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November 22, 2013 00:01
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/* | |
PolyK library | |
url: http://polyk.ivank.net | |
Released under MIT licence. | |
Copyright (c) 2012 Ivan Kuckir | |
Permission is hereby granted, free of charge, to any person | |
obtaining a copy of this software and associated documentation | |
files (the "Software"), to deal in the Software without | |
restriction, including without limitation the rights to use, | |
copy, modify, merge, publish, distribute, sublicense, and/or sell | |
copies of the Software, and to permit persons to whom the | |
Software is furnished to do so, subject to the following | |
conditions: | |
The above copyright notice and this permission notice shall be | |
included in all copies or substantial portions of the Software. | |
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, | |
EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES | |
OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND | |
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT | |
HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, | |
WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING | |
FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR | |
OTHER DEALINGS IN THE SOFTWARE. | |
*/ | |
var PolyK = {}; | |
/* | |
Is Polygon self-intersecting? | |
O(n^2) | |
*/ | |
PolyK.IsSimple = function(p) | |
{ | |
var n = p.length>>1; | |
if(n<4) return true; | |
var a1 = new PolyK._P(), a2 = new PolyK._P(); | |
var b1 = new PolyK._P(), b2 = new PolyK._P(); | |
var c = new PolyK._P(); | |
for(var i=0; i<n; i++) | |
{ | |
a1.x = p[2*i ]; | |
a1.y = p[2*i+1]; | |
if(i==n-1) { a2.x = p[0 ]; a2.y = p[1 ]; } | |
else { a2.x = p[2*i+2]; a2.y = p[2*i+3]; } | |
for(var j=0; j<n; j++) | |
{ | |
if(Math.abs(i-j) < 2) continue; | |
if(j==n-1 && i==0) continue; | |
if(i==n-1 && j==0) continue; | |
b1.x = p[2*j ]; | |
b1.y = p[2*j+1]; | |
if(j==n-1) { b2.x = p[0 ]; b2.y = p[1 ]; } | |
else { b2.x = p[2*j+2]; b2.y = p[2*j+3]; } | |
if(PolyK._GetLineIntersection(a1,a2,b1,b2,c) != null) return false; | |
} | |
} | |
return true; | |
} | |
PolyK.IsConvex = function(p) | |
{ | |
if(p.length<6) return true; | |
var l = p.length - 4; | |
for(var i=0; i<l; i+=2) | |
if(!PolyK._convex(p[i], p[i+1], p[i+2], p[i+3], p[i+4], p[i+5])) return false; | |
if(!PolyK._convex(p[l ], p[l+1], p[l+2], p[l+3], p[0], p[1])) return false; | |
if(!PolyK._convex(p[l+2], p[l+3], p[0 ], p[1 ], p[2], p[3])) return false; | |
return true; | |
} | |
PolyK.GetArea = function(p) | |
{ | |
if(p.length <6) return 0; | |
var l = p.length - 2; | |
var sum = 0; | |
for(var i=0; i<l; i+=2) | |
sum += (p[i+2]-p[i]) * (p[i+1]+p[i+3]); | |
sum += (p[0]-p[l]) * (p[l+1]+p[1]); | |
return - sum * 0.5; | |
} | |
PolyK.GetAABB = function(p) | |
{ | |
var minx = Infinity; | |
var miny = Infinity; | |
var maxx = -minx; | |
var maxy = -miny; | |
for(var i=0; i<p.length; i+=2) | |
{ | |
minx = Math.min(minx, p[i ]); | |
maxx = Math.max(maxx, p[i ]); | |
miny = Math.min(miny, p[i+1]); | |
maxy = Math.max(maxy, p[i+1]); | |
} | |
return {x:minx, y:miny, width:maxx-minx, height:maxy-miny}; | |
} | |
PolyK.Triangulate = function(p) | |
{ | |
var n = p.length>>1; | |
if(n<3) return []; | |
var tgs = []; | |
var avl = []; | |
for(var i=0; i<n; i++) avl.push(i); | |
var i = 0; | |
var al = n; | |
while(al > 3) | |
{ | |
var i0 = avl[(i+0)%al]; | |
var i1 = avl[(i+1)%al]; | |
var i2 = avl[(i+2)%al]; | |
var ax = p[2*i0], ay = p[2*i0+1]; | |
var bx = p[2*i1], by = p[2*i1+1]; | |
var cx = p[2*i2], cy = p[2*i2+1]; | |
var earFound = false; | |
if(PolyK._convex(ax, ay, bx, by, cx, cy)) | |
{ | |
earFound = true; | |
for(var j=0; j<al; j++) | |
{ | |
var vi = avl[j]; | |
if(vi==i0 || vi==i1 || vi==i2) continue; | |
if(PolyK._PointInTriangle(p[2*vi], p[2*vi+1], ax, ay, bx, by, cx, cy)) {earFound = false; break;} | |
} | |
} | |
if(earFound) | |
{ | |
tgs.push(i0, i1, i2); | |
avl.splice((i+1)%al, 1); | |
al--; | |
i= 0; | |
} | |
else if(i++ > 3*al) break; // no convex angles :( | |
} | |
tgs.push(avl[0], avl[1], avl[2]); | |
return tgs; | |
} | |
PolyK.ContainsPoint = function(p, px, py) | |
{ | |
var n = p.length>>1; | |
var ax, ay, bx = p[2*n-2]-px, by = p[2*n-1]-py; | |
var depth = 0; | |
for(var i=0; i<n; i++) | |
{ | |
ax = bx; ay = by; | |
bx = p[2*i ] - px; | |
by = p[2*i+1] - py; | |
if(ay< 0 && by< 0) continue; // both "up" or both "donw" | |
if(ay>=0 && by>=0) continue; // both "up" or both "donw" | |
if(ax< 0 && bx< 0) continue; | |
var lx = ax + (bx-ax)*(-ay)/(by-ay); | |
if(lx>0) depth++; | |
} | |
return (depth & 1) == 1; | |
} | |
PolyK.Slice = function(p, ax, ay, bx, by) | |
{ | |
if(PolyK.ContainsPoint(p, ax, ay) || PolyK.ContainsPoint(p, bx, by)) return [p.slice(0)]; | |
var a = new PolyK._P(ax, ay); | |
var b = new PolyK._P(bx, by); | |
var iscs = []; // intersections | |
var ps = []; // points | |
for(var i=0; i<p.length; i+=2) ps.push(new PolyK._P(p[i], p[i+1])); | |
for(var i=0; i<ps.length; i++) | |
{ | |
var isc = new PolyK._P(0,0); | |
isc = PolyK._GetLineIntersection(a, b, ps[i], ps[(i+1)%ps.length], isc); | |
if(isc) | |
{ | |
isc.flag = true; | |
iscs.push(isc); | |
ps.splice(i+1,0,isc); | |
i++; | |
} | |
} | |
if(iscs.length == 0) return [p.slice(0)]; | |
var comp = function(u,v) {return PolyK._P.dist(a,u) - PolyK._P.dist(a,v); } | |
iscs.sort(comp); | |
var pgs = []; | |
var dir = 0; | |
while(iscs.length > 0) | |
{ | |
var n = ps.length; | |
var i0 = iscs[0]; | |
var i1 = iscs[1]; | |
var ind0 = ps.indexOf(i0); | |
var ind1 = ps.indexOf(i1); | |
var solved = false; | |
if(PolyK._firstWithFlag(ps, ind0) == ind1) solved = true; | |
else | |
{ | |
i0 = iscs[1]; | |
i1 = iscs[0]; | |
ind0 = ps.indexOf(i0); | |
ind1 = ps.indexOf(i1); | |
if(PolyK._firstWithFlag(ps, ind0) == ind1) solved = true; | |
} | |
if(solved) | |
{ | |
dir--; | |
var pgn = PolyK._getPoints(ps, ind0, ind1); | |
pgs.push(pgn); | |
ps = PolyK._getPoints(ps, ind1, ind0); | |
i0.flag = i1.flag = false; | |
iscs.splice(0,2); | |
if(iscs.length == 0) pgs.push(ps); | |
} | |
else { dir++; iscs.reverse(); } | |
if(dir>1) break; | |
} | |
var result = []; | |
for(var i=0; i<pgs.length; i++) | |
{ | |
var pg = pgs[i]; | |
var npg = []; | |
for(var j=0; j<pg.length; j++) npg.push(pg[j].x, pg[j].y); | |
result.push(npg); | |
} | |
return result; | |
} | |
PolyK.Raycast = function(p, x, y, dx, dy, isc) | |
{ | |
var l = p.length - 2; | |
var tp = PolyK._tp; | |
var a1 = tp[0], a2 = tp[1], | |
b1 = tp[2], b2 = tp[3], c = tp[4]; | |
a1.x = x; a1.y = y; | |
a2.x = x+dx; a2.y = y+dy; | |
if(isc==null) isc = {dist:0, edge:0, norm:{x:0, y:0}, refl:{x:0, y:0}}; | |
isc.dist = Infinity; | |
for(var i=0; i<l; i+=2) | |
{ | |
b1.x = p[i ]; b1.y = p[i+1]; | |
b2.x = p[i+2]; b2.y = p[i+3]; | |
var nisc = PolyK._RayLineIntersection(a1, a2, b1, b2, c); | |
if(nisc) PolyK._updateISC(dx, dy, a1, b1, b2, c, i/2, isc); | |
} | |
b1.x = b2.x; b1.y = b2.y; | |
b2.x = p[0]; b2.y = p[1]; | |
var nisc = PolyK._RayLineIntersection(a1, a2, b1, b2, c); | |
if(nisc) PolyK._updateISC(dx, dy, a1, b1, b2, c, p.length/2, isc); | |
return (isc.dist != Infinity) ? isc : null; | |
} | |
PolyK.ClosestEdge = function(p, x, y, isc) | |
{ | |
var l = p.length - 2; | |
var tp = PolyK._tp; | |
var a1 = tp[0], | |
b1 = tp[2], b2 = tp[3], c = tp[4]; | |
a1.x = x; a1.y = y; | |
if(isc==null) isc = {dist:0, edge:0, point:{x:0, y:0}, norm:{x:0, y:0}}; | |
isc.dist = Infinity; | |
for(var i=0; i<l; i+=2) | |
{ | |
b1.x = p[i ]; b1.y = p[i+1]; | |
b2.x = p[i+2]; b2.y = p[i+3]; | |
PolyK._pointLineDist(a1, b1, b2, i>>1, isc); | |
} | |
b1.x = b2.x; b1.y = b2.y; | |
b2.x = p[0]; b2.y = p[1]; | |
PolyK._pointLineDist(a1, b1, b2, l>>1, isc); | |
var idst = 1/isc.dist; | |
isc.norm.x = (x-isc.point.x)*idst; | |
isc.norm.y = (y-isc.point.y)*idst; | |
return isc; | |
} | |
PolyK._pointLineDist = function(p, a, b, edge, isc) | |
{ | |
var x = p.x, y = p.y, x1 = a.x, y1 = a.y, x2 = b.x, y2 = b.y; | |
var A = x - x1; | |
var B = y - y1; | |
var C = x2 - x1; | |
var D = y2 - y1; | |
var dot = A * C + B * D; | |
var len_sq = C * C + D * D; | |
var param = dot / len_sq; | |
var xx, yy; | |
if (param < 0 || (x1 == x2 && y1 == y2)) { | |
xx = x1; | |
yy = y1; | |
} | |
else if (param > 1) { | |
xx = x2; | |
yy = y2; | |
} | |
else { | |
xx = x1 + param * C; | |
yy = y1 + param * D; | |
} | |
var dx = x - xx; | |
var dy = y - yy; | |
var dst = Math.sqrt(dx * dx + dy * dy); | |
if(dst<isc.dist) | |
{ | |
isc.dist = dst; | |
isc.edge = edge; | |
isc.point.x = xx; | |
isc.point.y = yy; | |
} | |
} | |
PolyK._updateISC = function(dx, dy, a1, b1, b2, c, edge, isc) | |
{ | |
var nrl = PolyK._P.dist(a1, c); | |
if(nrl<isc.dist) | |
{ | |
var ibl = 1/PolyK._P.dist(b1, b2); | |
var nx = -(b2.y-b1.y)*ibl; | |
var ny = (b2.x-b1.x)*ibl; | |
var ddot = 2*(dx*nx+dy*ny); | |
isc.dist = nrl; | |
isc.norm.x = nx; | |
isc.norm.y = ny; | |
isc.refl.x = -ddot*nx+dx; | |
isc.refl.y = -ddot*ny+dy; | |
isc.edge = edge; | |
} | |
} | |
PolyK._getPoints = function(ps, ind0, ind1) | |
{ | |
var n = ps.length; | |
var nps = []; | |
if(ind1<ind0) ind1 += n; | |
for(var i=ind0; i<= ind1; i++) nps.push(ps[i%n]); | |
return nps; | |
} | |
PolyK._firstWithFlag = function(ps, ind) | |
{ | |
var n = ps.length; | |
while(true) | |
{ | |
ind = (ind+1)%n; | |
if(ps[ind].flag) return ind; | |
} | |
} | |
PolyK._PointInTriangle = function(px, py, ax, ay, bx, by, cx, cy) | |
{ | |
var v0x = cx-ax; | |
var v0y = cy-ay; | |
var v1x = bx-ax; | |
var v1y = by-ay; | |
var v2x = px-ax; | |
var v2y = py-ay; | |
var dot00 = v0x*v0x+v0y*v0y; | |
var dot01 = v0x*v1x+v0y*v1y; | |
var dot02 = v0x*v2x+v0y*v2y; | |
var dot11 = v1x*v1x+v1y*v1y; | |
var dot12 = v1x*v2x+v1y*v2y; | |
var invDenom = 1 / (dot00 * dot11 - dot01 * dot01); | |
var u = (dot11 * dot02 - dot01 * dot12) * invDenom; | |
var v = (dot00 * dot12 - dot01 * dot02) * invDenom; | |
// Check if point is in triangle | |
return (u >= 0) && (v >= 0) && (u + v < 1); | |
} | |
PolyK._RayLineIntersection = function(a1, a2, b1, b2, c) | |
{ | |
var dax = (a1.x-a2.x), dbx = (b1.x-b2.x); | |
var day = (a1.y-a2.y), dby = (b1.y-b2.y); | |
var Den = dax*dby - day*dbx; | |
if (Den == 0) return null; // parallel | |
var A = (a1.x * a2.y - a1.y * a2.x); | |
var B = (b1.x * b2.y - b1.y * b2.x); | |
var I = c; | |
var iDen = 1/Den; | |
I.x = ( A*dbx - dax*B ) * iDen; | |
I.y = ( A*dby - day*B ) * iDen; | |
if(!PolyK._InRect(I, b1, b2)) return null; | |
if((day>0 && I.y>a1.y) || (day<0 && I.y<a1.y)) return null; | |
if((dax>0 && I.x>a1.x) || (dax<0 && I.x<a1.x)) return null; | |
return I; | |
} | |
PolyK._GetLineIntersection = function(a1, a2, b1, b2, c) | |
{ | |
var dax = (a1.x-a2.x), dbx = (b1.x-b2.x); | |
var day = (a1.y-a2.y), dby = (b1.y-b2.y); | |
var Den = dax*dby - day*dbx; | |
if (Den == 0) return null; // parallel | |
var A = (a1.x * a2.y - a1.y * a2.x); | |
var B = (b1.x * b2.y - b1.y * b2.x); | |
var I = c; | |
I.x = ( A*dbx - dax*B ) / Den; | |
I.y = ( A*dby - day*B ) / Den; | |
if(PolyK._InRect(I, a1, a2) && PolyK._InRect(I, b1, b2)) return I; | |
return null; | |
} | |
PolyK._InRect = function(a, b, c) | |
{ | |
if (b.x == c.x) return (a.y>=Math.min(b.y, c.y) && a.y<=Math.max(b.y, c.y)); | |
if (b.y == c.y) return (a.x>=Math.min(b.x, c.x) && a.x<=Math.max(b.x, c.x)); | |
if(a.x >= Math.min(b.x, c.x) && a.x <= Math.max(b.x, c.x) | |
&& a.y >= Math.min(b.y, c.y) && a.y <= Math.max(b.y, c.y)) | |
return true; | |
return false; | |
} | |
PolyK._convex = function(ax, ay, bx, by, cx, cy) | |
{ | |
return (ay-by)*(cx-bx) + (bx-ax)*(cy-by) >= 0; | |
} | |
PolyK._P = function(x,y) | |
{ | |
this.x = x; | |
this.y = y; | |
this.flag = false; | |
} | |
PolyK._P.prototype.toString = function() | |
{ | |
return "Point ["+this.x+", "+this.y+"]"; | |
} | |
PolyK._P.dist = function(a,b) | |
{ | |
var dx = b.x-a.x; | |
var dy = b.y-a.y; | |
return Math.sqrt(dx*dx + dy*dy); | |
} | |
PolyK._tp = []; | |
for(var i=0; i<10; i++) PolyK._tp.push(new PolyK._P(0,0)); |
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