diff --git a/piet-gpu-derive/src/glsl.rs b/piet-gpu-derive/src/glsl.rs
index 5164179..617669a 100644
--- a/piet-gpu-derive/src/glsl.rs
+++ b/piet-gpu-derive/src/glsl.rs
@@ -219,6 +219,7 @@ fn gen_struct_write(
     fields: &[(String, usize, LayoutType)],
 ) {
     writeln!(r, "void {}_write({}Ref ref, {} s) {{", name, name, name).unwrap();
+    writeln!(r, "    uint ix = ref.offset >> 2;").unwrap();
     let coverage = crate::layout::struct_coverage(fields, true);
     for (i, field_ixs) in coverage.iter().enumerate() {
         let mut pieces = Vec::new();
@@ -254,7 +255,7 @@ fn gen_struct_write(
             }
         }
         if !pieces.is_empty() {
-            write!(r, "    {}[{}] = ", bufname, i).unwrap();
+            write!(r, "    {}[ix + {}] = ", bufname, i).unwrap();
             for (j, piece) in pieces.iter().enumerate() {
                 if j != 0 {
                     write!(r, " | ").unwrap();
diff --git a/piet-gpu-hal/src/vulkan.rs b/piet-gpu-hal/src/vulkan.rs
index c4a07a4..e788919 100644
--- a/piet-gpu-hal/src/vulkan.rs
+++ b/piet-gpu-hal/src/vulkan.rs
@@ -449,13 +449,7 @@ impl crate::CmdBuf<VkDevice> for CmdBuf {
 
     unsafe fn clear_buffer(&self, buffer: &Buffer) {
         let device = &self.device.device;
-        device.cmd_fill_buffer(
-            self.cmd_buf,
-            buffer.buffer,
-            0,
-            vk::WHOLE_SIZE,
-            0
-        );
+        device.cmd_fill_buffer(self.cmd_buf, buffer.buffer, 0, vk::WHOLE_SIZE, 0);
     }
 
     unsafe fn copy_buffer(&self, src: &Buffer, dst: &Buffer) {
@@ -465,10 +459,7 @@ impl crate::CmdBuf<VkDevice> for CmdBuf {
             self.cmd_buf,
             src.buffer,
             dst.buffer,
-            &[vk::BufferCopy::builder()
-                .size(size)
-                .build()
-            ]
+            &[vk::BufferCopy::builder().size(size).build()],
         );
     }
 
diff --git a/piet-gpu-types/src/lib.rs b/piet-gpu-types/src/lib.rs
index 60c11ab..44d4843 100644
--- a/piet-gpu-types/src/lib.rs
+++ b/piet-gpu-types/src/lib.rs
@@ -1,3 +1,4 @@
 pub mod encoder;
 pub mod ptcl;
 pub mod scene;
+pub mod tilegroup;
diff --git a/piet-gpu-types/src/main.rs b/piet-gpu-types/src/main.rs
index 2a20c3b..7ed941f 100644
--- a/piet-gpu-types/src/main.rs
+++ b/piet-gpu-types/src/main.rs
@@ -5,6 +5,7 @@ fn main() {
         .expect("provide a module name");
     match mod_name.as_str() {
         "scene" => print!("{}", piet_gpu_types::scene::gen_gpu_scene()),
+        "tilegroup" => print!("{}", piet_gpu_types::tilegroup::gen_gpu_tilegroup()),
         "ptcl" => print!("{}", piet_gpu_types::ptcl::gen_gpu_ptcl()),
         _ => println!("Oops, unknown module name"),
     }
diff --git a/piet-gpu-types/src/scene.rs b/piet-gpu-types/src/scene.rs
index 8e4ec3c..5f95c40 100644
--- a/piet-gpu-types/src/scene.rs
+++ b/piet-gpu-types/src/scene.rs
@@ -8,8 +8,7 @@ piet_gpu! {
     #[rust_encode]
     mod scene {
         struct Bbox {
-            // TODO: this should be i16
-            bbox: [u16; 4],
+            bbox: [i16; 4],
         }
         struct Point {
             xy: [f32; 2],
@@ -19,6 +18,7 @@ piet_gpu! {
             // Note: both of the following items are actually arrays
             items: Ref<PietItem>,
             bboxes: Ref<Bbox>,
+            offset: Point,
         }
         struct PietCircle {
             rgba_color: u32,
@@ -45,6 +45,7 @@ piet_gpu! {
             points: Ref<Point>,
         }
         enum PietItem {
+            Group(SimpleGroup),
             Circle(PietCircle),
             Line(PietStrokeLine),
             Fill(PietFill),
diff --git a/piet-gpu-types/src/tilegroup.rs b/piet-gpu-types/src/tilegroup.rs
new file mode 100644
index 0000000..4824178
--- /dev/null
+++ b/piet-gpu-types/src/tilegroup.rs
@@ -0,0 +1,18 @@
+use piet_gpu_derive::piet_gpu;
+
+piet_gpu! {
+    #[gpu_write]
+    mod tilegroup {
+        struct Instance {
+            // Note: a better type would be `Ref<PietItem>` but to do that we
+            // would need cross-module references. Punt for now.
+            item_ref: u32,
+            // A better type would be Point.
+            offset: [f32; 2],
+        }
+        enum TileGroup {
+            Instance(Instance),
+            End,
+        }
+    }
+}
diff --git a/piet-gpu/shader/build.ninja b/piet-gpu/shader/build.ninja
index 037540b..5befa7f 100644
--- a/piet-gpu/shader/build.ninja
+++ b/piet-gpu/shader/build.ninja
@@ -8,3 +8,5 @@ rule glsl
   command = $glslang_validator -V -o $out $in
 
 build image.spv: glsl image.comp | scene.h
+
+build kernel1.spv: glsl kernel1.comp | scene.h tilegroup.h
diff --git a/piet-gpu/shader/image.comp b/piet-gpu/shader/image.comp
index b3e906c..60739d5 100644
--- a/piet-gpu/shader/image.comp
+++ b/piet-gpu/shader/image.comp
@@ -32,7 +32,7 @@ void main() {
     // which is horribly wasteful, but the goal is to get *some* output and
     // then optimize.
 
-    SimpleGroup group = SimpleGroup_read(SimpleGroupRef(0));
+    SimpleGroup group = PietItem_Group_read(PietItemRef(0));
     for (uint i = 0; i < group.n_items; i++) {
         PietItemRef item_ref = PietItem_index(group.items, i);
         uint tag = PietItem_tag(item_ref);
diff --git a/piet-gpu/shader/image.spv b/piet-gpu/shader/image.spv
index b1b6eb7..527c9ae 100644
Binary files a/piet-gpu/shader/image.spv and b/piet-gpu/shader/image.spv differ
diff --git a/piet-gpu/shader/kernel1.comp b/piet-gpu/shader/kernel1.comp
new file mode 100644
index 0000000..436b8bd
--- /dev/null
+++ b/piet-gpu/shader/kernel1.comp
@@ -0,0 +1,83 @@
+#version 450
+#extension GL_GOOGLE_include_directive : enable
+
+// It's possible we should lay this out with x and do our own math.
+layout(local_size_x = 1, local_size_y = 32) in;
+
+layout(set = 0, binding = 0) readonly buffer SceneBuf {
+    uint[] scene;
+};
+
+layout(set = 0, binding = 1) buffer TilegroupBuf {
+    uint[] tilegroup;
+};
+
+#include "scene.h"
+#include "tilegroup.h"
+
+// TODO: compute this
+#define WIDTH_IN_TILEGROUPS 4
+
+#define TILEGROUP_WIDTH 512
+#define TILEGROUP_HEIGHT 16
+
+#define INITIAL_ALLOC 1024
+
+#define MAX_STACK 8
+
+struct StackElement {
+    PietItemRef group;
+    uint index;
+    vec2 offset;
+};
+
+void main() {
+    StackElement stack[MAX_STACK];
+    uint stack_ix = 0;
+    uint tilegroup_ix = gl_GlobalInvocationID.y * WIDTH_IN_TILEGROUPS + gl_GlobalInvocationID.x;
+    TileGroupRef tg_ref = TileGroupRef(tilegroup_ix * INITIAL_ALLOC);
+    vec2 xy0 = vec2(gl_GlobalInvocationID.xy) * vec2(TILEGROUP_WIDTH, TILEGROUP_HEIGHT);
+    PietItemRef root = PietItemRef(0);
+    SimpleGroup group = PietItem_Group_read(root);
+    StackElement tos = StackElement(root, 0, group.offset.xy);
+
+    while (true) {
+        if (tos.index < group.n_items) {
+            Bbox bbox = Bbox_read(Bbox_index(group.bboxes, tos.index));
+            vec4 bb = vec4(bbox.bbox) + tos.offset.xyxy;
+            bool hit = max(bb.x, xy0.x) < min(bb.z, xy0.x + float(TILEGROUP_WIDTH))
+                && max(bb.y, xy0.y) < min(bb.w, xy0.y + float(TILEGROUP_HEIGHT));
+            bool is_group = false;
+            if (hit) {
+                PietItemRef item_ref = PietItem_index(group.items, tos.index);
+                is_group = PietItem_tag(item_ref) == PietItem_Group;
+            }
+            if (hit && !is_group) {
+                PietItemRef item_ref = PietItem_index(group.items, tos.index);
+                Instance ins = Instance(item_ref.offset, tos.offset);
+                TileGroup_Instance_write(tg_ref, ins);
+                tg_ref.offset += TileGroup_size;
+                // TODO: bump allocate if allocation exceeded
+            }
+            if (is_group) {
+                PietItemRef item_ref = PietItem_index(group.items, tos.index);
+                tos.index++;
+                if (tos.index < group.n_items) {
+                    stack[stack_ix++] = tos;
+                }
+                group = PietItem_Group_read(item_ref);
+                tos = StackElement(item_ref, 0, tos.offset + group.offset.xy);
+            } else {
+                tos.index++;
+            }
+        } else {
+            // processed all items in this group; pop the stack
+            if (stack_ix == 0) {
+                break;
+            }
+            tos = stack[--stack_ix];
+            group = PietItem_Group_read(tos.group);
+        }
+    }
+    TileGroup_End_write(tg_ref);
+}
diff --git a/piet-gpu/shader/kernel1.spv b/piet-gpu/shader/kernel1.spv
new file mode 100644
index 0000000..0e9a497
Binary files /dev/null and b/piet-gpu/shader/kernel1.spv differ
diff --git a/piet-gpu/shader/scene.h b/piet-gpu/shader/scene.h
index 440f491..5e36abc 100644
--- a/piet-gpu/shader/scene.h
+++ b/piet-gpu/shader/scene.h
@@ -33,7 +33,7 @@ struct PietItemRef {
 };
 
 struct Bbox {
-    uvec4 bbox;
+    ivec4 bbox;
 };
 
 #define Bbox_size 8
@@ -56,9 +56,10 @@ struct SimpleGroup {
     uint n_items;
     PietItemRef items;
     BboxRef bboxes;
+    Point offset;
 };
 
-#define SimpleGroup_size 12
+#define SimpleGroup_size 20
 
 SimpleGroupRef SimpleGroup_index(SimpleGroupRef ref, uint index) {
     return SimpleGroupRef(ref.offset + index * SimpleGroup_size);
@@ -116,10 +117,11 @@ PietStrokePolyLineRef PietStrokePolyLine_index(PietStrokePolyLineRef ref, uint i
     return PietStrokePolyLineRef(ref.offset + index * PietStrokePolyLine_size);
 }
 
-#define PietItem_Circle 0
-#define PietItem_Line 1
-#define PietItem_Fill 2
-#define PietItem_Poly 3
+#define PietItem_Group 0
+#define PietItem_Circle 1
+#define PietItem_Line 2
+#define PietItem_Fill 3
+#define PietItem_Poly 4
 #define PietItem_size 32
 
 PietItemRef PietItem_index(PietItemRef ref, uint index) {
@@ -131,7 +133,7 @@ Bbox Bbox_read(BboxRef ref) {
     uint raw0 = scene[ix + 0];
     uint raw1 = scene[ix + 1];
     Bbox s;
-    s.bbox = uvec4(raw0 & 0xffff, raw0 >> 16, raw1 & 0xffff, raw1 >> 16);
+    s.bbox = ivec4(int(raw0 << 16) >> 16, int(raw0) >> 16, int(raw1 << 16) >> 16, int(raw1) >> 16);
     return s;
 }
 
@@ -153,6 +155,7 @@ SimpleGroup SimpleGroup_read(SimpleGroupRef ref) {
     s.n_items = raw0;
     s.items = PietItemRef(raw1);
     s.bboxes = BboxRef(raw2);
+    s.offset = Point_read(PointRef(ref.offset + 12));
     return s;
 }
 
@@ -213,6 +216,10 @@ uint PietItem_tag(PietItemRef ref) {
     return scene[ref.offset >> 2];
 }
 
+SimpleGroup PietItem_Group_read(PietItemRef ref) {
+    return SimpleGroup_read(SimpleGroupRef(ref.offset + 4));
+}
+
 PietCircle PietItem_Circle_read(PietItemRef ref) {
     return PietCircle_read(PietCircleRef(ref.offset + 4));
 }
diff --git a/piet-gpu/shader/tilegroup.h b/piet-gpu/shader/tilegroup.h
new file mode 100644
index 0000000..f1d646f
--- /dev/null
+++ b/piet-gpu/shader/tilegroup.h
@@ -0,0 +1,64 @@
+// Code auto-generated by piet-gpu-derive
+
+struct InstanceRef {
+    uint offset;
+};
+
+struct TileGroupRef {
+    uint offset;
+};
+
+struct Instance {
+    uint item_ref;
+    vec2 offset;
+};
+
+#define Instance_size 12
+
+InstanceRef Instance_index(InstanceRef ref, uint index) {
+    return InstanceRef(ref.offset + index * Instance_size);
+}
+
+#define TileGroup_Instance 0
+#define TileGroup_End 1
+#define TileGroup_size 16
+
+TileGroupRef TileGroup_index(TileGroupRef ref, uint index) {
+    return TileGroupRef(ref.offset + index * TileGroup_size);
+}
+
+Instance Instance_read(InstanceRef ref) {
+    uint ix = ref.offset >> 2;
+    uint raw0 = tilegroup[ix + 0];
+    uint raw1 = tilegroup[ix + 1];
+    uint raw2 = tilegroup[ix + 2];
+    Instance s;
+    s.item_ref = raw0;
+    s.offset = vec2(uintBitsToFloat(raw1), uintBitsToFloat(raw2));
+    return s;
+}
+
+void Instance_write(InstanceRef ref, Instance s) {
+    uint ix = ref.offset >> 2;
+    tilegroup[ix + 0] = s.item_ref;
+    tilegroup[ix + 1] = floatBitsToUint(s.offset.x);
+    tilegroup[ix + 2] = floatBitsToUint(s.offset.y);
+}
+
+uint TileGroup_tag(TileGroupRef ref) {
+    return tilegroup[ref.offset >> 2];
+}
+
+Instance TileGroup_Instance_read(TileGroupRef ref) {
+    return Instance_read(InstanceRef(ref.offset + 4));
+}
+
+void TileGroup_Instance_write(TileGroupRef ref, Instance s) {
+    tilegroup[ref.offset >> 2] = TileGroup_Instance;
+    Instance_write(InstanceRef(ref.offset + 4), s);
+}
+
+void TileGroup_End_write(TileGroupRef ref) {
+    tilegroup[ref.offset >> 2] = TileGroup_End;
+}
+
diff --git a/piet-gpu/src/main.rs b/piet-gpu/src/main.rs
index 0bc4375..72f0d3c 100644
--- a/piet-gpu/src/main.rs
+++ b/piet-gpu/src/main.rs
@@ -21,7 +21,7 @@ const N_CIRCLES: usize = 100;
 fn make_scene() -> Vec<u8> {
     let mut rng = rand::thread_rng();
     let mut encoder = Encoder::new();
-    let _reserve_root = encoder.alloc_chunk(SimpleGroup::fixed_size() as u32);
+    let _reserve_root = encoder.alloc_chunk(PietItem::fixed_size() as u32);
 
     let mut items = Vec::new();
     let mut bboxes = Vec::new();
@@ -36,23 +36,30 @@ fn make_scene() -> Vec<u8> {
             },
             radius: rng.gen_range(0.0, 50.0),
         };
-        items.push(PietItem::Circle(circle));
         let bbox = Bbox {
-            // TODO: real bbox
-            bbox: [0, 0, 0, 0],
+            bbox: [
+                (circle.center.xy[0] - circle.radius).floor() as i16,
+                (circle.center.xy[1] - circle.radius).floor() as i16,
+                (circle.center.xy[0] + circle.radius).ceil() as i16,
+                (circle.center.xy[1] + circle.radius).ceil() as i16,
+            ],
         };
+        items.push(PietItem::Circle(circle));
         bboxes.push(bbox);
     }
 
     let n_items = bboxes.len() as u32;
     let bboxes = bboxes.encode(&mut encoder).transmute();
     let items = items.encode(&mut encoder).transmute();
+    let offset = Point { xy: [0.0, 0.0] };
     let simple_group = SimpleGroup {
         n_items,
         bboxes,
         items,
+        offset,
     };
-    simple_group.encode_to(&mut encoder.buf_mut()[0..SimpleGroup::fixed_size()]);
+    let root_item = PietItem::Group(simple_group);
+    root_item.encode_to(&mut encoder.buf_mut()[0..PietItem::fixed_size()]);
     // We should avoid this clone.
     encoder.buf().to_owned()
 }
@@ -66,6 +73,14 @@ fn dump_scene(buf: &[u8]) {
     }
 }
 
+fn dump_k1_data(k1_buf: &[u32]) {
+    for i in 0..k1_buf.len() {
+        if k1_buf[i] != 0 {
+            println!("{:4x}: {:8x}", i, k1_buf[i]);
+        }
+    }
+}
+
 fn main() {
     let instance = VkInstance::new().unwrap();
     unsafe {
@@ -81,35 +96,57 @@ fn main() {
             .create_buffer(std::mem::size_of_val(&scene[..]) as u64, dev)
             .unwrap();
         device.write_buffer(&scene_buf, &scene).unwrap();
+        let tilegroup_buf = device.create_buffer(384 * 1024, host).unwrap();
         let image_buf = device
             .create_buffer((WIDTH * HEIGHT * 4) as u64, host)
             .unwrap();
         let image_dev = device
             .create_buffer((WIDTH * HEIGHT * 4) as u64, dev)
             .unwrap();
+
+        let k1_code = include_bytes!("../shader/kernel1.spv");
+        let k1_pipeline = device.create_simple_compute_pipeline(k1_code, 2).unwrap();
+        let k1_ds = device
+            .create_descriptor_set(&k1_pipeline, &[&scene_dev, &tilegroup_buf])
+            .unwrap();
+
         let code = include_bytes!("../shader/image.spv");
         let pipeline = device.create_simple_compute_pipeline(code, 2).unwrap();
         let descriptor_set = device
             .create_descriptor_set(&pipeline, &[&scene_dev, &image_dev])
             .unwrap();
-        let query_pool = device.create_query_pool(2).unwrap();
+        let query_pool = device.create_query_pool(3).unwrap();
         let mut cmd_buf = device.create_cmd_buf().unwrap();
         cmd_buf.begin();
         cmd_buf.copy_buffer(&scene_buf, &scene_dev);
+        cmd_buf.clear_buffer(&tilegroup_buf);
         cmd_buf.memory_barrier();
         cmd_buf.write_timestamp(&query_pool, 0);
+        cmd_buf.dispatch(
+            &k1_pipeline,
+            &k1_ds,
+            ((WIDTH / 512) as u32, (HEIGHT / 512) as u32, 1),
+        );
+        cmd_buf.write_timestamp(&query_pool, 1);
+        cmd_buf.memory_barrier();
         cmd_buf.dispatch(
             &pipeline,
             &descriptor_set,
             ((WIDTH / TILE_W) as u32, (HEIGHT / TILE_H) as u32, 1),
         );
-        cmd_buf.write_timestamp(&query_pool, 1);
+        cmd_buf.write_timestamp(&query_pool, 2);
         cmd_buf.memory_barrier();
         cmd_buf.copy_buffer(&image_dev, &image_buf);
         cmd_buf.finish();
         device.run_cmd_buf(&cmd_buf).unwrap();
         let timestamps = device.reap_query_pool(query_pool).unwrap();
-        println!("Render time: {:.3}ms", timestamps[0] * 1e3);
+        println!("Kernel 1 time: {:.3}ms", timestamps[0] * 1e3);
+        println!("Render time: {:.3}ms", (timestamps[1] - timestamps[0]) * 1e3);
+
+        let mut k1_data: Vec<u32> = Default::default();
+        device.read_buffer(&tilegroup_buf, &mut k1_data).unwrap();
+        dump_k1_data(&k1_data);
+
         let mut img_data: Vec<u8> = Default::default();
         // Note: because png can use a `&[u8]` slice, we could avoid an extra copy
         // (probably passing a slice into a closure). But for now: keep it simple.