public Class MeshOptimizer

When a GPU renders triangle meshes, various stages of the GPU pipeline have to process vertex and index data. The efficiency of these stages depends on the data you feed to them; this library provides algorithms to help optimize meshes for these stages, as well as algorithms to reduce the mesh complexity and storage overhead.

Pipeline

When optimizing a mesh, you should typically feed it through a set of optimizations (the order is important!):

• Indexing
• Vertex cache optimization
• Overdraw optimization
• Vertex fetch optimization
• Vertex quantization
• (optional) Vertex/index buffer compression

Indexing

Most algorithms in this library assume that a mesh has a vertex buffer and an index buffer. For algorithms to work well and also for GPU to render your mesh efficiently, the vertex buffer has to have no redundant vertices; you can generate an index buffer from an unindexed vertex buffer or reindex an existing (potentially redundant) index buffer as follows:

First, generate a remap table from your existing vertex (and, optionally, index) data:

size_t index_count = face_count * 3;
std::vector<unsigned int> remap(index_count); // allocate temporary memory for the remap table
size_t vertex_count = meshopt_generateVertexRemap(&remap[0], NULL, index_count, &unindexed_vertices[0], index_count, sizeof(Vertex));

Note that in this case we only have an unindexed vertex buffer; the remap table is generated based on binary equivalence of the input vertices, so the resulting mesh will render the same way.

After generating the remap table, you can allocate space for the target vertex buffer (vertex_count elements) and index buffer (index_count elements) and generate them:

meshopt_remapIndexBuffer(indices, NULL, index_count, &remap[0]);
meshopt_remapVertexBuffer(vertices, &unindexed_vertices[0], index_count, sizeof(Vertex), &remap[0]);

You can then further optimize the resulting buffers by calling the other functions on them in-place.

Vertex cache optimization

When the GPU renders the mesh, it has to run the vertex shader for each vertex; usually GPUs have a built-in fixed size cache that stores the transformed vertices (the result of running the vertex shader), and uses this cache to reduce the number of vertex shader invocations. This cache is usually small, 16-32 vertices, and can have different replacement policies; to use this cache efficiently, you have to reorder your triangles to maximize the locality of reused vertex references like so:

meshopt_optimizeVertexCache(indices, indices, index_count, vertex_count);

Overdraw optimization

After transforming the vertices, GPU sends the triangles for rasterization which results in generating pixels that are usually first ran through the depth test, and pixels that pass it get the pixel shader executed to generate the final color. As pixel shaders get more expensive, it becomes more and more important to reduce overdraw. While in general improving overdraw requires view-dependent operations, this library provides an algorithm to reorder triangles to minimize the overdraw from all directions, which you should run after vertex cache optimization like this:

meshopt_optimizeOverdraw(indices, indices, index_count, &vertices[0].x, vertex_count, sizeof(Vertex), 1.05f);

The overdraw optimizer needs to read vertex positions as a float3 from the vertex; the code snippet above assumes that the vertex stores position as float x, y, z.

When performing the overdraw optimization you have to specify a floating-point threshold parameter. The algorithm tries to maintain a balance between vertex cache efficiency and overdraw; the threshold determines how much the algorithm can compromise the vertex cache hit ratio, with 1.05 meaning that the resulting ratio should be at most 5% worse than before the optimization.

Vertex fetch optimization

After the final triangle order has been established, we still can optimize the vertex buffer for memory efficiency. Before running the vertex shader GPU has to fetch the vertex attributes from the vertex buffer; the fetch is usually backed by a memory cache, and as such optimizing the data for the locality of memory access is important. You can do this by running this code:

To optimize the index/vertex buffers for vertex fetch efficiency, call:

meshopt_optimizeVertexFetch(vertices, indices, index_count, vertices, vertex_count, sizeof(Vertex));

This will reorder the vertices in the vertex buffer to try to improve the locality of reference, and rewrite the indices in place to match; if the vertex data is stored using multiple streams, you should use optimizeVertexFetchRemap instead. This optimization has to be performed on the final index buffer since the optimal vertex order depends on the triangle order.

Note that the algorithm does not try to model cache replacement precisely and instead just orders vertices in the order of use, which generally produces results that are close to optimal.

Vertex quantization

To optimize memory bandwidth when fetching the vertex data even further, and to reduce the amount of memory required to store the mesh, it is often beneficial to quantize the vertex attributes to smaller types. While this optimization can technically run at any part of the pipeline (and sometimes doing quantization as the first step can improve indexing by merging almost identical vertices), it generally is easier to run this after all other optimizations since some of them require access to float3 positions.

Quantization is usually domain specific; it's common to quantize normals using 3 8-bit integers but you can use higher-precision quantization (for example using 10 bits per component in a 10_10_10_2 format), or a different encoding to use just 2 components. For positions and texture coordinate data the two most common storage formats are half precision floats, and 16-bit normalized integers that encode the position relative to the AABB of the mesh or the UV bounding rectangle.

The number of possible combinations here is very large but this library does provide the building blocks, specifically functions to quantize floating point values to normalized integers, as well as half-precision floats. For example, here's how you can quantize a normal:

unsigned int normal =
    (meshopt_quantizeUnorm(v.nx, 10) << 20) |
    (meshopt_quantizeUnorm(v.ny, 10) << 10) |
     meshopt_quantizeUnorm(v.nz, 10);

and here's how you can quantize a position:

unsigned short px = meshopt_quantizeHalf(v.x);
unsigned short py = meshopt_quantizeHalf(v.y);
unsigned short pz = meshopt_quantizeHalf(v.z);

Vertex/index buffer compression

In case storage size or transmission bandwidth is of importance, you might want to additionally compress vertex and index data. While several mesh compression libraries, like Google Draco, are available, they typically are designed to maximize the compression ratio at the cost of disturbing the vertex/index order (which makes the meshes inefficient to render on GPU) or decompression performance. They also frequently don't support custom game-ready quantized vertex formats and thus require to re-quantize the data after loading it, introducing extra quantization errors and making decoding slower.

Alternatively you can use general purpose compression libraries like zstd or Oodle to compress vertex/index data - however these compressors aren't designed to exploit redundancies in vertex/index data and as such compression rates can be unsatisfactory.

To that end, this library provides algorithms to "encode" vertex and index data. The result of the encoding is generally significantly smaller than initial data, and remains compressible with general purpose compressors - so you can either store encoded data directly (for modest compression ratios and maximum decoding performance), or further compress it with zstd/Oodle to maximize compression ratio.

To encode, you need to allocate target buffers (preferably using the worst case bound) and call encoding functions:

std::vector<unsigned char> vbuf(meshopt_encodeVertexBufferBound(vertex_count, sizeof(Vertex)));
vbuf.resize(meshopt_encodeVertexBuffer(&vbuf[0], vbuf.size(), vertices, vertex_count, sizeof(Vertex)));

std::vector<unsigned char> ibuf(meshopt_encodeIndexBufferBound(index_count, vertex_count));
ibuf.resize(meshopt_encodeIndexBuffer(&ibuf[0], ibuf.size(), indices, index_count));

You can then either serialize vbuf/ibuf as is, or compress them further. To decode the data at runtime, call decoding functions:

int resvb = meshopt_decodeVertexBuffer(vertices, vertex_count, sizeof(Vertex), &vbuf[0], vbuf.size());
int resib = meshopt_decodeIndexBuffer(indices, index_count, &buffer[0], buffer.size());
assert(resvb == 0 && resib == 0);

Note that vertex encoding assumes that vertex buffer was optimized for vertex fetch, and that vertices are quantized; index encoding assumes that the vertex/index buffers were optimized for vertex cache and vertex fetch. Feeding unoptimized data into the encoders will produce poor compression ratios. Both codecs are lossless - the only lossy step is quantization that happens before encoding.

Decoding functions are heavily optimized and can directly target write-combined memory; you can expect both decoders to run at 1-3 GB/s on modern desktop CPUs. Compression ratios depend on the data; vertex data compression ratio is typically around 2-4x (compared to already quantized data), index data compression ratio is around 5-6x (compared to raw 16-bit index data). General purpose lossless compressors can further improve on these results.

Triangle strip conversion

On most hardware, indexed triangle lists are the most efficient way to drive the GPU. However, in some cases triangle strips might prove beneficial:

• On some older GPUs, triangle strips may be a bit more efficient to render
• On extremely memory constrained systems, index buffers for triangle strips could save a bit of memory

This library provides an algorithm for converting a vertex cache optimized triangle list to a triangle strip:

std::vector<unsigned int> strip(meshopt_stripifyBound(index_count));
unsigned int restart_index = ~0u;
size_t strip_size = meshopt_stripify(&strip[0], indices, index_count, vertex_count, restart_index);

Typically you should expect triangle strips to have ~50-60% of indices compared to triangle lists (~1.5-1.8 indices per triangle) and have ~5% worse ACMR. Note that triangle strips can be stitched with or without restart index support. Using restart indices can result in ~10% smaller index buffers, but on some GPUs restart indices may result in decreased performance.

Deinterleaved geometry

All of the examples above assume that geometry is represented as a single vertex buffer and a single index buffer. This requires storing all vertex attributes - position, normal, texture coordinate, skinning weights etc. - in a single contiguous struct. However, in some cases using multiple vertex streams may be preferable. In particular, if some passes require only positional data - such as depth pre-pass or shadow map - then it may be beneficial to split it from the rest of the vertex attributes to make sure the bandwidth use during these passes is optimal. On some mobile GPUs a position-only attribute stream also improves efficiency of tiling algorithms.

Most of the functions in this library either only need the index buffer (such as vertex cache optimization) or only need positional information (such as overdraw optimization). However, several tasks require knowledge about all vertex attributes.

For indexing, generateVertexRemap assumes that there's just one vertex stream; when multiple vertex streams are used, it's necessary to use generateVertexRemapMulti as follows:

meshopt_Stream streams[] = {
    {&unindexed_pos[0], sizeof(float) * 3, sizeof(float) * 3},
    {&unindexed_nrm[0], sizeof(float) * 3, sizeof(float) * 3},
    {&unindexed_uv[0], sizeof(float) * 2, sizeof(float) * 2},
};

std::vector<unsigned int> remap(index_count);
size_t vertex_count = meshopt_generateVertexRemapMulti(&remap[0], NULL, index_count, index_count, streams, sizeof(streams) / sizeof(streams[0]));

After this remapVertexBuffer needs to be called once for each vertex stream to produce the correctly reindexed stream.

Instead of calling optimizeVertexFetch for reordering vertices in a single vertex buffer for efficiency, calling optimizeVertexFetchRemap and then calling remapVertexBuffer for each stream again is recommended.

Finally, when compressing vertex data, encodeVertexBuffer should be used on each vertex stream separately - this allows the encoder to best utilize correlation between attribute values for different vertices.

Simplification

All algorithms presented so far don't affect visual appearance at all, with the exception of quantization that has minimal controlled impact. However, fundamentally the most effective way at reducing the rendering or transmission cost of a mesh is to make the mesh simpler.

This library provides two simplification algorithms that reduce the number of triangles in the mesh. Given a vertex and an index buffer, they generate a second index buffer that uses existing vertices in the vertex buffer. This index buffer can be used directly for rendering with the original vertex buffer (preferably after vertex cache optimization), or a new compact vertex/index buffer can be generated using optimizeVertexFetch that uses the optimal number and order of vertices.

The first simplification algorithm, simplify, follows the topology of the original mesh in an attempt to preserve attribute seams, borders and overall appearance. For meshes with inconsistent topology or many seams, such as faceted meshes, it can result in simplifier getting "stuck" and not being able to simplify the mesh fully; it's recommended to preprocess the index buffer with generateShadowIndexBuffer to discard any vertex attributes that aren't critical and can be rebuilt later such as normals.

float threshold = 0.2f;
size_t target_index_count = size_t(index_count * threshold);
float target_error = 1e-2f;

std::vector<unsigned int> lod(index_count);
lod.resize(meshopt_simplify(&lod[0], indices, index_count, &vertices[0].x, vertex_count, sizeof(Vertex), target_index_count, target_error));

Target error is an approximate measure of the deviation from the original mesh using distance normalized to 0..1 (so 1e-2f means that simplifier will try to maintain the error to be below 1% of the mesh extents). Note that because of topological restrictions and error bounds simplifier isn't guaranteed to reach the target index count and can stop earlier.

The second simplification algorithm, simplifySloppy, doesn't follow the topology of the original mesh. This means that it doesn't preserve attribute seams or borders, but it can collapse internal details that are too small to matter better because it can merge mesh features that are topologically disjoint but spatially close.

float threshold = 0.2f;
size_t target_index_count = size_t(index_count * threshold);

std::vector<unsigned int> lod(target_index_count);
lod.resize(meshopt_simplifySloppy(&lod[0], indices, index_count, &vertices[0].x, vertex_count, sizeof(Vertex), target_index_count));

This algorithm is guaranteed to return a result at or below the target index count. It is 5-6x faster than simplify when simplification ratio is large, and is able to reach ~20M triangles/sec on a desktop CPU (meshopt_simplify works at ~3M triangles/sec).

When a sequence of LOD meshes is generated that all use the original vertex buffer, care must be taken to order vertices optimally to not penalize mobile GPU architectures that are only capable of transforming a sequential vertex buffer range. It's recommended in this case to first optimize each LOD for vertex cache, then assemble all LODs in one large index buffer starting from the coarsest LOD (the one with fewest triangles), and call optimizeVertexFetch on the final large index buffer. This will make sure that coarser LODs require a smaller vertex range and are efficient wrt vertex fetch and transform.

Efficiency analyzers

While the only way to get precise performance data is to measure performance on the target GPU, it can be valuable to measure the impact of these optimization in a GPU-independent manner. To this end, the library provides analyzers for all three major optimization routines. For each optimization there is a corresponding analyze function, like analyzeOverdraw, that returns a struct with statistics.

analyzeVertexCache returns vertex cache statistics. The common metric to use is ACMR - average cache miss ratio, which is the ratio of the total number of vertex invocations to the triangle count. The worst-case ACMR is 3 (GPU has to process 3 vertices for each triangle); on regular grids the optimal ACMR approaches 0.5. On real meshes it usually is in [0.5..1.5] range depending on the amount of vertex splits. One other useful metric is ATVR - average transformed vertex ratio - which represents the ratio of vertex shader invocations to the total vertices, and has the best case of 1.0 regardless of mesh topology (each vertex is transformed once).

analyzeVertexFetch returns vertex fetch statistics. The main metric it uses is overfetch - the ratio between the number of bytes read from the vertex buffer to the total number of bytes in the vertex buffer. Assuming non-redundant vertex buffers, the best case is 1.0 - each byte is fetched once.

analyzeOverdraw returns overdraw statistics. The main metric it uses is overdraw - the ratio between the number of pixel shader invocations to the total number of covered pixels, as measured from several different orthographic cameras. The best case for overdraw is 1.0 - each pixel is shaded once.

Note that all analyzers use approximate models for the relevant GPU units, so the numbers you will get as the result are only a rough approximation of the actual performance.

Memory management

Many algorithms allocate temporary memory to store intermediate results or accelerate processing. The amount of memory allocated is a function of various input parameters such as vertex count and index count. By default memory is allocated using operator new and operator delete; if these operators are overloaded by the application, the overloads will be used instead. Alternatively it's possible to specify custom allocation/deallocation functions using setAllocator, e.g.

meshopt_setAllocator(malloc, free);

Note that the library expects the allocation function to either throw in case of out-of-memory (in which case the exception will propagate to the caller) or abort, so technically the use of malloc above isn't safe. If you want to handle out-of-memory errors without using C++ exceptions, you can use setjmp/longjmp instead.

Vertex and index decoders (decodeVertexBuffer and decodeIndexBuffer) do not allocate memory and work completely within the buffer space provided via arguments.

All functions have bounded stack usage that does not exceed 32 KB for any algorithms.

LWJGL note: meshoptimizer can be configured to use the LWJGL memory allocator with the following code:

nmeshopt_setAllocator(
    MemoryUtil.getAllocator().getMalloc(),
    MemoryUtil.getAllocator().getFree()
);