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Convex_Hull_1
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function convex_hull(points_array) | |
{ | |
// CONVEX HULL USING GRAHAM SCAN | |
var convex_points_array = new Array(); | |
// STEP1 : Find the lowest y and lowest x coord point . Call it P0. P[y_coord_min_index] has the minimum y . | |
var y_coord_max = 0 ; | |
for ( var i = 0 ; i < points_array.length ; i ++) | |
{ | |
if(points_array[i].y>y_coord_max) | |
{ | |
y_coord_max = points_array[i].y; | |
} | |
} | |
var y_coord_min = y_coord_max; | |
var y_coord_min_index = 0 ; | |
for( var i =0 ; i <points_array.length ; i ++) | |
{ | |
if(points_array[i].y<y_coord_min) | |
{ | |
y_coord_min = points_array[i].y; | |
y_coord_min_index = i ; | |
} | |
} | |
// making the first element of array lowest y point | |
var lowest_point = points_array[0]; | |
points_array[0]= points_array[y_coord_min_index]; | |
points_array[y_coord_min_index]= lowest_point; | |
// STEP2 : Sort the array using the angle it makes with P[y_coord_min]. Calculate the angle using slope . // Replace by heap sort to make it more efficient | |
var angle_with_ymin = new Array(); | |
for ( var m = 1 ; m < points_array.length ; m++) | |
{ | |
for ( var i = 1 ; i < points_array.length-1 ; i ++) | |
{ | |
var tan_1 = -(points_array[i].x-points_array[0].x) / (points_array[i].y-points_array[0].y) ; | |
var tan_2 = -(points_array[i+1].x-points_array[0].x) / (points_array[i+1].y-points_array[0].y) ; | |
// what happens when tan_1 or tan_2 becomes infinity . Need to put that point at point_array[1] or point_array[point_array.length -1] . use splice | |
if(points_array[i].y-points_array[0].y==0) | |
{ | |
if(points_array[i].x>points_array[0].x) | |
{ | |
points_array.splice(1,0,points_array[i]); // put this point at 1st array location . | |
points_array.splice(i+1,1); // remove this point from the current array location. | |
} | |
else if (points_array[i].x<points_array[0].x) | |
{ | |
points_array.splice(points_array.length-1,0,points_array[i]); // put this point at 1st array location . | |
points_array.splice(i,1); // remove this point from the current array location. | |
} | |
} | |
else if (tan_1>tan_2) | |
{ | |
var a = points_array[i]; | |
points_array[i]= points_array[i+1]; | |
points_array[i+1]=a; | |
} | |
} | |
} | |
//To connect the last point to the first point . | |
points_array[points_array.length]=points_array[0]; | |
// STEP3 : Push P0, P1, P2 in a stack | |
convex_points_array.push(points_array[0]); | |
convex_points_array.push(points_array[1]); | |
convex_points_array.push(points_array[2]); | |
//convex_points_array.pop() to remove topmost elements in case of left turn | |
// STEP4 : Performs Push and Pop operations on the stack depending on the angle it makes with the last element of the stack (left or right turn) | |
for( var t = 3; t < points_array.length ;t++) | |
{ | |
var cross_product = cross_product_of_vectors(convex_points_array,t); | |
while(cross_product.z <= 0 ) | |
{ | |
convex_points_array.pop(); | |
cross_product = cross_product_of_vectors(convex_points_array,t); | |
} | |
convex_points_array.push(points_array[t]); | |
} | |
function cross_product_of_vectors(convex_points_array,t) | |
{ | |
var a = new THREE.Vector3(convex_points_array[convex_points_array.length-1].x-convex_points_array[convex_points_array.length-2].x, | |
convex_points_array[convex_points_array.length-1].y-convex_points_array[convex_points_array.length-2].y, | |
convex_points_array[convex_points_array.length-1].z-convex_points_array[convex_points_array.length-2].z); | |
//vector connecting the current and last point . | |
var b = new THREE.Vector3(points_array[t].x-convex_points_array[convex_points_array.length-1].x, | |
points_array[t].y-convex_points_array[convex_points_array.length-1].y, | |
points_array[t].z-convex_points_array[convex_points_array.length-1].z); | |
var cross_product = a.cross(b); | |
return cross_product; | |
} | |
return convex_points_array; | |
} |
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// RANDOM POINT GENERATOR GIVEN A RECTANLE BOUNDING | |
function points_for_hull(number_of_points,x_min,x_max,y_min,y_max) | |
{ | |
var points_array_initial = new Array(); | |
for ( var i = 0 ; i < number_of_points ;i++) | |
{ | |
var x_coord_initial = (Math.random() * (x_max-x_min)) + x_min; | |
var y_coord_initial = (Math.random() * (y_max-y_min)) + y_min; | |
var z_coord = 0 ; | |
points_array_initial.push(new THREE.Vector3(Math.floor(x_coord_initial),Math.floor(y_coord_initial),Math.floor(z_coord))); | |
} | |
return points_array_initial; | |
} | |
// DRAWING FUNCTION | |
function recall(convex_hull_arrays,color_mesh,speed,spread,line) | |
{ | |
var points,line ,mesh; | |
var points_array = new Array(); | |
var convex_hull_points = new Array(); | |
// Motion of random points dervied from rendering and gui .Parameters of dependency are spread , progress and speed . | |
for (var t = 0; t<convex_hull_arrays.length;t++) | |
{ | |
var x_coord = convex_hull_arrays[t].x + spread*Math.sin(5*t*progress*Math.PI/speed); | |
var y_coord = convex_hull_arrays[t].y + spread*Math.cos(5*t*progress*Math.PI/speed); | |
var z_coord = convex_hull_arrays[t].z; | |
points_array.push(new THREE.Vector3(Math.floor(x_coord),Math.floor(y_coord),Math.floor(z_coord))); | |
} | |
convex_hull_points = convex_hull(points_array); // Draws convex hull | |
convex_hull_points.pop(); | |
points_array.pop(); | |
// Making Points | |
var geometry_points = new THREE.Geometry(); | |
geometry_points.vertices = points_array; | |
var dotMaterial = new THREE.PointsMaterial( { size: 3, sizeAttenuation: false, color:color_mesh } ); | |
points = new THREE.Points(geometry_points, dotMaterial); | |
//Making mesh | |
var holes = []; | |
var triangles; | |
var geometry_mesh = new THREE.Geometry(); | |
geometry_mesh.vertices = convex_hull_points; | |
triangles = THREE.Shape.Utils.triangulateShape( convex_hull_points, holes ); // in built triangulation to make the mesh . | |
for(var triangle_face = 0 ; triangle_face<triangles.length ; triangle_face++) | |
{ | |
geometry_mesh.faces.push(new THREE.Face3(triangles[triangle_face][0], triangles[triangle_face][1], triangles[triangle_face][2])); | |
} | |
var mesh_material = new THREE.MeshBasicMaterial({color: color_mesh, side: THREE.DoubleSide, opacity: 0.1, transparent: true, depthWrite: false}); | |
mesh = new THREE.Mesh(geometry_mesh,mesh_material); | |
// Draw convex hull lines , only if the GUI says to | |
if(line) | |
{ | |
var line_mesh = new THREE.Geometry(); | |
line_mesh.vertices = convex_hull_points; | |
line_mesh.vertices.push(convex_hull_points[0]); | |
var line_material = new THREE.LineBasicMaterial({color:color_mesh}) | |
line = new THREE.Line(line_mesh,line_material); | |
scene.add(line); | |
} | |
scene.add(mesh); | |
scene.add(points); | |
} | |
// FUNCTION TO REFRESH AT THE START OF EVERY FRAME. | |
function update() | |
{ | |
for(var b = 0 ; b < scene.children.length ; b++) | |
{ | |
scene.children[b].material.dispose(); | |
scene.children[b].geometry.dispose(); | |
scene.remove(scene.children[b]); | |
} | |
} | |
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<html> | |
<!-- | |
CONVEX HULLING PART 1 | |
FINAL PROJECT 200C | |
FALL 2016 | |
Ambika Yadav | |
Developed using the GRAHAM SCAN ALGORITHM TO MAKE CONVEX HULLS FOR N POINTS . | |
IMPLEMENTATION PART 1 : | |
FEATURES : | |
1. ABILITY TO DRAW ADD POINTS USING MOUSE AND SEE HOW CONVEX HULL IS CREATED. | |
2. THE INTERACTIONS USING CONTROL BOX . SPEED, SPREAD, NUMBER OF POINTS. | |
References : | |
1.http://www.math.ucsd.edu/~ronspubs/72_10_convex_hull.pdf | |
2.https://threejs.org/docs/ | |
3.http://stackoverflow.com/questions/13055214/mouse-canvas-x-y-to-three-js-world-x-y-z | |
4.https://www.youtube.com/watch?v=QYrpHE8iDGg | |
--> | |
<head> | |
<title>CONVEX HULL IMPLEMENTATION : MOUSE INTERACTIONS</title> | |
<style> | |
body { | |
margin: 0; | |
} | |
#info { | |
font-family:Monospace; | |
font-size:20px; | |
text-align:center; | |
position: absolute; | |
top: 0px; width: 100%; | |
padding: 5px; | |
color: #ddd; | |
rgba(0,0,0,1); | |
} | |
canvas { | |
background:#ffffff | |
width: 100%; | |
height: 100% | |
} | |
</style> | |
</head> | |
<div id="info"> | |
PART 1 <br/> | |
CONVEX HULL IMPLEMENTATION : MOUSE INTERACTIONS<br/> | |
Ambika Yadav<br/> | |
Implementation of Convex Hull using Graham Scan Algorithm | |
</div> | |
<body> | |
<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/r72/three.min.js"></script> | |
<script src="dat.gui.min.js"></script> | |
<script src="convex_hull.js"></script> | |
<script src="helpers_to_draw_convex.js"></script> | |
<script> | |
var scene = new THREE.Scene(); | |
var camera = new THREE.PerspectiveCamera(80, window.innerWidth / window.innerHeight, 0.1, 6000); | |
var frame_counter = 0; | |
var number_of_points = 5; | |
var number_of_points_range = 200; | |
var progress = 0.0; | |
var trial_variable = 0 ; | |
var x_min = -window.innerWidth/2; | |
var x_max = window.innerWidth/2; | |
var y_min = -window.innerHeight/2; | |
var y_max = window.innerHeight/2; | |
var convex_hull_arrays = points_for_hull(number_of_points,x_min,x_max,y_min,y_max); // making random points to determine convex hull | |
var extra_points = points_for_hull(number_of_points_range+20,x_min,x_max,y_min,y_max); // static extra random points to add if more number of points are desired. | |
var colors = 0xC70039 ; | |
var renderer = new THREE.WebGLRenderer(); | |
renderer.setClearColor( 0x404040); | |
renderer.setSize(window.innerWidth, window.innerHeight); | |
document.body.appendChild(renderer.domElement); | |
/* GUI For the following : | |
BUTTON LIKE | |
1. Option to start and stop animation . | |
2. Switch between line and Mesh | |
3. Switch between manual addition or random addition of points only if one convex hull is present. | |
SLIDER LIKE | |
1. Speed and Spread . | |
*/ | |
var guiControls = new function() | |
{ | |
this.Animation = 1; | |
this.Speed =50; | |
this.Spread =50; | |
this.CameraX = 0; | |
this.CameraY = 0; | |
this.CameraZ = 1000; | |
this.Line_Mesh = 1; | |
this.Points = number_of_points ; | |
} | |
var length_of_num = convex_hull_arrays.length; | |
var datGUI = new dat.GUI(); | |
datGUI.add(guiControls ,'Animation' ,0,1); | |
datGUI.add(guiControls ,'Speed' ,0,100); | |
datGUI.add(guiControls ,'Spread' ,0,300); | |
datGUI.add(guiControls ,'CameraX' ,-500,500); | |
datGUI.add(guiControls ,'CameraY' ,-500,500); | |
datGUI.add(guiControls ,'CameraZ' ,1000,2000); | |
datGUI.add(guiControls ,'Line_Mesh' ,0,1); | |
datGUI.add(guiControls ,'Points',length_of_num,length_of_num+number_of_points_range); | |
var render = function () { | |
requestAnimationFrame(render); | |
camera.position.x = guiControls.CameraX; | |
camera.position.y = guiControls.CameraY; | |
camera.position.z = guiControls.CameraZ; | |
frame_counter += 1; | |
// animate every 5th frame , depending on whether GUI animation variable . | |
if (frame_counter%5 ==0) | |
{ | |
trial_variable +=1; | |
if (guiControls.Animation > 0) | |
{ | |
progress+= 0.05; // animated | |
} | |
else if (guiControls.Animation == 0) | |
{ | |
progress = 0 ; // not animated | |
} | |
update(); // update the scene for next rendering . Mostly removing pre exsisting geometries and textures. | |
var e_points = extra_points.slice(0,guiControls.Points-length_of_num); // get the required number of extra points for the main array holder . | |
convex_hull_arrays = convex_hull_arrays.concat(e_points); // add the extra points to the main array . | |
recall(convex_hull_arrays,colors,Math.floor(guiControls.Speed),Math.floor(guiControls.Spread),Math.floor(guiControls.Line_Mesh)); // draw the scene | |
convex_hull_arrays = convex_hull_arrays.slice(0,length_of_num); // update main array by removing extra points addition for next frame . | |
} | |
renderer.render(scene, camera); | |
}; | |
// MOUSE INTERACTIONS TO ADD POINTS | |
window.addEventListener('click', onMouseDown, false); | |
var mouse = new THREE.Vector2(); | |
function onMouseDown(event) { | |
update(); | |
var vector = new THREE.Vector3(); | |
mouse.x = event.clientX ; | |
mouse.y = event.clientY ; | |
vector.set( | |
( mouse.x / window.innerWidth ) * 2 - 1, | |
- ( mouse.y / window.innerHeight ) * 2 + 1, | |
0.5 ); | |
vector.unproject( camera ); | |
var dir = vector.sub( camera.position ).normalize(); | |
var distance = - camera.position.z / dir.z; | |
var pos = camera.position.clone().add( dir.multiplyScalar( distance ) ); // 2D position of mouse on canvas to 3D position of the same in the 3D scene . | |
convex_hull_arrays.push(pos); // Push the mouse position to main array on mouse click | |
length_of_num +=1; | |
guiControls.Points +=1; | |
convex_hull_arrays = convex_hull_arrays.slice(0,length_of_num); // remove points to get ready for next rendering . | |
} | |
render(); | |
</script> | |
</body> | |
</html> |
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