hikari – Terrain Materials

Now that hikari’s material system can express ideas more complicated than “specific set of textures”, it’s time to implement the materials and shading for terrain.

Splat Maps:

The texture selection is going to be based off of splat maps, which means we need the vertex colors: something I conveniently ignored when doing mesh generation earlier. It’s a simple enough fix. I decided to go with layers of noise for testing again, both because it was easy (no need for tooling) and because it produces the worst-case scenario for performance (all pixels use all or most of the splats). If the splat / triplanar mapping is going to fall off the performance cliff I want to find out now, not later.

Splats are normalized (to sum to one) and packed into a 32 bit color per vertex:

inline u32
NormalizeSplat(float w0, float w1, float w2, float w3, float w4) {
    float sum = w0 + w1 + w2 + w3 + w4;
    Assert(sum != 0.0f, "Cannot have total weight of zero on terrain splat.");

    float r = w0 / sum;
    float g = w1 / sum;
    float b = w2 / sum;
    float a = w3 / sum;

    u32 ri = (((u32)(r * 255.0f) & 0xff) <<  0);
    u32 gi = (((u32)(g * 255.0f) & 0xff) <<  8);
    u32 bi = (((u32)(b * 255.0f) & 0xff) << 16);
    u32 ai = (((u32)(a * 255.0f) & 0xff) << 24);

    return ai | bi | gi | ri;
}

I wrote a basic shader to visualize the splat map (although, squeezing 5 values into 3 colors is not particularly effective):
splat_color.png

Textures:

By packing textures tightly, we can reduce the number of texture reads for each splat material to two:
– albedo color
– normal + AO + roughness

This requires encoding the normal map in two channels (which is completely fine for tangent space, just discard the Z component and reconstruct in the shader). It also assumes that none of the splat materials have a metal channel. This is not necessarily true, but the metal mask could be packed into the albedo’s alpha channel. For the textures I’m working with, the metal mask is a constant 0.

So, as a rough calculation:
2 textures per splat material
x 3 splat materials per splat (so that we can have different textures on each planar face)
x 5 splats
= 30 textures.

This immediately rules out the naive approach of binding each texture separately. GL_MAX_TEXTURE_IMAGE_UNITS, the maximum number of bound textures per draw, on my midrange GPU is 32. Since the lighting code uses several textures as well (shadow maps, environment probes, a lookup texture for the BRDF), we run out of texture units.

Fortunately, we don’t have to do things that way.

All of the terrain textures should be the same size, so that the resolution and variation is consistent between them. This in turn means we can pack all of the terrain textures into a set of texture arrays. Instead of binding different textures, each splat material provides an index into the texture arrays.

This does make some things, like streaming textures in and out, more complicated. I’ve ignored this for now, as hikari simply loads everything at startup anyway. (hikari’s handling of assets is not very good, and will need to be addressed sometime soon.)

Shader:

All of the shaders in hikari are plain GLSL, with some minor support for preprocessing (#includes). Material shaders share the same lighting code, via a function called AccumulateLighting() that takes a struct containing all of the surface parameters and returns an RGB color. The benefit of this is writing, debugging, and optimizing the lighting calculation and lookup *once*.

Writing a shader, then, is just a matter of filling out that structure.

For this terrain shader, we need to do two sets of blends: first, blending between splats; second, blending between the three planar projections.

The blending for splats is pretty much exactly what you’d expect:

vec3 SampleAlbedoSplat(vec2 uv, float spw0, float spw1, float spw2, float spw3, float spw4) {
    vec3 splat0 = texture(splat_albedo_array, vec3(uv, splat_id0)).rgb;
    vec3 splat1 = texture(splat_albedo_array, vec3(uv, splat_id1)).rgb;
    vec3 splat2 = texture(splat_albedo_array, vec3(uv, splat_id2)).rgb;
    vec3 splat3 = texture(splat_albedo_array, vec3(uv, splat_id3)).rgb;
    vec3 splat4 = texture(splat_albedo_array, vec3(uv, splat_id4)).rgb;

    vec3 splat_albedo = splat0 * spw0 +
                        splat1 * spw1 +
                        splat2 * spw2 +
                        splat3 * spw3 +
                        splat4 * spw4;

    return splat_albedo;
}

There is another, similar function for sampling and blending the surface properties (normal, roughness, AO).

The triplanar blending is more interesting. See these two blog posts for the fundamentals of what triplanar blending is and how it works:
Ben Golas – Normal Mapping for a Triplanar Shader
Martin Palko – Triplanar Mapping

The first step of triplanar blending is calculating the blend weights for each plane. I take the additional step of clamping weights below a threshold to zero. While this can create some visible artifacts if the threshold is too high, any plane we can avoid looking at is 10 fewer texture samples.

const float blend_sharpness = 4.0;
const float blend_threshold = 0.05;

// fs_in.normal is the interpolated vertex normal.
vec3 blend = pow(abs(fs_in.normal), vec3(blend_sharpness));

blend /= dot(blend, vec3(1.0));

if (blend.x < blend_threshold) blend.x = 0.0;
if (blend.y < blend_threshold) blend.y = 0.0;
if (blend.z < blend_threshold) blend.z = 0.0;

// Need to renormalize the blend
blend /= dot(blend, vec3(1.0));

By checking for a positive blend weight before sampling one of the projections, we can skip those that aren’t going to contribute much. This *does* seem to be a win (about a 0.25ms drop in render time in my test scene), but it’s pretty close to the noise level so I’m not certain.

Thresholding the splat weights may also be worthwhile; in the worst-case test I have set up it definitely isn’t, but actual artist-authored terrain is unlikely to use more than 2 or 3 channels per-pixel.

The actual blending is, mostly, exactly what you’d expect (multiply each planar projection with the corresponding weight and add them together.) The normal blending is slightly different, as described in Ben Golas’ blog post above:

// props_#.ts_normal is the tangent space normal for the plane facing that axis.
vec3 normal_x = vec3(0, props_x.ts_normal.yx);
vec3 normal_y = vec3(props_y.ts_normal.x, 0.0, props_y.ts_normal.y);
vec3 normal_z = vec3(props_z.ts_normal.xy, 0.0);
surf.N = normalize(fs_in.normal +
                   blend.x * normal_x +
                   blend.y * normal_y +
                   blend.z * normal_z);

The normal map for each plane is a linear blend of the splats. This is wrong, but looks okay in practice. I think the correct approach would be to swizzle *every* normal map sample out to world space and *then* blend? Not sure.

The result:
splat_texture.png

Per-plane Textures:

Stepping back a bit, let’s look at this render:
per_plane_color

The textures are placeholders, but each pixel is colorized based on the contribution by each planar mapping. For terrain rendering, this is really nice: it’s identified the slopes for us. In addition, we read a texture for each plane anyway — but there’s no need for it to be the *same* texture!

By exploiting this, we can use a different texture for slopes and level areas, “for free”:
grass_cliff

There’s more we can do here, too, like using different variants of a texture for X and Z planes to increase the amount of variation.

Performance:

I don’t have a very good feel on what makes shaders fast or slow. I was expecting 30+ texture reads to be a problem, but it doesn’t really appear to be. The depth prepass is possibly saving me a lot of pain here, as it means very little of the expensive shading goes to waste. I did notice some issues after first implementing the terrain shader, dropping to 30FPS on occasion, but after adding some GPU profiling code it turns out *shadow rendering* is slow, and just tipped over the threshold to cause problems. (Why does rendering the sun’s shadow cascade take upwards of 5-7ms? I dunno! Something to investigate.)

That said, the method I am using to time GPU operations (glQueryCounter) appears to be less than perfectly accurate (i.e., the UI pass seems to get billed the cost of waiting for vblank.) The GL specification, meanwhile, manages to be either extremely unclear or contradictory on the exact meaning of the timestamp recorded.

For now, I’m going to say this is fine and investigate more later. (ノ`Д´)ノ彡┻━┻

Continuing Work:

At this point, I have most of what I set out to implement, but there are a few things that still need to be done before I’d consider this terrain system complete:

– LOD mesh generation. In addition to simplifying the mesh itself, probably clamp low-weight splats to zero to make shading cheaper.
– Revisit hex tiling. I suspect it really is a more natural fit.
– Fix seams with normals and splats. These are still noticeable with real terrain textures.
– More detailed shading. The terrain materials I’m using all come with height maps; adding occlusion mapping would be interesting and would help sell the look up close.

Until next time.

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hikari – New Material System

The next step in building hikari’s terrain system is proper material handling. In order to do so, I need to completely revamp the material system. This is going to be extensive enough to earn its own post.

Current Material System:

Here is the current state of hikari’s material “system”, a single struct:

struct Material {
    GLuint normal_map;
    GLuint albedo_map;
    GLuint metallic_map;
    GLuint roughness_map;
    GLuint ao_map;

    bool has_alpha;
    bool is_leaf;
    bool is_terrain;
};

And its usage, from the per-mesh main render loop:

main_pass.Begin();
main_pass.SetRenderTarget(GL_FRAMEBUFFER, &hdr_buffer_rt_ms);

RenderMesh * rmesh = meshes + i;
IndexedMesh * mesh = rmesh->mesh;
Material * material = rmesh->material;
if (material->has_alpha) {
    glDepthMask(GL_TRUE);
    glDepthFunc(GL_LESS);
}
else {
    glDepthMask(GL_FALSE);
    glDepthFunc(GL_EQUAL);
}
Assert(mesh && material, "Cannot render without both mesh and material!");

GLuint shader_for_mat = default_shader;
if (material->is_leaf) {
    shader_for_mat = leaf_shader;
}
if (material->is_terrain) {
    shader_for_mat = terrain_shader;
}
main_pass.SetShader(shader_for_mat);

main_pass.BindTexture(GL_TEXTURE_2D, "normal_map", material->normal_map);
main_pass.BindTexture(GL_TEXTURE_2D, "albedo_map", material->albedo_map);
main_pass.BindTexture(GL_TEXTURE_2D, "metallic_map", material->metallic_map);
main_pass.BindTexture(GL_TEXTURE_2D, "roughness_map", material->roughness_map);
main_pass.BindTexture(GL_TEXTURE_2D, "ao_map", material->ao_map);

// Material independant shader setup (lights list, shadow map binding,
// environment maps, etc.), elided for space.

// Draw the mesh.
mesh->SetAttribPointersForShader(main_pass.active_shader);
mesh->Draw();

main_pass.End();

The current notion of material is a set of textures and some flags used to determine the correct shader. Needless to say, this is neither flexible nor particularly efficient. Instead, what I’d like is a Material that consists of two bags of data: render states (shader program, blend mode, depth test) and shader uniforms (texture maps).

New Material System, First Pass:

struct Material {
    GLuint shader_program;
    GLenum depth_mask;
    GLenum depth_func;

    struct Uniform {
        const char * name;
        union {
            float value_f[4];
            Texture value_texture;
        };

        enum UniformType {
            Float1,
            Float2,
            Float3,
            Float4,

            TexHandle,
        } type;
    };

    std::vector<Uniform> uniforms;

    // Uniform setup methods elided

    inline void
    BindForRenderPass(RenderPass * pass) {
        pass->SetShader(shader_program);
        glDepthMask(depth_mask);
        glDepthFunc(depth_func);

        for (u32 i = 0; i < uniforms.size(); ++i) {
             Uniform u = uniforms[i];
             switch (u.type) {
                 case Uniform::UniformType::Float1: {
                     pass->SetUniform1f(u.name, u.value_f[0]);
                } break;
                case Uniform::UniformType::Float2: {
                    pass->SetUniform2f(u.name, u.value_f[0], u.value_f[1]);
                } break;
                case Uniform::UniformType::Float3: {
                    pass->SetUniform3f(u.name, u.value_f[0], u.value_f[1], u.value_f[2]);
                } break;
                case Uniform::UniformType::Float4: {
                    pass->SetUniform4f(u.name, u.value_f[0], u.value_f[1], u.value_f[2], u.value_f[3]);
                } break;
                case Uniform::UniformType::TexHandle: {
                    pass->BindTexture(u.name, u.value_texture);
                } break;
            }
        }
    }
};

A good first step. No more branching to select shaders inside the render loop, no hardcoded set of textures. Still doing some silly things, like re-binding the shader for every mesh. Also still looking up uniform locations every time, though there is enough information here to cache those at load time now.

Let’s look at the entire main pass for a bit:

for (u32 i = 0; i < mesh_count; ++i) {     main_pass.Begin();     main_pass.SetRenderTarget(GL_FRAMEBUFFER, &hdr_buffer_rt_ms);     if (!visible_meshes[i]) {         continue;     }     RenderMesh * rmesh = meshes + i;     IndexedMesh * mesh = rmesh->mesh;
    Material * material = rmesh->material;

    Assert(mesh && material, "Cannot render without both mesh and material!");

    material->BindForRenderPass(&main_pass);

    main_pass.SetUniformMatrix44("clip_from_world", clip_from_world);
    main_pass.SetUniformMatrix44("world_from_local", rmesh->world_from_local);
    main_pass.SetUniform3f("view_pos", cam->position);
    main_pass.SetUniform1f("time", current_time_sec);

    main_pass.BindUBO("PointLightDataBlock", point_light_data_ubo);
    main_pass.BindUBO("SpotLightDataBlock", spot_light_data_ubo);
    main_pass.BindUBO("LightList", light_list_ubo);

    main_pass.BindTexture(GL_TEXTURE_CUBE_MAP, "irradiance_map", skybox_cubemaps.irradiance_map);
    main_pass.BindTexture(GL_TEXTURE_CUBE_MAP, "prefilter_map", skybox_cubemaps.prefilter_map);
    main_pass.BindTexture(GL_TEXTURE_2D, "brdf_lut", brdf_lut_texture);

    main_pass.BindTexture("ssao_map", ssao_blur_texture);
    main_pass.SetUniform2f("viewport_dim", hdr_buffer_rt_ms.viewport.z, hdr_buffer_rt_ms.viewport.w);

    main_pass.SetUniform3f("sun_direction", world->sun_direction);
    main_pass.SetUniform3f("sun_color", world->sun_color);
    main_pass.BindTexture("sun_shadow_map", sun_light.cascade.shadow_map);
    for (u32 split = 0; split < NUM_SPLITS; ++split) {
        char buffer[256];
        _snprintf_s(buffer, sizeof(buffer) - 1, "sun_clip_from_world[%d]", split);
        main_pass.SetUniformMatrix44(buffer, sun_light.cascade.sun_clip_from_world[split]);
    }
    mesh->SetAttribPointersForShader(main_pass.active_shader);
    mesh->Draw();
    main_pass.End();
}

There is still a *lot* of uniform setup going on per-mesh, and almost all of it is unnecessary. But, since Material binds the shader each time, all of the other uniforms need to be rebound (because BindForRenderPass() may have bound a different shader).

Ideally, here’s the inner loop we’re aiming for:

for (u32 i = 0; i < mesh_count; ++i) {     RenderMesh * rmesh = meshes + i;     IndexedMesh * mesh = rmesh->mesh;
    Material * material = rmesh->material;
    Assert(mesh && material, "Cannot render without both mesh and material!");

    material->BindForRenderPass(&main_pass);
    main_pass.SetUniformMatrix44("world_from_local", rmesh->world_from_local);
    mesh->SetAttribPointersForShader(main_pass.active_shader);
    mesh->Draw();
}

Material Instances:

When rendering the Sponza test scene, there are a few dozen materials loaded. However, there are only 3 different sets of render states: leaves (a shader doing alpha test and subsurface scattering), alpha tested, and default PBR. Within each class of material the only difference is the texture set.

If we were to separate the set of render states and the set of uniforms into different entities, we’d be able to minimize modifications to the render state in this loop. So that’s what I’ve decided to do.

A Material is a bag of render states, while a MaterialInstance is a bag of uniforms associated with a particular Material. For example, the vases, walls, columns, etc. in Sponza would all be instances of the same Material. If we sort and bucket the mesh list according to Materials, we only need to bind the full render state for each material once. (This is also a convenient point to eliminate culled meshes, removing the visibility check in the main loop.)

At least for now, I’ve done this in the most naive way possible; the list of uniforms is removed from Material and becomes MaterialInstance. Each instance also contains a pointer to its parent material. Done!

This is not a great solution, there are a lot of ways for one to shoot themselves in the foot. For example, a MaterialInstance that doesn’t contain the full set of expected uniforms (will render with stale data), or containing extras (will assert when the uniform bind fails). The Material should probably have “base instance” that defines what set of uniforms are required, and defaults for them; each instance would validate calls against this base. I have not implemented this yet.

Here’s where we end up with MaterialInstance:

BucketedRenderList render_list = MakeBucketedRenderList(meshes, mesh_count, visible_meshes);

for (RenderBucket bucket : render_list.buckets) {
    main_pass.Begin();
    main_pass.SetRenderTarget(GL_FRAMEBUFFER, &hdr_buffer_rt_ms);

    main_pass.BindMaterial(bucket.material);

    // Additional global setup, as above.

    for (u32 i = bucket.start; i < bucket.end; ++i) {
        assert(i < render_list.mesh_count);
        RenderMesh * rmesh = &render_list.mesh_list[i];
        IndexedMesh * mesh = rmesh->mesh;
        MaterialInstance * material_instance = rmesh->material_instance;

        RenderPass main_subpass = main_pass.BeginSubPass();

        main_subpass.BindMaterialInstance(material_instance);
        main_subpass.SetUniformMatrix44("world_from_local", rmesh->world_from_local);
        mesh->SetAttribPointersForShader(main_subpass.active_shader);
        mesh->Draw();

        main_pass.EndSubPass(main_subpass);
    }

    main_pass.End();
}

(Material binding has been moved into RenderPass, which is in hindsight a more natural place for it to live.)

By carving the mesh list up into buckets by Material, we only need to do the global setup once for each bucket, and then only set the specific instance materials per-mesh. Even better, the check for culled objects disappears. And this list is reusable between the depth prepass and main render pass.

Still a lot of room for performance improvement: the RenderMesh struct causes a lot of unnecessary pointer chasing, meshes using the same instance of a material could be batched as well, there are *sprintf* calls in the outer loop. It’s pretty clear I need to spend a lot more time here.

However, this is progress! More importantly, Materials are now general enough I can implement the terrain materials. So that’s next.

hikari – Terrain Mesh Generation

Continuing on from the last post, I have implemented the basic mesh generation for heightmapped terrain. This was probably the easiest part, but did require some cleanup of existing code first.

Mesh Handling Cleanup:

Up to this point, meshes have not been dealt with in a systematic manner in hikari. The Mesh struct contained buffer handles and an index count and that was it. All meshes were assumed to be triangle lists. This was workable, because all object meshes had a common vertex layout, and rendered with variants of a single shader with fixed attribute indices. Rendering a mesh was easy enough:

glBindVertexArray(mesh->vao);
glBindBuffer(GL_ARRAY_BUFFER, mesh->vertex_buffer);
glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, mesh->index_buffer);

glEnableVertexAttribArray(0);
glEnableVertexAttribArray(1);
glEnableVertexAttribArray(2);
glEnableVertexAttribArray(3);

glDrawElements(GL_TRIANGLES, mesh->index_count, GL_UNSIGNED_INT, NULL);

glDisableVertexAttribArray(3);
glDisableVertexAttribArray(2);
glDisableVertexAttribArray(1);
glDisableVertexAttribArray(0);

There were already other meshes with different layouts, but they were special cases: a quad used for full-screen render passes (with only position and uv), a cube used to render the skybox (position only), etc.

Rather than hack around the limitations here (such as using separate render pass for terrain), I decided a mesh should know its vertex layout and be able to do the attribute setup itself.

Enter VertexBufferLayout:

struct VertexBufferLayout {
    struct Property {
        char * name;
        u32 size;
        GLenum type;
        bool normalized;
        u32 offset;
    };
    
    u32 stride;
    std::vector<Property> props;

    u32 GetPropertySizeBytes(Property p) {
        static const u32 TypeToByteTable[] {
            GL_BYTE, 1,
            GL_UNSIGNED_BYTE, 1,
            GL_SHORT, 2,
            GL_UNSIGNED_SHORT, 2,
            GL_INT, 4,
            GL_UNSIGNED_INT, 4,
            GL_HALF_FLOAT, 2,
            GL_FLOAT, 4,
            GL_DOUBLE, 8,
        };

        for (u32 i = 0; i < array_count(TypeToByteTable); i += 2) {
            if (TypeToByteTable[i] == p.type) {
                u32 byte_size = TypeToByteTable[i + 1];
                return byte_size * p.size;
            }
        }
        return 0;
    }
    
    void AddProperty(char * name, u32 size, GLenum type, bool normalized) {
        Property p;
        p.name = name;
        p.size = size;
        p.type = type;
        p.normalized = normalized;
        p.offset = stride;
        u32 byte_size = GetPropertySizeBytes(p);
        if (byte_size > 0) {
            stride += byte_size;
            props.push_back(p);
        }
        else {
            Assert(false, "Invalid vertex buffer property type.");
        }
    }
};

No real surprises here, just stuffing everything into an array, with a bit of extra bookkeeping to prevent errors in calculating stride and offset pointers. This isn’t a general solution, it makes the assumption that vertex attributes are always stored interleaved (not necessarily true), and does not permit a base offset (for storing multiple meshes in one vertex buffer). But it works, and there’s little point buying more complexity than needed.

Meshes each store a pointer to a layout. Prior to rendering, the renderer passes the shader handle to the mesh, which then uses the handle plus its layout data to determine attribute indices in the shader and bind the pointer to the buffer:

void
SetAttribPointersForShader(GLuint shader_program) {
    Assert(layout != NULL && attrib_indices.size() == layout->props.size(),
            "Invalid vertex buffer layout.");

    glBindBuffer(GL_ARRAY_BUFFER, vertex_buffer);

    for (u32 i = 0; i < attrib_indices.size(); ++i) {
        VertexBufferLayout::Property p = layout->props[i];
        attrib_indices[i] = glGetAttribLocation(shader_program, p.name);
        if (attrib_indices[i] != -1) {
            glEnableVertexAttribArray(attrib_indices[i]);
            glVertexAttribPointer(attrib_indices[i], p.size, p.type, p.normalized, layout->stride, (void *)p.offset);
            glDisableVertexAttribArray(attrib_indices[i]);
        }
    }
    
    glBindBuffer(GL_ARRAY_BUFFER, 0);
}

(Ideally we’d like to cache this — the index lookup should only need to be run once per layout/shader combination, not per-mesh.)

Now we have the list of attribute indices to enable, so we can render very similarly to how we did before.

This still leaves a lot to be desired, but it is enough to unblock the terrain work, so let’s get back on track.

Terrain Mesh Generation:

After all that, generating the terrain mesh itself seems almost trivial. Here is the entire loop for building the vertex positions:

u32 vertex_count = x_count*y_count;
TerrainVertex * verts = (TerrainVertex *)calloc(vertex_count, sizeof(TerrainVertex));

float xo = x_count * 0.5f;
float yo = y_count * 0.5f;\
Vector3 bounds_min(FLT_MAX, FLT_MAX, FLT_MAX);
Vector3 bounds_max = -bounds_min;

for (u32 y = 0; y < y_count; ++y) {
    for (u32 x = 0; x < x_count; ++x) {
        float map_val = map->ReadPixel(x_off + x, y_off + y);

        Vector3 pos = Vector3(
            x - xo,
            map_val, 
            y - yo);

        // Scale up from pixel to world space.
        pos *= chunk_meters_per_pixel;

        verts[y * x_count + x].position = pos;

        bounds_min = MinV(bounds_min, pos);
        bounds_max = MaxV(bounds_max, pos);
    }
}

This is a regular grid of squares in the XZ plane, with the Y coordinate taken directly from the heightmap. Next we build an index buffer (in the most naive manner), and calculate surface normals from the resulting triangles.

All of this is pretty straightforward, but there are a few subtle issues that come up:

– Triangulation. Unlike triangles, the vertices of a quad do not necessarily all fall in one plane. This is in fact *usually* the case with terrain. So how we decide to split that quad into triangles has an effect on the final shape:

quad_triangulation_illust

Currently, I split all quads uniformly. Another option I explored is switching the split direction in a checkerboard fashion. With the noise-based heightmap I’m testing with, the difference is negligible. This may prove more of an issue when producing sparser, low-LOD meshes for distant terrain. It also would *absolutely* matter if the terrain was flat-shaded (i.e., constant normal for each face), but that isn’t the case here.

– Calculating vertex normals. I calculate normals for this terrain mesh the same as any other mesh: loop through the faces and add face normals to each vertex, then normalize in another pass:

for (u32 i = 0; i < index_buffer_count; i += 3) {
    u32 idx_a = indices[i + 0];
    u32 idx_b = indices[i + 1];
    u32 idx_c = indices[i + 2];

    Vector3 a = verts[idx_a].position;
    Vector3 b = verts[idx_b].position;
    Vector3 c = verts[idx_c].position;

    Vector3 normal = Cross(a - b, a - c);

    verts[idx_a].normal += normal;
    verts[idx_b].normal += normal;
    verts[idx_c].normal += normal;
}

// We sum the unnormalized normals for each triangle, and then normalize
// the sum.  Since the cross product is scaled by the area of the triangle,
// this means that larger triangles contribute more heavily to the resulting
// vertex normal.
for (u32 i = 0; i < vertex_count; ++i) {
    verts[i].normal = Normalize(verts[i].normal);
}

So far so good, but there is a crucial problem here.

We iterate the faces of the mesh. But some of the points in question actually belong to several meshes! When we’re at the edge of the terrain chunk, we only account for the face normals of the triangles inside the current chunk. Which means the same point, on two different chunks, may produce a different normal.

And so, we get seams:

normal_seams

This is not necessarily easy to fix. The simplest option would be to iterate over neighboring chunks, find the shared vertices, and average the normals — not 100% correct, but it eliminates the seam. It’s unclear, though, how this would interact with streaming: a new chunk being loaded might change the normals on a mesh that’s been loaded for a while; should we read that mesh data back from the GPU? Keep a CPU copy and update? In addition, one of the design goals is for the terrain system to be agnostic about the source of meshes. For a well-structured grid finding the adjacent vertex is simple, but how does that work with an arbitrary hand-produced mesh?

Ultimately, there’s also the question of whether this seam in the normals actually matters. Obviously it *is* a bug, but it is only so glaringly visible because of the shiny plastic material I’m using to debug. I’m not sure how many of these artifacts will remain visible when applying actual terrain materials.

I’m counting this as a bug but I’m going to leave it alone for now.

– Alternate tiling strategies. I started with laying a square grid over the world. Why squares? There are other good tiling arrangements. In fact, we can tile the plane with *just* triangles, and avoid the question of how to triangulate our tiles altogether.

It turns out this is *really* easy to do:

pos.x += (y & 1) * 0.5f;  // Offset odd rows by half a unit
pos.z *= sqrtf(3.0f) / 2.0f; // Scale vertically by sin(pi/3)

Make sure the triangles cut across the short diagonal of that skewed grid, and now the plane is tiled with equilateral triangles.

There isn’t a huge amount of difference with my noise terrain (just a scaling on the Z axis):

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However, tiling square chunks with equilateral triangles has a sticking point when it comes to downsampling the terrain for distant LOD meshes. The sawtooth edge can’t be merged into larger triangles without either breaking the tiling pattern or leaving gaps or overlap between chunks.

With that said, I feel like the triangle tiling has some really nice properties. No triangulation needed, and no ambiguity on the final mesh’s shape. It can still be represented easily in an image map (although, we’re pushing the limits on that). Grids make it easy to create 90 degree angles, which stick out, while a triangle tiling makes 60 degree angles which are less obviously objectionable. (This one is decidedly a matter of taste, but: my engine, my taste.)

Things get *really* interesting when we decide chunks don’t need to be rectangular. A hexagonal chunk tiles perfectly with equilateral triangles, which means the LOD reduction works fine as well. Using hexes for chunks also fits into the half-offset tiling described by Alan Wolfe here. (In addition to the memory savings he mentions in the post, the hex tiling also means a constant streaming cost as you move about the world, which is a very nice property to have.)

I haven’t implemented hex tiling, and this post is getting quite long as it is. I do think it is an avenue worth exploring, and will probably return to this after fixing up the material system.

Until next time!