Improved tesselation and speed for expand() and contract()
This commit is contained in:
Joost Nieuwenhuijse
parent
471b99d5ba
commit
07475364a6
2 changed files with 299 additions and 58 deletions
356
csg.js
356
csg.js
|
|
@ -212,8 +212,8 @@ CSG.prototype = {
|
|||
var newpolygons = a.allPolygons().concat(b.allPolygons());
|
||||
var result = CSG.fromPolygons(newpolygons);
|
||||
result.properties = this.properties._merge(csg.properties);
|
||||
if(canonicalize) result = result.canonicalized();
|
||||
if(retesselate) result = result.reTesselated();
|
||||
if(canonicalize) result = result.canonicalized();
|
||||
return result;
|
||||
}
|
||||
},
|
||||
|
|
@ -257,8 +257,8 @@ CSG.prototype = {
|
|||
a.invert();
|
||||
var result = CSG.fromPolygons(a.allPolygons());
|
||||
result.properties = this.properties._merge(csg.properties);
|
||||
if(canonicalize) result = result.canonicalized();
|
||||
if(retesselate) result = result.reTesselated();
|
||||
if(canonicalize) result = result.canonicalized();
|
||||
return result;
|
||||
},
|
||||
|
||||
|
|
@ -292,8 +292,8 @@ CSG.prototype = {
|
|||
a.invert();
|
||||
var result = CSG.fromPolygons(a.allPolygons());
|
||||
result.properties = this.properties._merge(csg.properties);
|
||||
if(canonicalize) result = result.canonicalized();
|
||||
if(retesselate) result = result.reTesselated();
|
||||
if(canonicalize) result = result.canonicalized();
|
||||
return result;
|
||||
},
|
||||
|
||||
|
|
@ -411,19 +411,7 @@ CSG.prototype = {
|
|||
// Expand the solid
|
||||
// resolution: number of points per 360 degree for the rounded corners
|
||||
expand: function(radius, resolution) {
|
||||
var result=this;
|
||||
var count = 0;
|
||||
this.polygons.map(function(p) {
|
||||
var expanded=p.expand(radius, resolution);
|
||||
result=result.unionSub(expanded, false, false);
|
||||
count++;
|
||||
if(count == 300)
|
||||
{
|
||||
result = result.reTesselated();
|
||||
count = 0;
|
||||
}
|
||||
});
|
||||
// result = result.canonicalized();
|
||||
var result = this.expandedShell(radius, resolution, true);
|
||||
result = result.reTesselated();
|
||||
result.properties = this.properties; // keep original properties
|
||||
return result;
|
||||
|
|
@ -432,15 +420,239 @@ CSG.prototype = {
|
|||
// Contract the solid
|
||||
// resolution: number of points per 360 degree for the rounded corners
|
||||
contract: function(radius, resolution) {
|
||||
var result=this;
|
||||
this.polygons.map(function(p) {
|
||||
var expanded=p.expand(radius, resolution);
|
||||
result=result.subtract(expanded);
|
||||
});
|
||||
var expandedshell = this.expandedShell(radius, resolution, false);
|
||||
var result = this.subtract(expandedshell);
|
||||
result = result.reTesselated();
|
||||
result.properties = this.properties; // keep original properties
|
||||
return result;
|
||||
},
|
||||
|
||||
// Create the expanded shell of the solid:
|
||||
// All faces are extruded to get a thickness of 2*radius
|
||||
// Cylinders are constructed around every side
|
||||
// Spheres are placed on every vertex
|
||||
// unionWithThis: if true, the resulting solid will be united with 'this' solid;
|
||||
// the result is a true expansion of the solid
|
||||
// If false, returns only the shell
|
||||
expandedShell: function(radius, resolution, unionWithThis) {
|
||||
var csg = this.reTesselated();
|
||||
var result;
|
||||
if(unionWithThis)
|
||||
{
|
||||
result = csg;
|
||||
}
|
||||
else
|
||||
{
|
||||
result = new CSG();
|
||||
}
|
||||
|
||||
// first extrude all polygons:
|
||||
csg.polygons.map(function(polygon){
|
||||
var extrudevector=polygon.plane.normal.unit().times(2*radius);
|
||||
var translatedpolygon = polygon.translate(extrudevector.times(-0.5));
|
||||
var extrudedface = translatedpolygon.extrude(extrudevector);
|
||||
result=result.unionSub(extrudedface, false, false);
|
||||
});
|
||||
|
||||
// Make a list of all unique vertex pairs (i.e. all sides of the solid)
|
||||
// For each vertex pair we collect the following:
|
||||
// v1: first coordinate
|
||||
// v2: second coordinate
|
||||
// planenormals: array of normal vectors of all planes touching this side
|
||||
var vertexpairs = {}; // map of 'vertex pair tag' to {v1, v2, planenormals}
|
||||
csg.polygons.map(function(polygon){
|
||||
var numvertices = polygon.vertices.length;
|
||||
var prevvertex = polygon.vertices[numvertices-1];
|
||||
var prevvertextag = prevvertex.getTag();
|
||||
for(var i = 0; i < numvertices; i++)
|
||||
{
|
||||
var vertex = polygon.vertices[i];
|
||||
var vertextag = vertex.getTag();
|
||||
var vertextagpair;
|
||||
if(vertextag < prevvertextag)
|
||||
{
|
||||
vertextagpair = vertextag+"-"+prevvertextag;
|
||||
}
|
||||
else
|
||||
{
|
||||
vertextagpair = prevvertextag+"-"+vertextag;
|
||||
}
|
||||
var obj;
|
||||
if(vertextagpair in vertexpairs)
|
||||
{
|
||||
obj = vertexpairs[vertextagpair];
|
||||
}
|
||||
else
|
||||
{
|
||||
obj = {
|
||||
v1: prevvertex,
|
||||
v2: vertex,
|
||||
planenormals: [],
|
||||
};
|
||||
vertexpairs[vertextagpair] = obj;
|
||||
}
|
||||
obj.planenormals.push(polygon.plane.normal);
|
||||
|
||||
prevvertextag = vertextag;
|
||||
prevvertex = vertex;
|
||||
}
|
||||
});
|
||||
|
||||
// now construct a cylinder on every side
|
||||
// The cylinder is always an approximation of a true cylinder: it will have <resolution> polygons
|
||||
// around the sides. We will make sure though that the cylinder will have an edge at every
|
||||
// face that touches this side. This ensures that we will get a smooth fill even
|
||||
// if two edges are at, say, 10 degrees and the resolution is low.
|
||||
// Note: the result is not retesselated yet but it really should be!
|
||||
for(vertextagpair in vertexpairs)
|
||||
{
|
||||
var vertexpair = vertexpairs[vertextagpair];
|
||||
var startpoint = vertexpair.v1.pos;
|
||||
var endpoint = vertexpair.v2.pos;
|
||||
// our x,y and z vectors:
|
||||
var zbase = endpoint.minus(startpoint).unit();
|
||||
var xbase = vertexpair.planenormals[0].unit();
|
||||
var ybase = xbase.cross(zbase);
|
||||
|
||||
// make a list of angles that the cylinder should traverse:
|
||||
var angles = [];
|
||||
|
||||
// first of all equally spaced around the cylinder:
|
||||
for(var i = 0; i < resolution; i++)
|
||||
{
|
||||
var angle = i * Math.PI * 2 / resolution;
|
||||
angles.push(angle);
|
||||
}
|
||||
|
||||
// and also at every normal of all touching planes:
|
||||
vertexpair.planenormals.map(function(planenormal){
|
||||
var si = ybase.dot(planenormal);
|
||||
var co = xbase.dot(planenormal);
|
||||
var angle = Math.atan2(si,co);
|
||||
if(angle < 0) angle += Math.PI*2;
|
||||
angles.push(angle);
|
||||
angle = Math.atan2(-si,-co);
|
||||
if(angle < 0) angle += Math.PI*2;
|
||||
angles.push(angle);
|
||||
});
|
||||
|
||||
// this will result in some duplicate angles but we will get rid of those later.
|
||||
// Sort:
|
||||
angles = angles.sort(function(a,b){return a-b;});
|
||||
|
||||
// Now construct the cylinder by traversing all angles:
|
||||
var numangles = angles.length;
|
||||
var prevp1, prevp2;
|
||||
var startfacevertices = [], endfacevertices = [];
|
||||
var polygons = [];
|
||||
var prevangle;
|
||||
for(var i = -1; i < numangles; i++)
|
||||
{
|
||||
var angle = angles[(i < 0)?(i+numangles):i];
|
||||
var si = Math.sin(angle);
|
||||
var co = Math.cos(angle);
|
||||
var p = xbase.times(co * radius).plus(ybase.times(si * radius));
|
||||
var p1 = startpoint.plus(p);
|
||||
var p2 = endpoint.plus(p);
|
||||
var skip = false;
|
||||
if(i >= 0)
|
||||
{
|
||||
if(p1.distanceTo(prevp1) < 1e-5)
|
||||
{
|
||||
skip = true;
|
||||
}
|
||||
}
|
||||
if(!skip)
|
||||
{
|
||||
if(i >= 0)
|
||||
{
|
||||
startfacevertices.push(new CSG.Vertex(p1));
|
||||
endfacevertices.push(new CSG.Vertex(p2));
|
||||
var polygonvertices = [
|
||||
new CSG.Vertex(prevp2),
|
||||
new CSG.Vertex(p2),
|
||||
new CSG.Vertex(p1),
|
||||
new CSG.Vertex(prevp1),
|
||||
];
|
||||
var polygon = new CSG.Polygon(polygonvertices);
|
||||
polygons.push(polygon);
|
||||
}
|
||||
prevp1 = p1;
|
||||
prevp2 = p2;
|
||||
}
|
||||
}
|
||||
endfacevertices.reverse();
|
||||
polygons.push(new CSG.Polygon(startfacevertices));
|
||||
polygons.push(new CSG.Polygon(endfacevertices));
|
||||
var cylinder = CSG.fromPolygons(polygons);
|
||||
result = result.unionSub(cylinder, false, false);
|
||||
}
|
||||
|
||||
// make a list of all unique vertices
|
||||
// For each vertex we also collect the list of normals of the planes touching the vertices
|
||||
var vertexmap = {};
|
||||
csg.polygons.map(function(polygon){
|
||||
polygon.vertices.map(function(vertex){
|
||||
var vertextag = vertex.getTag();
|
||||
var obj;
|
||||
if(vertextag in vertexmap)
|
||||
{
|
||||
obj = vertexmap[vertextag];
|
||||
}
|
||||
else
|
||||
{
|
||||
obj = {
|
||||
pos: vertex.pos,
|
||||
normals: [],
|
||||
};
|
||||
vertexmap[vertextag] = obj;
|
||||
}
|
||||
obj.normals.push(polygon.plane.normal);
|
||||
});
|
||||
});
|
||||
|
||||
// and build spheres at each vertex
|
||||
// We will try to set the x and z axis to the normals of 2 planes
|
||||
// This will ensure that our sphere tesselation somewhat matches 2 planes
|
||||
for(vertextag in vertexmap)
|
||||
{
|
||||
var vertexobj = vertexmap[vertextag];
|
||||
// use the first normal to be the x axis of our sphere:
|
||||
var xaxis = vertexobj.normals[0].unit();
|
||||
// and find a suitable z axis. We will use the normal which is most perpendicular to the x axis:
|
||||
var bestzaxis = null;
|
||||
var bestzaxisorthogonality = 0;
|
||||
for(var i = 1; i < vertexobj.normals.length; i++)
|
||||
{
|
||||
var normal = vertexobj.normals[i].unit();
|
||||
var cross = xaxis.cross(normal);
|
||||
var crosslength = cross.length();
|
||||
if(crosslength > 0.05)
|
||||
{
|
||||
if(crosslength > bestzaxisorthogonality)
|
||||
{
|
||||
bestzaxisorthogonality = crosslength;
|
||||
bestzaxis = normal;
|
||||
}
|
||||
}
|
||||
}
|
||||
if(! bestzaxis)
|
||||
{
|
||||
bestzaxis = xaxis.randomNonParallelVector();
|
||||
}
|
||||
var yaxis = xaxis.cross(bestzaxis).unit();
|
||||
var zaxis = yaxis.cross(xaxis);
|
||||
var sphere = CSG.sphere({
|
||||
center: vertexobj.pos,
|
||||
radius: radius,
|
||||
resolution: resolution,
|
||||
axes: [xaxis, yaxis, zaxis]});
|
||||
result = result.unionSub(sphere, false, false);
|
||||
}
|
||||
|
||||
return result;
|
||||
},
|
||||
|
||||
canonicalized: function () {
|
||||
if(this.isCanonicalized)
|
||||
{
|
||||
|
|
@ -493,7 +705,8 @@ CSG.prototype = {
|
|||
}
|
||||
var result = CSG.fromPolygons(destpolygons);
|
||||
result.isRetesselated = true;
|
||||
result.isCanonicalized = true;
|
||||
result=result.canonicalized();
|
||||
// result.isCanonicalized = true;
|
||||
result.properties = this.properties; // keep original properties
|
||||
return result;
|
||||
}
|
||||
|
|
@ -703,6 +916,31 @@ CSG.prototype = {
|
|||
return result;
|
||||
},
|
||||
|
||||
// For debugging
|
||||
// Creates a new solid with a tiny cube at every vertex of the source solid
|
||||
toPointCloud: function(cuberadius) {
|
||||
var csg = this.reTesselated();
|
||||
|
||||
var result = new CSG();
|
||||
|
||||
// make a list of all unique vertices
|
||||
// For each vertex we also collect the list of normals of the planes touching the vertices
|
||||
var vertexmap = {};
|
||||
csg.polygons.map(function(polygon){
|
||||
polygon.vertices.map(function(vertex){
|
||||
vertexmap[vertex.getTag()] = vertex.pos;
|
||||
});
|
||||
});
|
||||
|
||||
for(vertextag in vertexmap)
|
||||
{
|
||||
var pos = vertexmap[vertextag];
|
||||
var cube = CSG.cube({center: pos, radius: cuberadius});
|
||||
result = result.unionSub(cube, false, false);
|
||||
}
|
||||
result = result.reTesselated();
|
||||
return result;
|
||||
},
|
||||
|
||||
};
|
||||
|
||||
|
|
@ -820,6 +1058,7 @@ CSG.cube = function(options) {
|
|||
// center: center of sphere (default [0,0,0])
|
||||
// radius: radius of sphere (default 1), must be a scalar
|
||||
// resolution: determines the number of polygons per 360 degree revolution (default 12)
|
||||
// axes: (optional) an array with 3 vectors for the x, y and z base vectors
|
||||
//
|
||||
// Example usage:
|
||||
//
|
||||
|
|
@ -833,11 +1072,21 @@ CSG.sphere = function(options) {
|
|||
var center = CSG.parseOptionAs3DVector(options, "center", [0,0,0]);
|
||||
var radius = CSG.parseOptionAsFloat(options, "radius", 1);
|
||||
var resolution = CSG.parseOptionAsInt(options, "resolution", 12);
|
||||
var xvector, yvector, zvector;
|
||||
if('axes' in options)
|
||||
{
|
||||
xvector = options.axes[0].unit().times(radius);
|
||||
yvector = options.axes[1].unit().times(radius);
|
||||
zvector = options.axes[2].unit().times(radius);
|
||||
}
|
||||
else
|
||||
{
|
||||
xvector = new CSG.Vector3D([1,0,0]).times(radius);
|
||||
yvector = new CSG.Vector3D([0,-1,0]).times(radius);
|
||||
zvector = new CSG.Vector3D([0,0,1]).times(radius);
|
||||
}
|
||||
if(resolution < 4) resolution = 4;
|
||||
var qresolution = Math.round(resolution / 4);
|
||||
var xvector = new CSG.Vector3D([1,0,0]).times(radius);
|
||||
var yvector = new CSG.Vector3D([0,-1,0]).times(radius);
|
||||
var zvector = new CSG.Vector3D([0,0,1]).times(radius);
|
||||
var prevcylinderpoint;
|
||||
var polygons = [];
|
||||
for(var slice1 = 0; slice1 <= resolution; slice1++)
|
||||
|
|
@ -1082,7 +1331,7 @@ CSG.roundedCube = function(options) {
|
|||
sphere = CSG.sphere({center: p3, radius: roundradius, resolution: resolution});
|
||||
result = result.unionSub(sphere,false,false);
|
||||
sphere = CSG.sphere({center: p4, radius: roundradius, resolution: resolution});
|
||||
result = result.unionSub(sphere,true,true);
|
||||
result = result.unionSub(sphere,false,true);
|
||||
var cylinder = CSG.cylinder({start:p1, end: p2, radius: roundradius, resolution: resolution});
|
||||
result = result.unionSub(cylinder,false,false);
|
||||
cylinder = CSG.cylinder({start:p2, end: p3, radius: roundradius, resolution: resolution});
|
||||
|
|
@ -1100,9 +1349,10 @@ CSG.roundedCube = function(options) {
|
|||
cylinder = CSG.cylinder({start:p3, end: p3.plus(d), radius: roundradius, resolution: resolution});
|
||||
result = result.unionSub(cylinder);
|
||||
cylinder = CSG.cylinder({start:p4, end: p4.plus(d), radius: roundradius, resolution: resolution});
|
||||
result = result.unionSub(cylinder,true,true);
|
||||
result = result.unionSub(cylinder,false,true);
|
||||
}
|
||||
}
|
||||
result = result.reTesselated();
|
||||
result.properties.roundedCube = new CSG.Properties();
|
||||
result.properties.roundedCube.center = new CSG.Vertex(center);
|
||||
result.properties.roundedCube.facecenters = [
|
||||
|
|
@ -1729,35 +1979,7 @@ CSG.Polygon.prototype = {
|
|||
translate: function(offset) {
|
||||
return this.transform(CSG.Matrix4x4.translation(offset));
|
||||
},
|
||||
|
||||
// Expand the polygon with a certain radius
|
||||
// This extrudes the face of the polygon and adds rounded corners
|
||||
// Returns a CSG object (not a polygon anymore!)
|
||||
// resolution: number of points per 360 degree for the rounded corners
|
||||
expand: function(radius, resolution) {
|
||||
if( (!resolution) || (resolution < 4) ) resolution = 4;
|
||||
resolution = 4 * Math.floor(resolution / 4);
|
||||
|
||||
var result=new CSG();
|
||||
|
||||
// expand each side of the polygon. The expansion of a line is a roundedCylinder:
|
||||
var numvertices=this.vertices.length;
|
||||
for(var i=0; i < numvertices; i++)
|
||||
{
|
||||
var previ = (i == 0) ? (numvertices-1):i-1;
|
||||
var p1 = this.vertices[previ].pos;
|
||||
var p2 = this.vertices[i].pos;
|
||||
|
||||
var roundedCylinder = CSG.roundedCylinder({start: p1, end: p2, normal: this.plane.normal, radius: radius, resolution: resolution});
|
||||
result = result.unionSub(roundedCylinder, false, false);
|
||||
}
|
||||
var extrudevector=this.plane.normal.unit().times(2*radius);
|
||||
var translatedpolygon = this.translate(extrudevector.times(-0.5));
|
||||
var extrudedface = translatedpolygon.extrude(extrudevector);
|
||||
result=result.unionSub(extrudedface, false, false);
|
||||
return result;
|
||||
},
|
||||
|
||||
// returns an array with a CSG.Vector3D (center point) and a radius
|
||||
boundingSphere: function() {
|
||||
if(!this.cachedBoundingSphere)
|
||||
|
|
@ -2561,6 +2783,18 @@ CSG.Matrix4x4.rotationZ = function(degrees) {
|
|||
return new CSG.Matrix4x4(els);
|
||||
};
|
||||
|
||||
// Matrix for rotation about arbitrary point and axis
|
||||
CSG.Matrix4x4.rotation = function(rotationCenter, rotationAxis, degrees) {
|
||||
var rotationPlane = CSG.Plane.fromNormalAndPoint(rotationAxis, rotationCenter);
|
||||
var orthobasis = new CSG.OrthoNormalBasis(rotationPlane);
|
||||
var transformation = CSG.Matrix4x4.translation(rotationCenter.negated());
|
||||
transformation = transformation.multiply(orthobasis.getProjectionMatrix());
|
||||
transformation = transformation.multiply(CSG.Matrix4x4.rotationZ(degrees));
|
||||
transformation = transformation.multiply(orthobasis.getInverseProjectionMatrix());
|
||||
transformation = transformation.multiply(CSG.Matrix4x4.translation(rotationCenter));
|
||||
return transformation;
|
||||
};
|
||||
|
||||
// Create an affine matrix for translation:
|
||||
CSG.Matrix4x4.translation = function(v) {
|
||||
// parse as CSG.Vector3D, so we can pass an array or a CSG.Vector3D
|
||||
|
|
@ -3048,11 +3282,12 @@ CSG.OrthoNormalBasis.prototype = {
|
|||
},
|
||||
|
||||
getInverseProjectionMatrix: function() {
|
||||
var wtimesnormal = this.plane.normal.times(this.plane.w);
|
||||
return new CSG.Matrix4x4([
|
||||
this.u.x, this.u.y, this.u.z, 0,
|
||||
this.v.x, this.v.y, this.v.z, 0,
|
||||
this.plane.normal.x, this.plane.normal.y, this.plane.normal.z, this.plane.w,
|
||||
0,0,0,1
|
||||
this.plane.normal.x, this.plane.normal.y, this.plane.normal.z, 0,
|
||||
wtimesnormal.x, wtimesnormal.y, wtimesnormal.z, 1
|
||||
]);
|
||||
},
|
||||
|
||||
|
|
@ -3905,6 +4140,10 @@ CSG.Connector.prototype = {
|
|||
transformation = transformation.multiply(CSG.Matrix4x4.translation(other.point));
|
||||
var usAligned = us.transform(transformation);
|
||||
return transformation;
|
||||
},
|
||||
|
||||
axisLine: function() {
|
||||
return new CSG.Line3D(this.point, this.axisvector);
|
||||
},
|
||||
};
|
||||
|
||||
|
|
@ -4219,4 +4458,5 @@ CSG.Path2D.prototype = {
|
|||
});
|
||||
return new CSG.Path2D(newpoints, this.closed);
|
||||
},
|
||||
};
|
||||
};
|
||||
|
||||
|
|
@ -653,6 +653,7 @@ var vec2d = m1.leftMultiply1x2Vector(vec2d); // vector * matrix
|
|||
var m = CSG.Matrix4x4.rotationX(degrees); // matrix for rotation about X axis
|
||||
var m = CSG.Matrix4x4.rotationY(degrees); // matrix for rotation about Y axis
|
||||
var m = CSG.Matrix4x4.rotationZ(degrees); // matrix for rotation about Z axis
|
||||
var m = CSG.Matrix4x4.rotation(rotationCenter, rotationAxis, degrees); // rotation about arbitrary point and axis
|
||||
var m = CSG.Matrix4x4.translation(vec3d); // translation
|
||||
var m = CSG.Matrix4x4.scaling(vec3d); // scale
|
||||
var m = CSG.Matrix4x4.mirroring(plane); // mirroring in a plane; the argument must be a CSG.Plane
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue