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• By elect
Hi,
ok, so, we are having problems with our current mirror reflection implementation.
At the moment we are doing it very simple, so for the i-th frame, we calculate the reflection vectors given the viewPoint and some predefined points on the mirror surface (position and normal).
Then, using the least squared algorithm, we find the point that has the minimum distance from all these reflections vectors. This is going to be our virtual viewPoint (with the right orientation).
After that, we render offscreen to a texture by setting the OpenGL camera on the virtual viewPoint.
And finally we use the rendered texture on the mirror surface.
So far this has always been fine, but now we are having some more strong constraints on accuracy.
What are our best options given that:
- we have a dynamic scene, the mirror and parts of the scene can change continuously from frame to frame
- we have about 3k points (with normals) per mirror, calculated offline using some cad program (such as Catia)
- all the mirror are always perfectly spherical (with different radius vertically and horizontally) and they are always convex
- a scene can have up to 10 mirror
- it should be fast enough also for vr (Htc Vive) on fastest gpus (only desktops)

Looking around, some papers talk about calculating some caustic surface derivation offline, but I don't know if this suits my case
Also, another paper, used some acceleration structures to detect the intersection between the reflection vectors and the scene, and then adjust the corresponding texture coordinate. This looks the most accurate but also very heavy from a computational point of view.

Other than that, I couldn't find anything updated/exhaustive around, can you help me?

• Hello all,
I am currently working on a game engine for use with my game development that I would like to be as flexible as possible.  As such the exact requirements for how things should work can't be nailed down to a specific implementation and I am looking for, at least now, a default good average case scenario design.
Here is what I have implemented:
Deferred rendering using OpenGL Arbitrary number of lights and shadow mapping Each rendered object, as defined by a set of geometry, textures, animation data, and a model matrix is rendered with its own draw call Skeletal animations implemented on the GPU.   Model matrix transformation implemented on the GPU Frustum and octree culling for optimization Here are my questions and concerns:
Doing the skeletal animation on the GPU, currently, requires doing the skinning for each object multiple times per frame: once for the initial geometry rendering and once for the shadow map rendering for each light for which it is not culled.  This seems very inefficient.  Is there a way to do skeletal animation on the GPU only once across these render calls? Without doing the model matrix transformation on the CPU, I fail to see how I can easily batch objects with the same textures and shaders in a single draw call without passing a ton of matrix data to the GPU (an array of model matrices then an index for each vertex into that array for transformation purposes?) If I do the matrix transformations on the CPU, It seems I can't really do the skinning on the GPU as the pre-transformed vertexes will wreck havoc with the calculations, so this seems not viable unless I am missing something Overall it seems like simplest solution is to just do all of the vertex manipulation on the CPU and pass the pre-transformed data to the GPU, using vertex shaders that do basically nothing.  This doesn't seem the most efficient use of the graphics hardware, but could potentially reduce the number of draw calls needed.

Really, I am looking for some advice on how to proceed with this, how something like this is typically handled.  Are the multiple draw calls and skinning calculations not a huge deal?  I would LIKE to save as much of the CPU's time per frame so it can be tasked with other things, as to keep CPU resources open to the implementation of the engine.  However, that becomes a moot point if the GPU becomes a bottleneck.

• Hello!
I would like to introduce Diligent Engine, a project that I've been recently working on. Diligent Engine is a light-weight cross-platform abstraction layer between the application and the platform-specific graphics API. Its main goal is to take advantages of the next-generation APIs such as Direct3D12 and Vulkan, but at the same time provide support for older platforms via Direct3D11, OpenGL and OpenGLES. Diligent Engine exposes common front-end for all supported platforms and provides interoperability with underlying native API. Shader source code converter allows shaders authored in HLSL to be translated to GLSL and used on all platforms. Diligent Engine supports integration with Unity and is designed to be used as a graphics subsystem in a standalone game engine, Unity native plugin or any other 3D application. It is distributed under Apache 2.0 license and is free to use. Full source code is available for download on GitHub.
Features:
True cross-platform Exact same client code for all supported platforms and rendering backends No #if defined(_WIN32) ... #elif defined(LINUX) ... #elif defined(ANDROID) ... No #if defined(D3D11) ... #elif defined(D3D12) ... #elif defined(OPENGL) ... Exact same HLSL shaders run on all platforms and all backends Modular design Components are clearly separated logically and physically and can be used as needed Only take what you need for your project (do not want to keep samples and tutorials in your codebase? Simply remove Samples submodule. Only need core functionality? Use only Core submodule) No 15000 lines-of-code files Clear object-based interface No global states Key graphics features: Automatic shader resource binding designed to leverage the next-generation rendering APIs Multithreaded command buffer generation 50,000 draw calls at 300 fps with D3D12 backend Descriptor, memory and resource state management Modern c++ features to make code fast and reliable The following platforms and low-level APIs are currently supported:
Windows Desktop: Direct3D11, Direct3D12, OpenGL Universal Windows: Direct3D11, Direct3D12 Linux: OpenGL Android: OpenGLES MacOS: OpenGL iOS: OpenGLES API Basics
Initialization
The engine can perform initialization of the API or attach to already existing D3D11/D3D12 device or OpenGL/GLES context. For instance, the following code shows how the engine can be initialized in D3D12 mode:
#include "RenderDeviceFactoryD3D12.h" using namespace Diligent; // ...  GetEngineFactoryD3D12Type GetEngineFactoryD3D12 = nullptr; // Load the dll and import GetEngineFactoryD3D12() function LoadGraphicsEngineD3D12(GetEngineFactoryD3D12); auto *pFactoryD3D11 = GetEngineFactoryD3D12(); EngineD3D12Attribs EngD3D12Attribs; EngD3D12Attribs.CPUDescriptorHeapAllocationSize[0] = 1024; EngD3D12Attribs.CPUDescriptorHeapAllocationSize[1] = 32; EngD3D12Attribs.CPUDescriptorHeapAllocationSize[2] = 16; EngD3D12Attribs.CPUDescriptorHeapAllocationSize[3] = 16; EngD3D12Attribs.NumCommandsToFlushCmdList = 64; RefCntAutoPtr<IRenderDevice> pRenderDevice; RefCntAutoPtr<IDeviceContext> pImmediateContext; SwapChainDesc SwapChainDesc; RefCntAutoPtr<ISwapChain> pSwapChain; pFactoryD3D11->CreateDeviceAndContextsD3D12( EngD3D12Attribs, &pRenderDevice, &pImmediateContext, 0 ); pFactoryD3D11->CreateSwapChainD3D12( pRenderDevice, pImmediateContext, SwapChainDesc, hWnd, &pSwapChain ); Creating Resources
Device resources are created by the render device. The two main resource types are buffers, which represent linear memory, and textures, which use memory layouts optimized for fast filtering. To create a buffer, you need to populate BufferDesc structure and call IRenderDevice::CreateBuffer(). The following code creates a uniform (constant) buffer:
BufferDesc BuffDesc; BufferDesc.Name = "Uniform buffer"; BuffDesc.BindFlags = BIND_UNIFORM_BUFFER; BuffDesc.Usage = USAGE_DYNAMIC; BuffDesc.uiSizeInBytes = sizeof(ShaderConstants); BuffDesc.CPUAccessFlags = CPU_ACCESS_WRITE; m_pDevice->CreateBuffer( BuffDesc, BufferData(), &m_pConstantBuffer ); Similar, to create a texture, populate TextureDesc structure and call IRenderDevice::CreateTexture() as in the following example:
TextureDesc TexDesc; TexDesc.Name = "My texture 2D"; TexDesc.Type = TEXTURE_TYPE_2D; TexDesc.Width = 1024; TexDesc.Height = 1024; TexDesc.Format = TEX_FORMAT_RGBA8_UNORM; TexDesc.Usage = USAGE_DEFAULT; TexDesc.BindFlags = BIND_SHADER_RESOURCE | BIND_RENDER_TARGET | BIND_UNORDERED_ACCESS; TexDesc.Name = "Sample 2D Texture"; m_pRenderDevice->CreateTexture( TexDesc, TextureData(), &m_pTestTex ); Initializing Pipeline State
Diligent Engine follows Direct3D12 style to configure the graphics/compute pipeline. One big Pipelines State Object (PSO) encompasses all required states (all shader stages, input layout description, depth stencil, rasterizer and blend state descriptions etc.)
To create a shader, populate ShaderCreationAttribs structure. An important member is ShaderCreationAttribs::SourceLanguage. The following are valid values for this member:
SHADER_SOURCE_LANGUAGE_DEFAULT  - The shader source format matches the underlying graphics API: HLSL for D3D11 or D3D12 mode, and GLSL for OpenGL and OpenGLES modes. SHADER_SOURCE_LANGUAGE_HLSL  - The shader source is in HLSL. For OpenGL and OpenGLES modes, the source code will be converted to GLSL. See shader converter for details. SHADER_SOURCE_LANGUAGE_GLSL  - The shader source is in GLSL. There is currently no GLSL to HLSL converter. To allow grouping of resources based on the frequency of expected change, Diligent Engine introduces classification of shader variables:
Static variables (SHADER_VARIABLE_TYPE_STATIC) are variables that are expected to be set only once. They may not be changed once a resource is bound to the variable. Such variables are intended to hold global constants such as camera attributes or global light attributes constant buffers. Mutable variables (SHADER_VARIABLE_TYPE_MUTABLE) define resources that are expected to change on a per-material frequency. Examples may include diffuse textures, normal maps etc. Dynamic variables (SHADER_VARIABLE_TYPE_DYNAMIC) are expected to change frequently and randomly. This post describes the resource binding model in Diligent Engine.
The following is an example of shader initialization:
To create a pipeline state object, define instance of PipelineStateDesc structure. The structure defines the pipeline specifics such as if the pipeline is a compute pipeline, number and format of render targets as well as depth-stencil format:
// This is a graphics pipeline PSODesc.IsComputePipeline = false; PSODesc.GraphicsPipeline.NumRenderTargets = 1; PSODesc.GraphicsPipeline.RTVFormats[0] = TEX_FORMAT_RGBA8_UNORM_SRGB; PSODesc.GraphicsPipeline.DSVFormat = TEX_FORMAT_D32_FLOAT; The structure also defines depth-stencil, rasterizer, blend state, input layout and other parameters. For instance, rasterizer state can be defined as in the code snippet below:
// Init rasterizer state RasterizerStateDesc &RasterizerDesc = PSODesc.GraphicsPipeline.RasterizerDesc; RasterizerDesc.FillMode = FILL_MODE_SOLID; RasterizerDesc.CullMode = CULL_MODE_NONE; RasterizerDesc.FrontCounterClockwise = True; RasterizerDesc.ScissorEnable = True; //RSDesc.MultisampleEnable = false; // do not allow msaa (fonts would be degraded) RasterizerDesc.AntialiasedLineEnable = False; When all fields are populated, call IRenderDevice::CreatePipelineState() to create the PSO:
Shader resource binding in Diligent Engine is based on grouping variables in 3 different groups (static, mutable and dynamic). Static variables are variables that are expected to be set only once. They may not be changed once a resource is bound to the variable. Such variables are intended to hold global constants such as camera attributes or global light attributes constant buffers. They are bound directly to the shader object:

m_pPSO->CreateShaderResourceBinding(&m_pSRB); Dynamic and mutable resources are then bound through SRB object:
m_pSRB->GetVariable(SHADER_TYPE_VERTEX, "tex2DDiffuse")->Set(pDiffuseTexSRV); m_pSRB->GetVariable(SHADER_TYPE_VERTEX, "cbRandomAttribs")->Set(pRandomAttrsCB); The difference between mutable and dynamic resources is that mutable ones can only be set once for every instance of a shader resource binding. Dynamic resources can be set multiple times. It is important to properly set the variable type as this may affect performance. Static variables are generally most efficient, followed by mutable. Dynamic variables are most expensive from performance point of view. This post explains shader resource binding in more details.
Setting the Pipeline State and Invoking Draw Command
Before any draw command can be invoked, all required vertex and index buffers as well as the pipeline state should be bound to the device context:
// Clear render target const float zero[4] = {0, 0, 0, 0}; m_pContext->ClearRenderTarget(nullptr, zero); // Set vertex and index buffers IBuffer *buffer[] = {m_pVertexBuffer}; Uint32 offsets[] = {0}; Uint32 strides[] = {sizeof(MyVertex)}; m_pContext->SetVertexBuffers(0, 1, buffer, strides, offsets, SET_VERTEX_BUFFERS_FLAG_RESET); m_pContext->SetIndexBuffer(m_pIndexBuffer, 0); m_pContext->SetPipelineState(m_pPSO); Also, all shader resources must be committed to the device context:
m_pContext->CommitShaderResources(m_pSRB, COMMIT_SHADER_RESOURCES_FLAG_TRANSITION_RESOURCES); When all required states and resources are bound, IDeviceContext::Draw() can be used to execute draw command or IDeviceContext::DispatchCompute() can be used to execute compute command. Note that for a draw command, graphics pipeline must be bound, and for dispatch command, compute pipeline must be bound. Draw() takes DrawAttribs structure as an argument. The structure members define all attributes required to perform the command (primitive topology, number of vertices or indices, if draw call is indexed or not, if draw call is instanced or not, if draw call is indirect or not, etc.). For example:
DrawAttribs attrs; attrs.IsIndexed = true; attrs.IndexType = VT_UINT16; attrs.NumIndices = 36; attrs.Topology = PRIMITIVE_TOPOLOGY_TRIANGLE_LIST; pContext->Draw(attrs); Tutorials and Samples
The GitHub repository contains a number of tutorials and sample applications that demonstrate the API usage.

AntTweakBar sample demonstrates how to use AntTweakBar library to create simple user interface.

Atmospheric scattering sample is a more advanced example. It demonstrates how Diligent Engine can be used to implement various rendering tasks: loading textures from files, using complex shaders, rendering to textures, using compute shaders and unordered access views, etc.

The repository includes Asteroids performance benchmark based on this demo developed by Intel. It renders 50,000 unique textured asteroids and lets compare performance of D3D11 and D3D12 implementations. Every asteroid is a combination of one of 1000 unique meshes and one of 10 unique textures.

Integration with Unity
Diligent Engine supports integration with Unity through Unity low-level native plugin interface. The engine relies on Native API Interoperability to attach to the graphics API initialized by Unity. After Diligent Engine device and context are created, they can be used us usual to create resources and issue rendering commands. GhostCubePlugin shows an example how Diligent Engine can be used to render a ghost cube only visible as a reflection in a mirror.

• By Yxjmir
I'm trying to load data from a .gltf file into a struct to use to load a .bin file. I don't think there is a problem with how the vertex positions are loaded, but with the indices. This is what I get when drawing with glDrawArrays(GL_LINES, ...):

Also, using glDrawElements gives a similar result. Since it looks like its drawing triangles using the wrong vertices for each face, I'm assuming it needs an index buffer/element buffer. (I'm not sure why there is a line going through part of it, it doesn't look like it belongs to a side, re-exported it without texture coordinates checked, and its not there)
I'm using jsoncpp to load the GLTF file, its format is based on JSON. Here is the gltf struct I'm using, and how I parse the file:
glBindVertexArray(g_pGame->m_VAO);
glDrawElements(GL_LINES, g_pGame->m_indices.size(), GL_UNSIGNED_BYTE, (void*)0); // Only shows with GL_UNSIGNED_BYTE
glDrawArrays(GL_LINES, 0, g_pGame->m_vertexCount);
So, I'm asking what type should I use for the indices? it doesn't seem to be unsigned short, which is what I selected with the Khronos Group Exporter for blender. Also, am I reading part or all of the .bin file wrong?
Test.gltf
Test.bin

• That means how do I use base DirectX or OpenGL api's to make a physics based destruction simulation?
Will it be just smart rendering or something else is required?

This topic is 2564 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi Gamedev,

I am writing a simple OpenGL/Freetype2 font engine for a project I am working on. I got it up and running so far, but there are a couple of things I hope someone can explain to me since I used some code I copied from the internet, and could not fully understand it.

I was unable to color my fonts using the original method (it was always black) and I don't understand how the new loading technique (gotten from NeHe tut #43) works to solve this. Moreover, why didn't the original method work? Could I still do it somehow by passing some other combination of GL enums to glTexImage2D? I am also not sure I understand the GL_* enums I pass. I would appreciate it if someone could explain it to me

 bool Font::Load(const char* fontFilePath, int pixelSize) { // Error checking if (fontFilePath == "") { std::cerr << "sl::Font: Empty file path passed as argument" << std::endl; return false; } if (pixelSize == 0) { std::cerr << "sl::Font: Passed a zero character size" << std::endl; return false; } if (!Font::library) { std::cerr << "sl::Font: FreeType2 library not initialized properly (" << ErrorString() << ")" << std::endl; return false; } if (error = (FT_New_Face(Font::library, fontFilePath, 0, &face))) { std::cerr << "sl::Font: Unable to create new face (" << ErrorString() << ")" << std::endl; return false; } source.assign(fontFilePath); this->pixelSize = pixelSize; // Warn the user if the font is not scalable (i.e. vector graphics/outline font) if(!(face->face_flags & FT_FACE_FLAG_SCALABLE) || !(face->face_flags & FT_FACE_FLAG_HORIZONTAL)) std::cerr << "sl::Font warning: Font is not scalable (" << fontFilePath << ")" << std::endl; FT_Set_Pixel_Sizes(face, pixelSize, pixelSize); int textureWidth = 0; int textureHeight = 0; for(int c = 0; c < 256; ++c) { // Load the character into the face's glyph slot FT_Load_Char(face, (char)c, FT_LOAD_RENDER); // Save glyph stats Glyph glyph; glyph.Advance = face->glyph->advance.x >> 6; glyph.Width = face->glyph->bitmap.width; glyph.Height = face->glyph->bitmap.rows; glyph.LeftBearing = face->glyph->bitmap_left; glyph.TopBearing = face->glyph->bitmap_top; textureWidth = NextPowerOf2(glyph.Width); textureHeight = NextPowerOf2(glyph.Height); // Adjust texture coordinate for glyph glyph.texCoordX = (float)glyph.Width/(float)textureWidth; glyph.texCoordY = (float)glyph.Height/(float)textureHeight; // Array to hold pixel data GLubyte* data = new GLubyte[2 * textureWidth * textureHeight]; // Pixel positions out of range (in padding area) are set to zero for (int y = 0; y < textureHeight; ++y) { for (int x = 0; x < textureWidth; ++x) { //data[x + y * textureWidth] = // (x >= glyph.Width || y >= glyph.Height) ? // 0 : // face->glyph->bitmap.buffer[x + y * glyph.Width]; data[2 * (x + y * textureWidth)] = data[2 * (x + y * textureWidth) + 1] = (x >= glyph.Width || y >= glyph.Height) ? 0 : face->glyph->bitmap.buffer[x + glyph.Width * y]; } } if (!data) { std::cerr << "sl::Font: Font data is corrupt" << std::endl; return false; } glGenTextures(1, &glyph.TextureID); glBindTexture(GL_TEXTURE_2D, glyph.TextureID); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, textureWidth, textureHeight, 0, GL_LUMINANCE_ALPHA, GL_UNSIGNED_BYTE, data); glyphList.push_back(glyph); delete[] data; } std::cout << "Size: " << glyphList.size() << std::endl; return true; } 

This is part of the original loading code (everything else is identical to the above):

 // Same code here as above // Array to hold pixel data GLubyte* data = new GLubyte[textureWidth * textureHeight]; for (int y = 0; y < textureHeight; ++y) { for (int x = 0; x < textureWidth; ++x) { //data[x + y * textureWidth] = // (x >= glyph.Width || y >= glyph.Height) ? // 0 : // face->glyph->bitmap.buffer[x + y * glyph.Width]; data[(x + y * textureWidth)] = (x >= glyph.Width || y >= glyph.Height) ? 0 : face->glyph->bitmap.buffer[x + glyph.Width * y]; } } // Same code here, but different call to glTexImage2D glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, textureWidth, textureHeight, 0, GL_ALPHA, GL_UNSIGNED_BYTE, data); 

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From the documentation for glTexImage2D:

format determines the composition of each element in pixels. It can assume one of the following symbolic values:

GL_ALPHA
Each element is a single alpha component. The GL converts it to floating point and assembles it into an RGBA element by attaching 0 for red, green, and blue.[/quote]

You could try using GL_ALPHA as your internal texture format, though that would rely on hardware support.

For the GL_LUMINANCE_ALPHA input, you should store 255 for the luminance value. You might be able to use GL_LUMINANCE_ALPHA for your internal texture format, too. Try it and see.

...

As an aside, you should combine all your glyph bitmaps into one texture so you can avoid texture changes while drawing text.

My suggestion is to pick a texture width proportional to the size of your font. For example, you could add up the width of all your glyphs, divide by eight, and rounding up to the next power of two. Alternatively, you could pick it based on font height, such as 2048 for 60+, 1024 for 30-59, 512 for 15-29, and 256 for 0-14). Whatever method you choose, the next step is to fit the glyphs into rows in reading order (across, then down), leaving a bit of padding between them. Once you've laid them all out, you can measure how tall your texture will need to be and allocate it. Then just copy the glyph bitmaps to the proper locations.

When drawing text, use texture coordinates based on the generated positions.

(Incidentally, you should apply a half-pixel shift toward the upper-left when drawing the text instead of the traditional half-texel shift. While both work just fine without antialiasing, the half-pixel shift works with antialiasing in D3D9 while the half-texel shift doesn't. I only found this out recently...)

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I read the docs, but I wasn't sure I understood it all.

For the GL_LUMINANCE_ALPHA input, you should store 255 for the luminance value.[/quote]

Could you clarify that? I am still somewhat new to OpenGL texture loading...at least with FreeType2

You might be able to use GL_LUMINANCE_ALPHA for your internal texture format, too. Try it and see. [/quote]

Yep. Works with GL_LUMINANCE_ALPHA as the internal format.

I plan on recoding my texture loading to load all fonts into a single texture in the future, but I thought I would try and load them separately first, but thanks for the note, it is very helpful

When I load my fonts using the original method, the program crashes with an "Unhandled exception at...Access violation reading location..." message and points to the call to glTexImage2D. Why is that and why do I need to make my array twice as big in the current method as opposed to the original method?

I.e.:
GLubyte* data = new GLubyte[2 * textureWidth * textureHeight]
VS.
GLubyte* data = new Glubyte[textureWidth * textureHeight]

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GL_LUMINANCE_ALPHA has two channels so it needs two bytes per pixel.

You can set the luminance for each pixel to white like this:
 // Pixel positions out of range (in padding area) are set to zero for (int y = 0; y < textureHeight; ++y) { for (int x = 0; x < textureWidth; ++x) { //data[x + y * textureWidth] = // (x >= glyph.Width || y >= glyph.Height) ? // 0 : // face->glyph->bitmap.buffer[x + y * glyph.Width]; // luminance data[2 * (x + y * textureWidth)] = 255; // alpha data[2 * (x + y * textureWidth) + 1] = (x >= glyph.Width || y >= glyph.Height) ? 0 : face->glyph->bitmap.buffer[x + glyph.Width * y]; } } 

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I get a much nicer and smooth result if I set the luminance channel to 255, thanks Afaik, I'm simply setting the perceived brightness of the texture to "100%" and storing the colors in the second channel (converted to floating numbers by OpenGL), right?

Still have a couple of questions though .
Is this the "only" way of loading FreeType2 image information in OpenGL (possibly because of the way they are loaded)? A vague question, I know...

I also tried the following using 4 channels:

 GLubyte* data = new GLubyte[4 * textureWidth * textureHeight]; // Pixel positions out of range (in padding area) are set to zero for (int y = 0; y < textureHeight; ++y) { for (int x = 0; x < textureWidth; ++x) { // read in r, g, b and a components data[4 * (x + y * textureWidth)] = (x >= glyph.Width || y >= glyph.Height) ? 0 : face->glyph->bitmap.buffer[x + glyph.Width * y]; data[4 * (x + y * textureWidth) + 1] = (x >= glyph.Width || y >= glyph.Height) ? 0 : face->glyph->bitmap.buffer[x + glyph.Width * y]; data[4 * (x + y * textureWidth) + 2] = (x >= glyph.Width || y >= glyph.Height) ? 0 : face->glyph->bitmap.buffer[x + glyph.Width * y]; data[4 * (x + y * textureWidth) + 3] = (x >= glyph.Width || y >= glyph.Height) ? 0 : face->glyph->bitmap.buffer[x + glyph.Width * y]; } } 

While it worked, but yielded a less satisfying result for some reason...
Thanks for all your help so far! I think I'm beginning to grasp the concepts