lemmings/decomp.js

670 lines
21 KiB
JavaScript

!function(e){"object"==typeof exports?module.exports=e():"function"==typeof define&&define.amd?define(e):"undefined"!=typeof window?window.decomp=e():"undefined"!=typeof global?global.decomp=e():"undefined"!=typeof self&&(self.decomp=e())}(function(){var define,module,exports;
return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);throw new Error("Cannot find module '"+o+"'")}var f=n[o]={exports:{}};t[o][0].call(f.exports,function(e){var n=t[o][1][e];return s(n?n:e)},f,f.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
var Scalar = require('./Scalar');
module.exports = Line;
/**
* Container for line-related functions
* @class Line
*/
function Line(){};
/**
* Compute the intersection between two lines.
* @static
* @method lineInt
* @param {Array} l1 Line vector 1
* @param {Array} l2 Line vector 2
* @param {Number} precision Precision to use when checking if the lines are parallel
* @return {Array} The intersection point.
*/
Line.lineInt = function(l1,l2,precision){
precision = precision || 0;
var i = [0,0]; // point
var a1, b1, c1, a2, b2, c2, det; // scalars
a1 = l1[1][1] - l1[0][1];
b1 = l1[0][0] - l1[1][0];
c1 = a1 * l1[0][0] + b1 * l1[0][1];
a2 = l2[1][1] - l2[0][1];
b2 = l2[0][0] - l2[1][0];
c2 = a2 * l2[0][0] + b2 * l2[0][1];
det = a1 * b2 - a2*b1;
if (!Scalar.eq(det, 0, precision)) { // lines are not parallel
i[0] = (b2 * c1 - b1 * c2) / det;
i[1] = (a1 * c2 - a2 * c1) / det;
}
return i;
};
/**
* Checks if two line segments intersects.
* @method segmentsIntersect
* @param {Array} p1 The start vertex of the first line segment.
* @param {Array} p2 The end vertex of the first line segment.
* @param {Array} q1 The start vertex of the second line segment.
* @param {Array} q2 The end vertex of the second line segment.
* @return {Boolean} True if the two line segments intersect
*/
Line.segmentsIntersect = function(p1, p2, q1, q2){
var dx = p2[0] - p1[0];
var dy = p2[1] - p1[1];
var da = q2[0] - q1[0];
var db = q2[1] - q1[1];
// segments are parallel
if(da*dy - db*dx == 0)
return false;
var s = (dx * (q1[1] - p1[1]) + dy * (p1[0] - q1[0])) / (da * dy - db * dx)
var t = (da * (p1[1] - q1[1]) + db * (q1[0] - p1[0])) / (db * dx - da * dy)
return (s>=0 && s<=1 && t>=0 && t<=1);
};
},{"./Scalar":4}],2:[function(require,module,exports){
module.exports = Point;
/**
* Point related functions
* @class Point
*/
function Point(){};
/**
* Get the area of a triangle spanned by the three given points. Note that the area will be negative if the points are not given in counter-clockwise order.
* @static
* @method area
* @param {Array} a
* @param {Array} b
* @param {Array} c
* @return {Number}
*/
Point.area = function(a,b,c){
return (((b[0] - a[0])*(c[1] - a[1]))-((c[0] - a[0])*(b[1] - a[1])));
};
Point.left = function(a,b,c){
return Point.area(a,b,c) > 0;
};
Point.leftOn = function(a,b,c) {
return Point.area(a, b, c) >= 0;
};
Point.right = function(a,b,c) {
return Point.area(a, b, c) < 0;
};
Point.rightOn = function(a,b,c) {
return Point.area(a, b, c) <= 0;
};
var tmpPoint1 = [],
tmpPoint2 = [];
/**
* Check if three points are collinear
* @method collinear
* @param {Array} a
* @param {Array} b
* @param {Array} c
* @param {Number} [thresholdAngle=0] Threshold angle to use when comparing the vectors. The function will return true if the angle between the resulting vectors is less than this value. Use zero for max precision.
* @return {Boolean}
*/
Point.collinear = function(a,b,c,thresholdAngle) {
if(!thresholdAngle)
return Point.area(a, b, c) == 0;
else {
var ab = tmpPoint1,
bc = tmpPoint2;
ab[0] = b[0]-a[0];
ab[1] = b[1]-a[1];
bc[0] = c[0]-b[0];
bc[1] = c[1]-b[1];
var dot = ab[0]*bc[0] + ab[1]*bc[1],
magA = Math.sqrt(ab[0]*ab[0] + ab[1]*ab[1]),
magB = Math.sqrt(bc[0]*bc[0] + bc[1]*bc[1]),
angle = Math.acos(dot/(magA*magB));
return angle < thresholdAngle;
}
};
Point.sqdist = function(a,b){
var dx = b[0] - a[0];
var dy = b[1] - a[1];
return dx * dx + dy * dy;
};
},{}],3:[function(require,module,exports){
var Line = require("./Line")
, Point = require("./Point")
, Scalar = require("./Scalar")
module.exports = Polygon;
/**
* Polygon class.
* @class Polygon
* @constructor
*/
function Polygon(){
/**
* Vertices that this polygon consists of. An array of array of numbers, example: [[0,0],[1,0],..]
* @property vertices
* @type {Array}
*/
this.vertices = [];
}
/**
* Get a vertex at position i. It does not matter if i is out of bounds, this function will just cycle.
* @method at
* @param {Number} i
* @return {Array}
*/
Polygon.prototype.at = function(i){
var v = this.vertices,
s = v.length;
return v[i < 0 ? i % s + s : i % s];
};
/**
* Get first vertex
* @method first
* @return {Array}
*/
Polygon.prototype.first = function(){
return this.vertices[0];
};
/**
* Get last vertex
* @method last
* @return {Array}
*/
Polygon.prototype.last = function(){
return this.vertices[this.vertices.length-1];
};
/**
* Clear the polygon data
* @method clear
* @return {Array}
*/
Polygon.prototype.clear = function(){
this.vertices.length = 0;
};
/**
* Append points "from" to "to"-1 from an other polygon "poly" onto this one.
* @method append
* @param {Polygon} poly The polygon to get points from.
* @param {Number} from The vertex index in "poly".
* @param {Number} to The end vertex index in "poly". Note that this vertex is NOT included when appending.
* @return {Array}
*/
Polygon.prototype.append = function(poly,from,to){
if(typeof(from) == "undefined") throw new Error("From is not given!");
if(typeof(to) == "undefined") throw new Error("To is not given!");
if(to-1 < from) throw new Error("lol1");
if(to > poly.vertices.length) throw new Error("lol2");
if(from < 0) throw new Error("lol3");
for(var i=from; i<to; i++){
this.vertices.push(poly.vertices[i]);
}
};
/**
* Make sure that the polygon vertices are ordered counter-clockwise.
* @method makeCCW
*/
Polygon.prototype.makeCCW = function(){
var br = 0,
v = this.vertices;
// find bottom right point
for (var i = 1; i < this.vertices.length; ++i) {
if (v[i][1] < v[br][1] || (v[i][1] == v[br][1] && v[i][0] > v[br][0])) {
br = i;
}
}
// reverse poly if clockwise
if (!Point.left(this.at(br - 1), this.at(br), this.at(br + 1))) {
this.reverse();
}
};
/**
* Reverse the vertices in the polygon
* @method reverse
*/
Polygon.prototype.reverse = function(){
var tmp = [];
for(var i=0, N=this.vertices.length; i!==N; i++){
tmp.push(this.vertices.pop());
}
this.vertices = tmp;
};
/**
* Check if a point in the polygon is a reflex point
* @method isReflex
* @param {Number} i
* @return {Boolean}
*/
Polygon.prototype.isReflex = function(i){
return Point.right(this.at(i - 1), this.at(i), this.at(i + 1));
};
var tmpLine1=[],
tmpLine2=[];
/**
* Check if two vertices in the polygon can see each other
* @method canSee
* @param {Number} a Vertex index 1
* @param {Number} b Vertex index 2
* @return {Boolean}
*/
Polygon.prototype.canSee = function(a,b) {
var p, dist, l1=tmpLine1, l2=tmpLine2;
if (Point.leftOn(this.at(a + 1), this.at(a), this.at(b)) && Point.rightOn(this.at(a - 1), this.at(a), this.at(b))) {
return false;
}
dist = Point.sqdist(this.at(a), this.at(b));
for (var i = 0; i !== this.vertices.length; ++i) { // for each edge
if ((i + 1) % this.vertices.length === a || i === a) // ignore incident edges
continue;
if (Point.leftOn(this.at(a), this.at(b), this.at(i + 1)) && Point.rightOn(this.at(a), this.at(b), this.at(i))) { // if diag intersects an edge
l1[0] = this.at(a);
l1[1] = this.at(b);
l2[0] = this.at(i);
l2[1] = this.at(i + 1);
p = Line.lineInt(l1,l2);
if (Point.sqdist(this.at(a), p) < dist) { // if edge is blocking visibility to b
return false;
}
}
}
return true;
};
/**
* Copy the polygon from vertex i to vertex j.
* @method copy
* @param {Number} i
* @param {Number} j
* @param {Polygon} [targetPoly] Optional target polygon to save in.
* @return {Polygon} The resulting copy.
*/
Polygon.prototype.copy = function(i,j,targetPoly){
var p = targetPoly || new Polygon();
p.clear();
if (i < j) {
// Insert all vertices from i to j
for(var k=i; k<=j; k++)
p.vertices.push(this.vertices[k]);
} else {
// Insert vertices 0 to j
for(var k=0; k<=j; k++)
p.vertices.push(this.vertices[k]);
// Insert vertices i to end
for(var k=i; k<this.vertices.length; k++)
p.vertices.push(this.vertices[k]);
}
return p;
};
/**
* Decomposes the polygon into convex pieces. Returns a list of edges [[p1,p2],[p2,p3],...] that cuts the polygon.
* Note that this algorithm has complexity O(N^4) and will be very slow for polygons with many vertices.
* @method getCutEdges
* @return {Array}
*/
Polygon.prototype.getCutEdges = function() {
var min=[], tmp1=[], tmp2=[], tmpPoly = new Polygon();
var nDiags = Number.MAX_VALUE;
for (var i = 0; i < this.vertices.length; ++i) {
if (this.isReflex(i)) {
for (var j = 0; j < this.vertices.length; ++j) {
if (this.canSee(i, j)) {
tmp1 = this.copy(i, j, tmpPoly).getCutEdges();
tmp2 = this.copy(j, i, tmpPoly).getCutEdges();
for(var k=0; k<tmp2.length; k++)
tmp1.push(tmp2[k]);
if (tmp1.length < nDiags) {
min = tmp1;
nDiags = tmp1.length;
min.push([this.at(i), this.at(j)]);
}
}
}
}
}
return min;
};
/**
* Decomposes the polygon into one or more convex sub-Polygons.
* @method decomp
* @return {Array} An array or Polygon objects.
*/
Polygon.prototype.decomp = function(){
var edges = this.getCutEdges();
if(edges.length > 0)
return this.slice(edges);
else
return [this];
};
/**
* Slices the polygon given one or more cut edges. If given one, this function will return two polygons (false on failure). If many, an array of polygons.
* @method slice
* @param {Array} cutEdges A list of edges, as returned by .getCutEdges()
* @return {Array}
*/
Polygon.prototype.slice = function(cutEdges){
if(cutEdges.length == 0) return [this];
if(cutEdges instanceof Array && cutEdges.length && cutEdges[0] instanceof Array && cutEdges[0].length==2 && cutEdges[0][0] instanceof Array){
var polys = [this];
for(var i=0; i<cutEdges.length; i++){
var cutEdge = cutEdges[i];
// Cut all polys
for(var j=0; j<polys.length; j++){
var poly = polys[j];
var result = poly.slice(cutEdge);
if(result){
// Found poly! Cut and quit
polys.splice(j,1);
polys.push(result[0],result[1]);
break;
}
}
}
return polys;
} else {
// Was given one edge
var cutEdge = cutEdges;
var i = this.vertices.indexOf(cutEdge[0]);
var j = this.vertices.indexOf(cutEdge[1]);
if(i != -1 && j != -1){
return [this.copy(i,j),
this.copy(j,i)];
} else {
return false;
}
}
};
/**
* Checks that the line segments of this polygon do not intersect each other.
* @method isSimple
* @param {Array} path An array of vertices e.g. [[0,0],[0,1],...]
* @return {Boolean}
* @todo Should it check all segments with all others?
*/
Polygon.prototype.isSimple = function(){
var path = this.vertices;
// Check
for(var i=0; i<path.length-1; i++){
for(var j=0; j<i-1; j++){
if(Line.segmentsIntersect(path[i], path[i+1], path[j], path[j+1] )){
return false;
}
}
}
// Check the segment between the last and the first point to all others
for(var i=1; i<path.length-2; i++){
if(Line.segmentsIntersect(path[0], path[path.length-1], path[i], path[i+1] )){
return false;
}
}
return true;
};
function getIntersectionPoint(p1, p2, q1, q2, delta){
delta = delta || 0;
var a1 = p2[1] - p1[1];
var b1 = p1[0] - p2[0];
var c1 = (a1 * p1[0]) + (b1 * p1[1]);
var a2 = q2[1] - q1[1];
var b2 = q1[0] - q2[0];
var c2 = (a2 * q1[0]) + (b2 * q1[1]);
var det = (a1 * b2) - (a2 * b1);
if(!Scalar.eq(det,0,delta))
return [((b2 * c1) - (b1 * c2)) / det, ((a1 * c2) - (a2 * c1)) / det]
else
return [0,0]
}
/**
* Quickly decompose the Polygon into convex sub-polygons.
* @method quickDecomp
* @param {Array} result
* @param {Array} [reflexVertices]
* @param {Array} [steinerPoints]
* @param {Number} [delta]
* @param {Number} [maxlevel]
* @param {Number} [level]
* @return {Array}
*/
Polygon.prototype.quickDecomp = function(result,reflexVertices,steinerPoints,delta,maxlevel,level){
maxlevel = maxlevel || 100;
level = level || 0;
delta = delta || 25;
result = typeof(result)!="undefined" ? result : [];
reflexVertices = reflexVertices || [];
steinerPoints = steinerPoints || [];
var upperInt=[0,0], lowerInt=[0,0], p=[0,0]; // Points
var upperDist=0, lowerDist=0, d=0, closestDist=0; // scalars
var upperIndex=0, lowerIndex=0, closestIndex=0; // Integers
var lowerPoly=new Polygon(), upperPoly=new Polygon(); // polygons
var poly = this,
v = this.vertices;
if(v.length < 3) return result;
level++;
if(level > maxlevel){
console.warn("quickDecomp: max level ("+maxlevel+") reached.");
return result;
}
for (var i = 0; i < this.vertices.length; ++i) {
if (poly.isReflex(i)) {
reflexVertices.push(poly.vertices[i]);
upperDist = lowerDist = Number.MAX_VALUE;
for (var j = 0; j < this.vertices.length; ++j) {
if (Point.left(poly.at(i - 1), poly.at(i), poly.at(j))
&& Point.rightOn(poly.at(i - 1), poly.at(i), poly.at(j - 1))) { // if line intersects with an edge
p = getIntersectionPoint(poly.at(i - 1), poly.at(i), poly.at(j), poly.at(j - 1)); // find the point of intersection
if (Point.right(poly.at(i + 1), poly.at(i), p)) { // make sure it's inside the poly
d = Point.sqdist(poly.vertices[i], p);
if (d < lowerDist) { // keep only the closest intersection
lowerDist = d;
lowerInt = p;
lowerIndex = j;
}
}
}
if (Point.left(poly.at(i + 1), poly.at(i), poly.at(j + 1))
&& Point.rightOn(poly.at(i + 1), poly.at(i), poly.at(j))) {
p = getIntersectionPoint(poly.at(i + 1), poly.at(i), poly.at(j), poly.at(j + 1));
if (Point.left(poly.at(i - 1), poly.at(i), p)) {
d = Point.sqdist(poly.vertices[i], p);
if (d < upperDist) {
upperDist = d;
upperInt = p;
upperIndex = j;
}
}
}
}
// if there are no vertices to connect to, choose a point in the middle
if (lowerIndex == (upperIndex + 1) % this.vertices.length) {
//console.log("Case 1: Vertex("+i+"), lowerIndex("+lowerIndex+"), upperIndex("+upperIndex+"), poly.size("+this.vertices.length+")");
p[0] = (lowerInt[0] + upperInt[0]) / 2;
p[1] = (lowerInt[1] + upperInt[1]) / 2;
steinerPoints.push(p);
if (i < upperIndex) {
//lowerPoly.insert(lowerPoly.end(), poly.begin() + i, poly.begin() + upperIndex + 1);
lowerPoly.append(poly, i, upperIndex+1);
lowerPoly.vertices.push(p);
upperPoly.vertices.push(p);
if (lowerIndex != 0){
//upperPoly.insert(upperPoly.end(), poly.begin() + lowerIndex, poly.end());
upperPoly.append(poly,lowerIndex,poly.vertices.length);
}
//upperPoly.insert(upperPoly.end(), poly.begin(), poly.begin() + i + 1);
upperPoly.append(poly,0,i+1);
} else {
if (i != 0){
//lowerPoly.insert(lowerPoly.end(), poly.begin() + i, poly.end());
lowerPoly.append(poly,i,poly.vertices.length);
}
//lowerPoly.insert(lowerPoly.end(), poly.begin(), poly.begin() + upperIndex + 1);
lowerPoly.append(poly,0,upperIndex+1);
lowerPoly.vertices.push(p);
upperPoly.vertices.push(p);
//upperPoly.insert(upperPoly.end(), poly.begin() + lowerIndex, poly.begin() + i + 1);
upperPoly.append(poly,lowerIndex,i+1);
}
} else {
// connect to the closest point within the triangle
//console.log("Case 2: Vertex("+i+"), closestIndex("+closestIndex+"), poly.size("+this.vertices.length+")\n");
if (lowerIndex > upperIndex) {
upperIndex += this.vertices.length;
}
closestDist = Number.MAX_VALUE;
if(upperIndex < lowerIndex){
return result;
}
for (var j = lowerIndex; j <= upperIndex; ++j) {
if (Point.leftOn(poly.at(i - 1), poly.at(i), poly.at(j))
&& Point.rightOn(poly.at(i + 1), poly.at(i), poly.at(j))) {
d = Point.sqdist(poly.at(i), poly.at(j));
if (d < closestDist) {
closestDist = d;
closestIndex = j % this.vertices.length;
}
}
}
if (i < closestIndex) {
lowerPoly.append(poly,i,closestIndex+1);
if (closestIndex != 0){
upperPoly.append(poly,closestIndex,v.length);
}
upperPoly.append(poly,0,i+1);
} else {
if (i != 0){
lowerPoly.append(poly,i,v.length);
}
lowerPoly.append(poly,0,closestIndex+1);
upperPoly.append(poly,closestIndex,i+1);
}
}
// solve smallest poly first
if (lowerPoly.vertices.length < upperPoly.vertices.length) {
lowerPoly.quickDecomp(result,reflexVertices,steinerPoints,delta,maxlevel,level);
upperPoly.quickDecomp(result,reflexVertices,steinerPoints,delta,maxlevel,level);
} else {
upperPoly.quickDecomp(result,reflexVertices,steinerPoints,delta,maxlevel,level);
lowerPoly.quickDecomp(result,reflexVertices,steinerPoints,delta,maxlevel,level);
}
return result;
}
}
result.push(this);
return result;
};
/**
* Remove collinear points in the polygon.
* @method removeCollinearPoints
* @param {Number} [precision] The threshold angle to use when determining whether two edges are collinear. Use zero for finest precision.
* @return {Number} The number of points removed
*/
Polygon.prototype.removeCollinearPoints = function(precision){
var num = 0;
for(var i=this.vertices.length-1; this.vertices.length>3 && i>=0; --i){
if(Point.collinear(this.at(i-1),this.at(i),this.at(i+1),precision)){
// Remove the middle point
this.vertices.splice(i%this.vertices.length,1);
i--; // Jump one point forward. Otherwise we may get a chain removal
num++;
}
}
return num;
};
},{"./Line":1,"./Point":2,"./Scalar":4}],4:[function(require,module,exports){
module.exports = Scalar;
/**
* Scalar functions
* @class Scalar
*/
function Scalar(){}
/**
* Check if two scalars are equal
* @static
* @method eq
* @param {Number} a
* @param {Number} b
* @param {Number} [precision]
* @return {Boolean}
*/
Scalar.eq = function(a,b,precision){
precision = precision || 0;
return Math.abs(a-b) < precision;
};
},{}],5:[function(require,module,exports){
module.exports = {
Polygon : require("./Polygon"),
Point : require("./Point"),
};
},{"./Point":2,"./Polygon":3}]},{},[5])
(5)
});
;