diff --git a/NDimensionalAffineTransform/build.sbt b/NDimensionalAffineTransform/build.sbt
new file mode 100644
index 00000000..f3bba66c
--- /dev/null
+++ b/NDimensionalAffineTransform/build.sbt
@@ -0,0 +1 @@
+libraryDependencies += "org.scalatest" %% "scalatest" % "3.0.4" % Test
diff --git a/NDimensionalAffineTransform/src/main/scala/com/thoughtworks/compute/NDimensionalAffineTransform.scala b/NDimensionalAffineTransform/src/main/scala/com/thoughtworks/compute/NDimensionalAffineTransform.scala
new file mode 100644
index 00000000..5a14608d
--- /dev/null
+++ b/NDimensionalAffineTransform/src/main/scala/com/thoughtworks/compute/NDimensionalAffineTransform.scala
@@ -0,0 +1,99 @@
+package com.thoughtworks.compute
+
+import scala.annotation.tailrec
+
+/**
+  * @author 杨博 (Yang Bo)
+  */
+object NDimensionalAffineTransform {
+
+  def preConcatenate(matrix01: Array[Double], matrix12: Array[Double], length0: Int): Array[Double] = {
+    val length1 = matrix01.length / (length0 + 1)
+    val length2 = matrix12.length / (length1 + 1)
+    val matrix02 = Array.ofDim[Double]((length0 + 1) * length2)
+    concatenate(matrix01, matrix12, matrix02, length0, length1, length2)
+    matrix02
+  }
+
+  def concatenate(matrix01: Array[Double],
+                  matrix12: Array[Double],
+                  matrix02: Array[Double],
+                  length0: Int,
+                  length1: Int,
+                  length2: Int): Unit = {
+
+    @tailrec
+    def loop2(index2: Int): Unit = {
+      if (index2 < length2) {
+        @tailrec
+        def loop0(index0: Int): Unit = {
+          if (index0 < length0) {
+            @tailrec
+            def loop1(index1: Int, accumulator: Double): Double = {
+              if (index1 < length1) {
+                loop1(index1 + 1,
+                      accumulator +
+                        matrix12(index2 * (length1 + 1) + index1) *
+                          matrix01(index1 * (length0 + 1) + index0))
+              } else {
+                accumulator
+              }
+            }
+            matrix02(index2 * (length0 + 1) + index0) = loop1(0, 0.0)
+
+            loop0(index0 + 1)
+          }
+        }
+        loop0(0)
+        @tailrec
+        def loop1(index1: Int, accumulator: Double): Double = {
+          if (index1 < length1) {
+            loop1(index1 + 1,
+                  accumulator +
+                    matrix12(index2 * (length1 + 1) + index1) *
+                      matrix01(index1 * (length0 + 1) + length0))
+          } else {
+            accumulator
+          }
+        }
+        matrix02(index2 * (length0 + 1) + length0) = loop1(0, matrix12(index2 * (length1 + 1) + length1))
+        loop2(index2 + 1)
+      }
+    }
+    loop2(0)
+
+  }
+
+  def transform(matrix: Array[Double], source: Array[Double]): Array[Double] = {
+    val sourceLength = source.length
+    val destination = Array.ofDim[Double](matrix.length / (sourceLength + 1))
+    transform(matrix, source, destination)
+    destination
+  }
+
+  private def transform(matrix: Array[Double], source: Array[Double], destination: Array[Double]): Unit = {
+    val sourceLength = source.length
+    val destinationLength = destination.length
+    if (matrix.length != (sourceLength + 1) * destinationLength) {
+      throw new IllegalArgumentException
+    }
+    @tailrec
+    def rowLoop(y: Int): Unit = {
+      if (y < destinationLength) {
+        @tailrec
+        def columnLoop(x: Int, accumulator: Double): Double = {
+          if (x < sourceLength) {
+            columnLoop(x + 1, accumulator + matrix(y * (sourceLength + 1) + x) * source(x))
+          } else {
+            accumulator
+          }
+        }
+        destination(y) = columnLoop(0, matrix(y * (sourceLength + 1) + sourceLength))
+
+        rowLoop(y + 1)
+      }
+    }
+    rowLoop(0)
+  }
+
+}
diff --git a/NDimensionalAffineTransform/src/test/scala/com/thoughtworks/compute/NDimensionalAffineTransformSpec.scala b/NDimensionalAffineTransform/src/test/scala/com/thoughtworks/compute/NDimensionalAffineTransformSpec.scala
new file mode 100644
index 00000000..34cc14a3
--- /dev/null
+++ b/NDimensionalAffineTransform/src/test/scala/com/thoughtworks/compute/NDimensionalAffineTransformSpec.scala
@@ -0,0 +1,48 @@
+package com.thoughtworks.compute
+
+import java.awt.geom.AffineTransform
+
+import org.scalatest._
+
+/**
+  * @author 杨博 (Yang Bo)
+  */
+final class NDimensionalAffineTransformSpec extends FreeSpec with Matchers {
+
+  def arrayToAffineTransform(matrix: Array[Double]): AffineTransform = {
+    matrix match {
+      case Array(m00, m01, m02, m10, m11, m12) =>
+        new AffineTransform(m00, m10, m01, m11, m02, m12)
+      case _ =>
+        throw new IllegalArgumentException
+    }
+  }
+
+  private def checkConcatenate2D(matrix0: Array[Double], matrix1: Array[Double]) = {
+    val at = arrayToAffineTransform(matrix0)
+    at.preConcatenate(arrayToAffineTransform(matrix1))
+
+    val expected = arrayToAffineTransform(NDimensionalAffineTransform.preConcatenate(matrix0, matrix1, 2))
+    at should be(expected)
+
+  }
+
+  "concatenate 2D" in {
+    checkConcatenate2D(
+      Array(
+        1.0, 0.0, 3.5, //
+        0.0, 1.0, 4.2
+      ),
+      Array(
+        3.0, 0.0, 0.0, //
+        0.0, 2.0, 0.0
+      )
+    )
+
+    checkConcatenate2D(
+      Array.fill(6)(math.random()),
+      Array.fill(6)(math.random())
+    )
+  }
+
+}
diff --git a/build.sbt b/build.sbt
index 7d0d8b59..e537f263 100644
--- a/build.sbt
+++ b/build.sbt
@@ -10,7 +10,9 @@ lazy val Expressions = project
 
 lazy val Trees = project.dependsOn(Expressions)
 
-lazy val OpenCLKernelBuilder = project.dependsOn(Expressions, Trees % Test)
+lazy val NDimensionalAffineTransform = project
+
+lazy val OpenCLKernelBuilder = project.dependsOn(NDimensionalAffineTransform, Expressions, Trees % Test)
 
 lazy val Tensors = project.dependsOn(OpenCLKernelBuilder, OpenCL, Trees)