Added csg.cutByPlane() and CSG.Plane.fromNormalAndPoint()

csg.js

@@ -371,7 +371,43 @@ CSG.prototype = {
       this.cachedBoundingBox = [minpoint, maxpoint];
     }
     return this.cachedBoundingBox;
-  }  
+  },
+  
+  // Cut the solid by a plane. Returns the solid on the back side of the plane
+  cutByPlane: function(plane) {
+    // Ideally we would like to do an intersection with a polygon of inifinite size
+    // but this is not supported by our implementation. As a workaround, we will create
+    // a cube, with one face on the plane, and a size larger enough so that the entire
+    // solid fits in the cube.
+
+    // find the max distance of any vertex to the center of the plane:
+    var planecenter = plane.normal.times(plane.w);
+    var maxdistance = 0;
+    this.polygons.map(function(polygon){
+      polygon.vertices.map(function(vertex){
+        var distance = vertex.pos.distanceToSquared(planecenter);
+        if(distance > maxdistance) maxdistance = distance;
+      });
+    });
+    maxdistance = Math.sqrt(maxdistance);
+    maxdistance *= 1.01; // make sure it's really larger
+    
+    // Now build a polygon on the plane, at any point farther than maxdistance from the plane center:
+    var vertices = [];
+    var orthobasis = new CSG.OrthoNormalBasis(plane);
+    vertices.push(new CSG.Vertex(orthobasis.to3D(new CSG.Vector2D(maxdistance,maxdistance))));
+    vertices.push(new CSG.Vertex(orthobasis.to3D(new CSG.Vector2D(-maxdistance,maxdistance))));
+    vertices.push(new CSG.Vertex(orthobasis.to3D(new CSG.Vector2D(-maxdistance,-maxdistance))));
+    vertices.push(new CSG.Vertex(orthobasis.to3D(new CSG.Vector2D(maxdistance,-maxdistance))));
+    var polygon = new CSG.Polygon(vertices, null, plane.flipped());
+    
+    // and extrude the polygon into a cube, backwards of the plane:
+    var cube = polygon.extrude(plane.normal.times(-maxdistance));
+    
+    // Now we can do the intersection:
+    return this.intersect(cube);
+  },
+    
 };
 
 // Parse an option from the options object
@@ -938,6 +974,14 @@ CSG.Plane.fromPoints = function(a, b, c) {
   return CSG.Plane.fromVector3Ds(a, b, c);
 };
 
+CSG.Plane.fromNormalAndPoint = function(normal, point) {
+  normal = new CSG.Vector3D(normal);
+  point = new CSG.Vector3D(point);
+  normal = normal.unit();
+  var w = point.dot(normal);
+  return new CSG.Plane(normal, w);
+};
+
 CSG.Plane.prototype = {
   flipped: function() {
     return new CSG.Plane(this.normal.negated(), -this.w);

index.html

@@ -276,6 +276,26 @@ var plane = CSG.Plane.fromPoints([5,0,0], [5, 1, 0], [3, 1, 7]);
 var cube5 = cube.mirrored(plane);
 </pre>
 
+<h2>Cutting by a plane</h2>
+A solid can be cut by a plane; only the part on the back side is kept:
+
+<pre>
+var cube = CSG.cube({radius: 10});
+
+// create a plane by specifying 3 points:
+var plane1 = CSG.Plane.fromPoints([5,0,0], [7, 1, 0], [3, 1, 7]);
+
+// or by specifying a normal and a point on the plane:
+var plane2 = CSG.Plane.fromNormalAndPoint([3, 1, 2], [5, 0, 0]);
+
+// and cut by the plane:
+var part1 = cube.cutByPlane(plane2);
+
+// or if we need the other half of the cube:
+var part2 = cube.cutByPlane(plane2.flipped());
+</pre>
+
+
 <h2>Expansion and contraction</h2>
 Expansion can be seen
 as the 3D convolution of an object with a sphere. Contraction is the reverse: the area outside the solid