicPause();
if (AB.abortRun) AB.msg(" <br> <font color=red> <B> Agent trapped.</B> </font> ", 3);
else AB.msg(" <br> <font color=green> <B> Run over. </B> </font> ", 3);
};
AB.world.getScore = function () {
// only called at end - do not use AB.step because it may have just incremented past AB.maxSteps
var s = (goodsteps / AB.maxSteps) * 100; // float like 93.4372778
var x = Math.round(s * 100); // 9344
return (x / 100); // 93.44
};
// Draw the A* algortihm on the screen
// Needs more work in terms of the path changing and colours, but good enough
// To slow down the path and see it.
var lastProofLine = [];
var previousLine;
function drawProof()
{
var point1; // local "Spots"
var point2; // local "Spots"
var line;
var oldMaterial = new THREE.LineBasicMaterial({color:0x222222, linewidth:1 });
// clear old line
if (lastProofLine.length > 0){
line = lastProofLine.shift();
lastProofLine[0].material = oldMaterial;
if (previousLine)
{
ABWorld.scene.remove(previousLine);
}
ABWorld.scene.add(line);
previousLine = line;
}
var mat = new THREE.LineBasicMaterial({color:'blue', linewidth:2 });
var geo = new THREE.Geometry();
// in the proofArray
for ( i = proofArray.length; i > 1; i--)
{
point1 = proofArray.shift();
// geo.vertices.push( translate(point1.i, point1.j) );
if (point1.parent){
point1 = point1.parent;
// drawline between proofArrayPoints
geo.vertices.push( translate(point1.i, point1.j) );
console.log("Line between " + point1.i + "," + point1.j + " and ")
}
else {
geo.vertices.push( translate(point1.i, point1.j) );
console.log("Line between " + point1.i + "," + point1.j + " and ")
}
}
line = new THREE.Line(geo, mat);
// line.castShadow = true;
lastProofLine.push(line);
ABWorld.scene.add(line);
}