Magellan index

build.sbt

@@ -1,6 +1,6 @@
 name := "magellan"
 
-version := "1.0.4"
+version := "1.0.5-SNAPSHOT"
 
 organization := "harsha2010"
 

src/main/scala/magellan/BoundingBox.scala

@@ -0,0 +1,92 @@
+/**
+ * Copyright 2015 Ram Sriharsha
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package magellan
+
+import com.fasterxml.jackson.annotation.JsonProperty
+
+/**
+ * A bounding box is an axis parallel rectangle. It is completely specified by
+ * the bottom left and top right points.
+ *
+ * @param xmin the minimum x coordinate of the rectangle.
+ * @param ymin the minimum y coordinate of the rectangle.
+ * @param xmax the maximum x coordinate of the rectangle.
+ * @param ymax the maximum y coordinate of the rectangle.
+ */
+case class BoundingBox(xmin: Double, ymin: Double, xmax: Double, ymax: Double) {
+
+  private def this() {this(0, 0, 0, 0)}
+
+  @JsonProperty
+  def getXmin(): Double = xmin
+
+  @JsonProperty
+  def getYmin(): Double = ymin
+
+  @JsonProperty
+  def getXmax(): Double = xmax
+
+  @JsonProperty
+  def getYmax(): Double = ymax
+
+  private [magellan] def intersects(other: BoundingBox): Boolean = {
+    val BoundingBox(otherxmin, otherymin, otherxmax, otherymax) = other
+    !(otherxmin >= xmax || otherymin >= ymax || otherymax <= ymin || otherxmax <= xmin)
+  }
+
+  private [magellan] def contains(other: BoundingBox): Boolean = {
+    val BoundingBox(otherxmin, otherymin, otherxmax, otherymax) = other
+    (xmin <= otherxmin && ymin <= otherymin && xmax >= otherxmax && ymax >= otherymax)
+  }
+
+  private [magellan] def contains(point: Point): Boolean = {
+    val (x, y) = (point.getX(), point.getY())
+    (xmin <= x && ymin <= y && xmax >= x && ymax >= y)
+  }
+
+  private [magellan] def intersects(point: Point): Boolean = {
+    val lines = Array(
+      Line(Point(xmin, ymin), Point(xmax, ymin)),
+      Line(Point(xmin, ymin), Point(xmin, ymax)),
+      Line(Point(xmax, ymin), Point(xmax, ymax)),
+      Line(Point(xmin, ymax), Point(xmax, ymax)))
+
+    lines exists (_ contains point)
+  }
+
+  private [magellan] def disjoint(shape: Shape): Boolean = {
+    // a bounding box is disjoint from a shape if it does not intersect the shape
+    // nor is contained in nor contains the shape.
+
+    val vertices = Array(Point(xmin, ymin),
+      Point(xmax, ymin),
+      Point(xmax, ymax),
+      Point(xmin, ymax)
+    )
+
+    val lines = Array(
+      Line(Point(xmin, ymin), Point(xmax, ymin)),
+      Line(Point(xmin, ymin), Point(xmin, ymax)),
+      Line(Point(xmax, ymin), Point(xmax, ymax)),
+      Line(Point(xmin, ymax), Point(xmax, ymax)))
+
+    !contains(shape.boundingBox) &&
+    !(vertices exists (shape contains _)) &&
+    !(lines exists(shape intersects _))
+  }
+
+}

src/main/scala/magellan/Line.scala

@@ -125,7 +125,7 @@ class Line extends Shape {
    */
   override def transform(fn: (Point) => Point): Shape = ???
 
-  override def boundingBox: ((Double, Double), (Double, Double)) = {
+  override def boundingBox: BoundingBox = {
     val (xmin, xmax) = if (start.getX() < end.getX()) {
       (start.getX(), end.getX())
     } else {
@@ -136,7 +136,7 @@ class Line extends Shape {
     } else {
       (end.getY(), start.getY())
     }
-    ((xmin, ymin), (xmax, ymax))
+    BoundingBox(xmin, ymin, xmax, ymax)
   }
 
   def canEqual(other: Any): Boolean = other.isInstanceOf[Line]

src/main/scala/magellan/Point.scala

@@ -89,7 +89,7 @@ class Point extends Shape {
       ("y" -> y)
 
   @JsonProperty
-  override def boundingBox: ((Double, Double), (Double, Double)) = ((x, y), (x, y))
+  override def boundingBox = BoundingBox(x, y, x, y)
 
   @JsonIgnore
   override def isEmpty(): Boolean = true

src/main/scala/magellan/PolyLine.scala

@@ -32,7 +32,9 @@ class PolyLine(
     val indices: Array[Int],
     val xcoordinates: Array[Double],
     val ycoordinates: Array[Double],
-    override val boundingBox: Tuple2[Tuple2[Double, Double], Tuple2[Double, Double]]) extends Shape {
+    override val boundingBox: BoundingBox) extends Shape {
+
+  private def this() {this(Array(0), Array(), Array(), BoundingBox(0,0,0,0))}
 
   override def getType(): Int = 3
 
@@ -69,8 +71,8 @@ class PolyLine(
   }
 
   def exceedsBounds(point:Point):Boolean = {
-    val ((pt_xmin, pt_ymin), (pt_xmax, pt_ymax)) = point.boundingBox
-    val ((xmin, ymin), (xmax, ymax)) = boundingBox
+    val BoundingBox(pt_xmin, pt_ymin, pt_xmax, pt_ymax) = point.boundingBox
+    val BoundingBox(xmin, ymin, xmax, ymax) = boundingBox
 
     pt_xmin < xmin && pt_ymin < ymin ||
     pt_xmax > xmax && pt_ymax > ymax
@@ -170,7 +172,7 @@ object PolyLine {
       indices,
       points.map(_.getX()),
       points.map(_.getY()),
-      ((xmin, ymin), (xmax, ymax))
+      BoundingBox(xmin, ymin, xmax, ymax)
     )
   }
 }

src/main/scala/magellan/Polygon.scala

@@ -35,7 +35,9 @@ class Polygon(
     val indices: Array[Int],
     val xcoordinates: Array[Double],
     val ycoordinates: Array[Double],
-    override val boundingBox: Tuple2[Tuple2[Double, Double], Tuple2[Double, Double]]) extends Shape {
+    override val boundingBox: BoundingBox) extends Shape {
+
+  private def this() {this(Array(0), Array(), Array(), BoundingBox(0,0,0,0))}
 
   @inline private def intersects(point: Point, line: Line): Boolean = {
     val (start, end) = (line.getStart(), line.getEnd())
@@ -251,6 +253,57 @@ class Polygon(
     }
   }
 
+  private [magellan] def contains(box: BoundingBox): Boolean = {
+    val BoundingBox(xmin, ymin, xmax, ymax) = box
+    val lines = Array(
+      Line(Point(xmin, ymin), Point(xmax, ymin)),
+      Line(Point(xmin, ymin), Point(xmin, ymax)),
+      Line(Point(xmax, ymin), Point(xmax, ymax)),
+      Line(Point(xmin, ymax), Point(xmax, ymax)))
+
+    !(lines exists (!contains(_)))
+  }
+
+  private [magellan] def intersects(box: BoundingBox): Boolean = {
+    val BoundingBox(xmin, ymin, xmax, ymax) = box
+    val lines = Array(
+      Line(Point(xmin, ymin), Point(xmax, ymin)),
+      Line(Point(xmin, ymin), Point(xmin, ymax)),
+      Line(Point(xmax, ymin), Point(xmax, ymax)),
+      Line(Point(xmin, ymax), Point(xmax, ymax)))
+
+    lines exists (intersects(_))
+  }
+
+  private [magellan] def intersects(point: Point): Boolean = {
+    // Check if any edge intersects this line
+    var i = 0
+    val length = xcoordinates.length
+    var found = false
+    var start:Point = null
+    var end:Point = new Point()
+    val edge = new Line()
+
+    while (i < length && !found) {
+      if (start == null) {
+        start = new Point()
+        start.setX(xcoordinates(i))
+        start.setY(ycoordinates(i))
+      } else {
+        start = end
+        end = new Point()
+        end.setX(xcoordinates(i))
+        end.setY(ycoordinates(i))
+        edge.setStart(start)
+        edge.setEnd(end)
+        found = edge.contains(point)
+      }
+      i += 1
+    }
+    found
+  }
+
+
   @JsonProperty
   override def getType(): Int = 5
 
@@ -312,7 +365,7 @@ object Polygon {
         indices,
         points.map(_.getX()),
         points.map(_.getY()),
-        ((xmin, ymin), (xmax, ymax))
+        BoundingBox(xmin, ymin, xmax, ymax)
       )
   }
-}
+}

src/main/scala/magellan/Shape.scala

@@ -25,13 +25,11 @@ import org.apache.spark.sql.types._
  */
 trait Shape extends DataType with Serializable {
 
-  type BoundingBox = Tuple2[Tuple2[Double, Double], Tuple2[Double, Double]]
-
   override def defaultSize: Int = 4096
 
   override def asNullable: DataType = this
 
-  @JsonProperty
+  @JsonIgnore
   def getType(): Int
 
   /**
@@ -50,6 +48,7 @@ trait Shape extends DataType with Serializable {
    *
    * @return <code>true</code> if this <code>Shape</code> is valid
    */
+  @JsonIgnore
   def isValid(): Boolean = true
 
   /**
@@ -93,10 +92,9 @@ trait Shape extends DataType with Serializable {
    * @see Shape#disjoint
    */
   def intersects(other: Shape, bitMask: Int): Boolean = {
-    val ((xmin, ymin), (xmax, ymax)) = this.boundingBox
-    val ((otherxmin, otherymin), (otherxmax, otherymax)) = other.boundingBox
-    if ((xmin <= otherxmin && xmax >= otherxmin && ymin <= otherymin && ymax >= otherymin) ||
-      (otherxmin <= xmin && otherxmax >= xmin && otherymin <= ymin && otherymax >= ymin)) {
+    if (boundingBox.intersects(other.boundingBox) ||
+        boundingBox.contains(other.boundingBox) ||
+        other.boundingBox.contains(boundingBox)) {
       (this, other) match {
         case (p: Point, q: Point) => p.equals(q)
         case (p: Point, q: Polygon) => q.intersects(Line(p, p))
@@ -130,7 +128,12 @@ trait Shape extends DataType with Serializable {
    *                Returns <code>false</code> if both <code>Shape</code>s are points
    */
   def touches(other: Shape): Boolean = {
-    ???
+    (this, other) match {
+      case (p: Point, q: Point) => p.equals(q)
+      case (p: Point, q: Polygon) => q.touches(p)
+      case (p: Polygon, q: Point) => p.touches(q)
+      case _ => ???
+    }
   }
 
   /**
@@ -155,11 +158,10 @@ trait Shape extends DataType with Serializable {
    * @return true if this shape contains the other.
    */
   def contains(other: Shape): Boolean = {
-    // check if the bounding box encompasses other's bounding box.
+    // check if the bounding box intersects other's bounding box.
     // if not, no need to check further
-    val ((xmin, ymin), (xmax, ymax)) = this.boundingBox
-    val ((otherxmin, otherymin), (otherxmax, otherymax)) = other.boundingBox
-    if (xmin <= otherxmin && ymin <= otherymin && xmax >= otherxmax && ymax >= otherymax) {
+
+    if (boundingBox.contains(other.boundingBox)) {
       (this, other) match {
         case (p: Point, q: Point) => p.equals(q)
         case (p: Point, q: Polygon) => false
@@ -176,7 +178,7 @@ trait Shape extends DataType with Serializable {
   }
 
   @JsonProperty
-  def boundingBox: Tuple2[Tuple2[Double, Double], Tuple2[Double, Double]]
+  def boundingBox: BoundingBox
 
   /**
    * Tests whether this shape is within the
@@ -296,9 +298,9 @@ object NullShape extends Shape {
 
   override def transform(fn: (Point) => Point): Shape = this
 
-  override def boundingBox: ((Double, Double), (Double, Double)) = (
-      (Int.MinValue, Int.MinValue),
-      (Int.MaxValue, Int.MaxValue)
+  override def boundingBox = BoundingBox(
+      Int.MinValue, Int.MinValue,
+      Int.MaxValue, Int.MaxValue
     )
 }
 

src/main/scala/magellan/dsl/package.scala

@@ -44,6 +44,8 @@ package object dsl {
 
     def transform(fn: Point => Point) = Transformer(expr, fn)
 
+    def geohash(other: Expression, precision: Int) = GeohashIndexer(other, precision)
+
   }
 
   trait ExpressionConversions {
@@ -69,6 +71,8 @@ package object dsl {
 
       def transform(fn: Point => Point): Column = Column(Transformer(c.expr, fn))
 
+      def geohash(precision: Int): Column = Column(GeohashIndexer(c.expr, precision))
+
     }
 
     implicit def point(x: Expression, y: Expression) = PointConverter(x, y)

src/main/scala/magellan/index/Index.scala

@@ -0,0 +1,37 @@
+/**
+ * Copyright 2015 Ram Sriharsha
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package magellan.index
+
+import magellan.BoundingBox
+
+/**
+ * An abstraction for a spatial curve based 2D Index.
+ * A spatial curve represents a two dimensional grid of a given precision.
+ */
+trait Index extends Serializable {
+
+  def precision(): Int
+
+  def code(): String
+
+  def bits(): Long
+
+  def boundingBox(): BoundingBox
+
+  def toBase32(): String
+
+}