diff --git a/MetaballsKit/MarchingSquares.swift b/MetaballsKit/MarchingSquares.swift
index 8806a9b..dfce055 100644
--- a/MetaballsKit/MarchingSquares.swift
+++ b/MetaballsKit/MarchingSquares.swift
@@ -8,6 +8,7 @@
 
 import Foundation
 import Metal
+import simd
 
 class MarchingSquares {
     private var field: Field
@@ -15,10 +16,13 @@ class MarchingSquares {
 
     private var semaphore: DispatchSemaphore
 
+    private var samplingPipeline: MTLComputePipelineState?
+
+    private var parametersBuffer: MTLBuffer?
     /// Samples of the field's current state.
     private(set) var samplesBuffer: MTLBuffer?
     /// Indexes of geometry to render.
-    private(set) var indexes: MTLTexture?
+    private(set) var indexBuffer: MTLBuffer?
 
     private(set) var gridGeometry: MTLBuffer?
 
@@ -41,31 +45,45 @@ class MarchingSquares {
         semaphore = DispatchSemaphore(value: 1)
     }
 
-    func setupMetal(withDevice device: MTLDevice) {
-//        let samplesDesc = MTLTextureDescriptor()
-//        samplesDesc.textureType = .type2D
-//        samplesDesc.width = xSamples
-//        samplesDesc.height = ySamples
-//        samplesDesc.pixelFormat = .r32Float
-//        samples = device.makeTexture(descriptor: samplesDesc)
-//
-//        let indexesDesc = MTLTextureDescriptor()
-//        indexesDesc.textureType = .type2D
-//        indexesDesc.width = xSamples - 1
-//        indexesDesc.height = ySamples - 1
-//        indexesDesc.pixelFormat = .a8Unorm
-//        indexes = device.makeTexture(descriptor: indexesDesc)
+    func setupMetal(withDevice device: MTLDevice, library: MTLLibrary) {
+        guard let samplingFunction = library.makeFunction(name: "samplingKernel") else {
+            fatalError("Couldn't get samplingKernel function from library")
+        }
+        do {
+            samplingPipeline = try device.makeComputePipelineState(function: samplingFunction)
+        } catch let e {
+            fatalError("Error building compute pipeline state for sampling kernel: \(e)")
+        }
+
+        let parametersLength = MemoryLayout<simd.packed_int2>.stride * 3 + MemoryLayout<simd.uint>.stride
+        parametersBuffer = device.makeBuffer(length: parametersLength, options: .storageModeShared)
+        populateParametersBuffer()
     }
 
     func fieldDidResize() {
         guard let device = gridGeometry?.device else {
             return
         }
+        populateParametersBuffer()
         populateGrid(withDevice: device)
         populateSamples(withDevice: device)
         lastSamplesCount = samplesCount
     }
 
+    func populateParametersBuffer() {
+        guard let buffer = parametersBuffer else {
+            print("Tried to copy parameters buffer before buffer was allocated!")
+            return
+        }
+        let params: [uint] = [
+            field.size.x, field.size.y,
+            uint(xSamples), uint(ySamples),
+            sampleGridSize.x, sampleGridSize.y,
+            uint(field.balls.count)
+        ]
+        memcpy(buffer.contents(), params, MemoryLayout<uint>.stride * params.count)
+    }
+
     func populateGrid(withDevice device: MTLDevice) {
         guard lastSamplesCount != samplesCount else {
             return
@@ -97,24 +115,45 @@ class MarchingSquares {
     }
 
     func populateSamples(withDevice device: MTLDevice) {
-        var samples = [Float]()
-        samples.reserveCapacity(samplesCount)
+//        var samples = [Float]()
+//        samples.reserveCapacity(samplesCount)
 
-        for ys in 0..<ySamples {
-            let y = Float(ys * Int(sampleGridSize.y))
-            for xs in 0..<xSamples {
-                let x = Float(xs * Int(sampleGridSize.x))
-                let sample = field.sample(at: Float2(x: x, y: y))
-                samples.append(sample)
-            }
-        }
+//        for ys in 0..<ySamples {
+//            let y = Float(ys * Int(sampleGridSize.y))
+//            for xs in 0..<xSamples {
+//                let x = Float(xs * Int(sampleGridSize.x))
+//                let sample = field.sample(at: Float2(x: x, y: y))
+//                samples.append(sample)
+//            }
+//        }
 
         let samplesLength = MemoryLayout<Float>.stride * samplesCount
-        if let buffer = device.makeBuffer(length: MemoryLayout<Float>.stride * samples.count, options: .storageModeShared) {
-            memcpy(buffer.contents(), samples, samplesLength)
-            samplesBuffer = buffer
-        } else {
-            fatalError("Couldn't create buffer for samples")
+        samplesBuffer = device.makeBuffer(length: samplesLength, options: .storageModePrivate)
+        if samplesBuffer == nil {
+            fatalError("Couldn't create samplesBuffer!")
         }
     }
+
+    func encodeSamplingKernel(intoBuffer buffer: MTLCommandBuffer) {
+        guard let samplingPipeline = samplingPipeline else {
+            print("Encode called before sampling pipeline was set up!")
+            return
+        }
+        guard let encoder = buffer.makeComputeCommandEncoder() else {
+            print("Couldn't create compute encoder")
+            return
+        }
+        encoder.label = "Sample Field"
+        encoder.setComputePipelineState(samplingPipeline)
+        encoder.setBuffer(parametersBuffer, offset: 0, index: 0)
+        encoder.setBuffer(field.ballBuffer, offset: 0, index: 1)
+        encoder.setBuffer(samplesBuffer, offset: 0, index: 2)
+
+        // Dispatch!
+        let gridSize = MTLSize(width: xSamples, height: ySamples, depth: 1)
+        let threadgroupSize = MTLSize(width: xSamples, height: 1, depth: 1)
+        encoder.dispatchThreads(gridSize, threadsPerThreadgroup: threadgroupSize)
+
+        encoder.endEncoding()
+    }
 }
diff --git a/MetaballsKit/Renderer.swift b/MetaballsKit/Renderer.swift
index d7a554e..731d0c7 100644
--- a/MetaballsKit/Renderer.swift
+++ b/MetaballsKit/Renderer.swift
@@ -43,7 +43,7 @@ public class Renderer: NSObject, MTKViewDelegate {
             configureMarchingSquaresPipeline(withPixelFormat: view.colorPixelFormat)
 
             delegate.field.setupMetal(withDevice: device)
-            delegate.marchingSquares.setupMetal(withDevice: device)
+            delegate.marchingSquares.setupMetal(withDevice: device, library: library)
             delegate.marchingSquares.populateGrid(withDevice: device)
             delegate.marchingSquares.populateSamples(withDevice: device)
         }
@@ -51,9 +51,9 @@ public class Renderer: NSObject, MTKViewDelegate {
 
     private var device: MTLDevice
 
-    private lazy var library: MTLLibrary? = {
+    private lazy var library: MTLLibrary = {
         let bundle = Bundle(for: type(of: self))
-        return try? device.makeDefaultLibrary(bundle: bundle)
+        return try! device.makeDefaultLibrary(bundle: bundle)
     }()
 
     private var commandQueue: MTLCommandQueue
@@ -90,10 +90,6 @@ public class Renderer: NSObject, MTKViewDelegate {
     }
 
     private func configurePixelPipeline(withPixelFormat pixelFormat: MTLPixelFormat) {
-        guard let library = library else {
-            fatalError("Couldn't get Metal library")
-        }
-
         let vertexShader = library.makeFunction(name: "passthroughVertexShader")
         let fragmentShader = library.makeFunction(name: "sampleToColorShader")
 
@@ -124,10 +120,6 @@ public class Renderer: NSObject, MTKViewDelegate {
     }
 
     private func configureMarchingSquaresPipeline(withPixelFormat pixelFormat: MTLPixelFormat) {
-        guard let library = library else {
-            fatalError("Couldn't get Metal library")
-        }
-
         guard let vertexShader = library.makeFunction(name: "gridVertexShader"),
               let fragmentShader = library.makeFunction(name: "gridFragmentShader") else {
             fatalError("Couldn't get marching squares vertex or fragment function from library")
@@ -209,7 +201,7 @@ public class Renderer: NSObject, MTKViewDelegate {
 
         field.update()
         if let ms = delegate?.marchingSquares {
-            ms.populateSamples(withDevice: device)
+            ms.populateParametersBuffer()
         }
 
         if self.pixelGeometry == nil {
@@ -233,6 +225,9 @@ public class Renderer: NSObject, MTKViewDelegate {
 //            }
 
             if let marchingSquares = delegate?.marchingSquares {
+                // Compute samples first.
+                marchingSquares.encodeSamplingKernel(intoBuffer: buffer)
+
                 // Render the marching squares version over top of the pixel version.
                 // We need our own render pass descriptor that specifies that we load the results of the previous pass to make this render pass appear on top of the other.
                 let pass = renderPass.copy() as! MTLRenderPassDescriptor
diff --git a/MetaballsKit/Shaders/MarchingSquares.metal b/MetaballsKit/Shaders/MarchingSquares.metal
index d5051ba..1a8b9a3 100644
--- a/MetaballsKit/Shaders/MarchingSquares.metal
+++ b/MetaballsKit/Shaders/MarchingSquares.metal
@@ -10,6 +10,17 @@
 #include "ShaderTypes.hh"
 using namespace metal;
 
+struct MarchingSquaresParameters {
+    /// Field size in pixels.
+    packed_uint2 pixelSize;
+    /// Field size in grid units.
+    packed_uint2 gridSize;
+    /// Size of a cell in pixels.
+    packed_uint2 cellSize;
+    /// Number of balls in the array above.
+    uint ballsCount;
+};
+
 struct Rect {
     float4x4 transform;
     float4 color;
@@ -22,6 +33,37 @@ struct RasterizerData {
     int instance;
 };
 
+kernel void
+generateGridGeometry()
+{
+}
+
+/// Sample the field at regularly spaced intervals and populate `samples` with the resulting values.
+kernel void
+samplingKernel(constant MarchingSquaresParameters &parameters [[buffer(0)]],
+               constant Ball *balls [[buffer(1)]],
+               device float *samples [[buffer(2)]],
+               uint2 position [[thread_position_in_grid]])
+{
+    // Find the midpoint of this grid cell.
+    const float2 point = float2(position.x * parameters.cellSize.x + (parameters.cellSize.x / 2.0),
+                                position.y * parameters.cellSize.y + (parameters.cellSize.y / 2.0));
+
+    // Sample the grid.
+    float sample = 0.0;
+    for (uint i = 0; i < parameters.ballsCount; i++) {
+        constant Ball &ball = balls[i];
+        float r2 = ball.z * ball.z;
+        float xDiff = point.x - ball.x;
+        float yDiff = point.y - ball.y;
+        sample += r2 / ((xDiff * xDiff) + (yDiff * yDiff));
+    }
+
+    // Playing a bit fast and loose with these values here. The compute grid is the size of the grid itself, so parameters.gridSize == [[threads_per_grid]].
+    uint idx = position.y * parameters.gridSize.x + position.x;
+    samples[idx] = sample;
+}
+
 vertex RasterizerData
 gridVertexShader(constant Vertex *vertexes [[buffer(0)]],
                  constant Rect *rects [[buffer(1)]],
diff --git a/MetaballsKit/Shaders/ShaderTypes.hh b/MetaballsKit/Shaders/ShaderTypes.hh
index a75ebcb..904e721 100644
--- a/MetaballsKit/Shaders/ShaderTypes.hh
+++ b/MetaballsKit/Shaders/ShaderTypes.hh
@@ -11,6 +11,9 @@
 
 #include <metal_stdlib>
 
+/// A Ball is a float 3-tuple: (x, y, r).
+typedef float3 Ball;
+
 struct Vertex {
     float2 position;
     float2 textureCoordinate;
diff --git a/MetaballsKit/Shaders/Shaders.metal b/MetaballsKit/Shaders/Shaders.metal
index 52cd4b4..48caa42 100644
--- a/MetaballsKit/Shaders/Shaders.metal
+++ b/MetaballsKit/Shaders/Shaders.metal
@@ -39,8 +39,6 @@ struct Parameters {
     float3x3 colorTransform;
 };
 
-typedef float3 Ball;
-
 #pragma mark - Vertex
 
 vertex RasterizerData