# OpenGL Rotation Matrix about point

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Hey, would you help me a bit? I'm struggling with making matrices to rotate about point. My rotation part of the matrix construction looks like that:

 boneMatrices[offs + 0] = cos(rx) * cos(ry); boneMatrices[offs + 1] = -cos(rz) * sin(rx) - cos(rx)*sin(ry)*sin(rz); boneMatrices[offs + 2] = cos(rx) * cos(rz) * sin(ry) + sin(rx) * sin(rz); boneMatrices[offs + 4] = cos(ry) * sin(rx); boneMatrices[offs + 5] = cos(rx) * cos(rz) - sin(rx)*sin(ry)*sin(rz); boneMatrices[offs + 6] = cos(rz) * sin(rx) * sin(ry) - cos(rx) * sin(rz); boneMatrices[offs + 8] = -sin(ry); boneMatrices[offs + 9] = cos(ry) * sin(rz); boneMatrices[offs + 10] = cos(ry) * cos(rz); 

I pass origin for rotation instead of scaling part of the matrix, and then, in vertex shader i do:

1) subtract origin from vertex

2) rotate vertex

It works, but it sucks. too much operations, ugly code;

I want to pass to my shader matrices that already do rotation about specific point. but really i need someone's help here. how can i make above matrix to rotate about specific point? i couldn't find any descriprion adoptable in my case.

i use opengl, if it matters.

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Assuming that you use column vectors, if T(c) is the translation matrix to the center of rotation and R is the rotation matrix, then the product
M := T(c) * R * T(-c)
defines the desired new rotation matrix. It translates by -c, rotates, and translates back by c like you do now separately.

EDIT:
You can take advantage from knowing the structures of the matrices when you compute the above product. Think of M having a 3x3 sub-marix M[sub]R[/sub] on the upper left and a 1x3 sub-matrix M[sub]T[/sub] on the upper right, and doing so with R and T as well, then
M[sub]R[/sub] := R[sub]R[/sub]
M[sub]T[/sub] := R[sub]R[/sub] * T[sub]T[/sub](-c) + T[sub]T[/sub](c)
means the minimum computations to be done for yielding in M.

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1) subtract origin from vertex

2) rotate vertex

I know you might not want to hear this, but the way you listed above is the correct way. If you want your code to still look good, you can write it like this (writen in psuedocode of course):

 function RotateAboutPoint(Point,Rotation){ return MoveToAxis * Rotate * MoveFromAxis; } 

It might even perform better than your "beautiful" code since matrix multiplication is accelerated while multiplying every element in your matrix separately is not... (Not sure about this one though...)

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Well i've tried to do it like haegarr described:

 //Origins oMat.make_identity(); oMat2.make_identity(); oMat.element(0, 3) = -ox; oMat.element(1, 3) = -oy; oMat.element(2, 3) = -oz; oMat2.element(0, 3) = ox; oMat2.element(1, 3) = oy; oMat2.element(2, 3) = oz; //Rotation(tested) bMat.make_identity(); bMat.element(0, 0) = cos(rx) * cos(ry); bMat.element(1, 0) = -cos(rz) * sin(rx) - cos(rx)*sin(ry)*sin(rz); bMat.element(2, 0) = cos(rx) * cos(rz) * sin(ry) + sin(rx) * sin(rz);; bMat.element(0, 1) = cos(ry) * sin(rx); bMat.element(1, 1) = cos(rx) * cos(rz) - sin(rx)*sin(ry)*sin(rz); bMat.element(2, 1) = cos(rz) * sin(rx) * sin(ry) - cos(rx) * sin(rz); bMat.element(0, 2) = -sin(ry); bMat.element(1, 2) = cos(ry) * sin(rz); bMat.element(2, 2) = cos(ry) * cos(rz); //Bone translation bMat.element(0, 3) = translation.x; bMat.element(1, 3) = translation.y; bMat.element(2, 3) = translation.z; //M := R * T(-c) + T© ?? bMat *= oMat; bMat += oMat2;

and rotation\translation is now rigth, but for some reason i[color="#8b0000"]t's about 2x weaker than it should be and it looks like it scales vertices a bit then rotating

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 bMat *= oMat; bMat += oMat2;

Why are you adding? All matrix chaining transformations should be multiplications...

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Ok, fixed by

 bMat *= oMat; oMat2 *= bMat; bMat = oMat2;//(or just pass oMat2 to shader)

(equialent of -T * R * T)

but i'm not sure if it's ok to use such a matrix for tangent and normal? looks ok, but just want to know.

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[quote name='SingularOne' timestamp='1313485221' post='4849759']
 bMat *= oMat; bMat += oMat2;

Why are you adding? All matrix chaining transformations should be multiplications...
[/quote]
[font="arial, verdana, tahoma, sans-serif"]Please let me clarify what
[color="#1C2837"]M[sub]T[/sub] := R[sub]R[/sub] * T[sub]T[/sub](-c) + T[sub]T[/sub](c)[/font]
actually means. As mentioned my post above, [color="#1C2837"]R[sub]R[/sub] is a 3x3 matrix and [color="#1C2837"]T[sub]T[/sub] is a 1x3 matrix (a.k.a. column vector). Multiplying a 3x3 matrix on the left and a 1x3 matrix on the right gives you a 1x3 matrix. Adding a 1x3 matrix onto a 1x3 matrix gives you a 1x3 matrix.

So notice that the result [color="#1C2837"]M[sub]T[/sub] is a 1x3 matrix (and that [color="#1C2837"]M[sub]R[/sub] is a 3x3 matrix), while M itself is a usual homogeneous 4x4 matrix. The correct assembly then looks like
 bMat.make_identity(); // MR bMat.element(0, 0) = cos(rx) * cos(ry); bMat.element(1, 0) = -cos(rz) * sin(rx) - cos(rx)*sin(ry)*sin(rz); bMat.element(2, 0) = cos(rx) * cos(rz) * sin(ry) + sin(rx) * sin(rz);; bMat.element(0, 1) = cos(ry) * sin(rx); bMat.element(1, 1) = cos(rx) * cos(rz) - sin(rx)*sin(ry)*sin(rz); bMat.element(2, 1) = cos(rz) * sin(rx) * sin(ry) - cos(rx) * sin(rz); bMat.element(0, 2) = -sin(ry); bMat.element(1, 2) = cos(ry) * sin(rz); bMat.element(2, 2) = cos(ry) * cos(rz); // MT = MR * TT(-c) + TT(c) bMat.element(0, 3) = bMat.element(0, 0) * (-ox) + bMat.element(0, 1) * (-oy) + bMat.element(0, 2) * (-oz) + ox; bMat.element(1, 3) = bMat.element(1, 0) * (-ox) + bMat.element(1, 1) * (-oy) + bMat.element(1, 2) * (-oz) + oy; bMat.element(2, 3) = bMat.element(2, 0) * (-ox) + bMat.element(2, 1) * (-oy) + bMat.element(2, 2) * (-oz) + oz; 
if I have interpreted the indexing scheme correctly.

EDIT: It is for sure possible to compose the desired rotation simply by computing [color="#1C2837"]T(c) * R * T(-c). The above way just shows (as mentioned) the minimal computational effort to do; it avoids all that nasty scalar products with 0 and 1. However, this kind of optimization will probably not be noticeable.

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[color="#1C2837"]
i don't know how to thank you for your effort, your method works fine and it's much more efficient
[color="#1c2837"]

thank you too for pointing out the part i misunderstood.

[color="#1c2837"]and yeah, i've alredy noticed, that it's not really good to rotate normals.

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...
(equialent of -T * R * T)

but i'm not sure if it's ok to use such a matrix for tangent and normal? looks ok, but just want to know.

Well, please notice that -T is not the same as T(-c), because the elements on the main diagonal will be negated in -T but not in T(-c)!

However, you can apply T(-c) * R * T(c) to a normal / tangent because
a) normals and tangents are direction vectors and are hence invariant to translations, and
b) there is no scaling or shearing in this formula.
Hence for normals and tangents the above formula does the same as the lonely R does: It simply rotates the vector.

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yes it looks like problem is in my shader.

here shader that i found in nvidia example of hardware skinning:

 attribute vec4 position; attribute vec3 normal; attribute vec4 weight; attribute vec4 index; attribute float numBones; uniform mat4 boneMatrices[30]; uniform vec4 color; uniform vec4 lightPos; void main() { vec4 transformedPosition = vec4(0.0); vec3 transformedNormal = vec3(0.0); vec4 curIndex = index; vec4 curWeight = weight; for (int i = 0; i < int(numBones); i++) { mat4 m44 = boneMatrices[int(curIndex.x)]; // transform the offset by bone i transformedPosition += m44 * position * curWeight.x; mat3 m33 = mat3(m44[0].xyz, m44[1].xyz, m44[2].xyz); // transform normal by bone i transformedNormal += m33 * normal * curWeight.x; // shift over the index/weight variables, this moves the index and // weight for the current bone into the .x component of the index // and weight variables curIndex = curIndex.yzwx; curWeight = curWeight.yzwx; } gl_Position = gl_ModelViewProjectionMatrix * transformedPosition; transformedNormal = normalize(transformedNormal); gl_FrontColor = dot(transformedNormal, lightPos.xyz) * color; }

and significant part of my adoption(maximum 2 bones affecting vertex, 1st one is always most effective, so 2nd affecting bone might exist only if 1st one is):

 V = gl_Vertex; vec3 n2 = gl_Normal; vec3 t2 = Tangent; if(Bones.x >= 0.0)//Bone1 ID { mat4 tmat = BonesMat[int(Bones.x)]; //Bone matrix mat3 nmat = mat3(tmat[0].xyz, tmat[1].xyz, tmat[2].xyz); V = tmat * gl_Vertex * Bones.z; //Bones.z - Bone 1 weight n2 = nmat * gl_Normal * Bones.z; t2 = nmat * Tangent * Bones.z; if(Bones.y >= 0.0)//Bone2 ID { tmat = BonesMat[int(Bones.y)]; nmat = mat3(tmat[0].xyz, tmat[1].xyz, tmat[2].xyz); V += tmat * gl_Vertex * Bones.w; //Bones.w - Bone2 weight n2 += nmat * gl_Normal * Bones.w; t2 += nmat * Tangent * Bones.w; } } 
Further - using V,N,T as regular;

result: rotation\translation is alright.
problem: lighting glitches. then i move camera away from object - vertices that affected by 2 bones become dark with the distance(lambert decreasing).

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IMHO the shown adopted code snippet is missing a normalization of both n2 and t2 (assuming that "using V,N,T as regular" doesn't include it). The code snippet probably only works well if Bones.z == 1 and Bones.y < 0. In all other cases the lengths of n2 and t2 may be anything but are later expected to be 1.

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yes, i've noticed before, it works ok if bone1 weight = 1.0 and bone2 is ineffective, but i do normalize resulting normal and tangent

 vec3 T = normalize(gl_NormalMatrix * normalize(t2)); vec3 N = normalize(gl_NormalMatrix * normalize(n2)); vec3 B = cross(N, T);

and even if i remove normal rotation, problem doesn't go away.
also i modified code so second bone weight = 1.0 - FirstBoneWeight (because outside shader my program actually calculates weights for all affecting bones, but in examples i use to test it's always <= 2 bones affecting vertex);

and to avoid wasting your time with snippets:
full code of stuff that actually affects that problem,
[spoiler]
#version 110 attribute vec4 Bones; attribute vec3 Tangent; uniform mat4 BonesMat[30]; varying vec3 ld; varying vec3 eye; varying vec4 V; void main() { V = gl_Vertex; vec3 n2 = gl_Normal; vec3 t2 = Tangent; if(Bones.x >= 0.0) { mat4 tmat = BonesMat[int(Bones.x)]; mat3 nmat = mat3(tmat[0].xyz, tmat[1].xyz, tmat[2].xyz); V = tmat * gl_Vertex * Bones.z; n2 = nmat * gl_Normal * Bones.z; t2 = nmat * Tangent * Bones.z; if(Bones.y >= 0.0) { tmat = BonesMat[int(Bones.y)]; nmat = mat3(tmat[0].xyz, tmat[1].xyz, tmat[2].xyz); V += tmat * gl_Vertex * (1.0-Bones.z); n2 += nmat * gl_Normal * (1.0-Bones.z); t2 += nmat * Tangent * (1.0-Bones.z); } } gl_TexCoord[0] = gl_MultiTexCoord0; V = gl_ModelViewMatrix * V; vec3 T = -normalize(gl_NormalMatrix * normalize(t2)); vec3 N = normalize(gl_NormalMatrix * normalize(n2)); vec3 B = cross(N, T); vec3 lv = (gl_LightSource[0].position - V).xyz; ld.x = dot(lv, B); ld.y = dot(lv, T); ld.z = dot(lv, N); vec3 vt = -V.xyz; eye.x = dot(vt, B); eye.y = dot(vt, T); eye.z = dot(vt, N); gl_Position = gl_ProjectionMatrix * V; }

[/spoiler]

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The problem was i'm using 3-component vectors for all my lighting calculation, so vertex w-component was modified by rotation matrix correctly, but wasn't affecting lighting. so i should do it manually.

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Introduction
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Overview
Diligent Engine API takes some features from Direct3D11 and Direct3D12 as well as introduces new concepts to hide certain platform-specific details and make the system easy to use. It contains the following main components:
Render device (IRenderDevice  interface) is responsible for creating all other objects (textures, buffers, shaders, pipeline states, etc.).
Device context (IDeviceContext interface) is the main interface for recording rendering commands. Similar to Direct3D11, there are immediate context and deferred contexts (which in Direct3D11 implementation map directly to the corresponding context types). Immediate context combines command queue and command list recording functionality. It records commands and submits the command list for execution when it contains sufficient number of commands. Deferred contexts are designed to only record command lists that can be submitted for execution through the immediate context.
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Swap Chain (ISwapChain interface). Swap chain interface represents a chain of back buffers and is responsible for showing the final rendered image on the screen.
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Creating the Pipeline State Object
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// Define input layout InputLayoutDesc &Layout = PSODesc.GraphicsPipeline.InputLayout; LayoutElement TextLayoutElems[] = {     LayoutElement( 0, 0, 3, VT_FLOAT32, False ),     LayoutElement( 1, 0, 4, VT_UINT8, True ),     LayoutElement( 2, 0, 2, VT_FLOAT32, False ), }; Layout.LayoutElements = TextLayoutElems; Layout.NumElements = _countof( TextLayoutElems ); Finally, pipeline state defines primitive topology type. When all required members are initialized, a pipeline state object can be created by IRenderDevice::CreatePipelineState() method:
// Define shader and primitive topology PSODesc.GraphicsPipeline.PrimitiveTopologyType = PRIMITIVE_TOPOLOGY_TYPE_TRIANGLE; PSODesc.GraphicsPipeline.pVS = pVertexShader; PSODesc.GraphicsPipeline.pPS = pPixelShader; PSODesc.Name = "My pipeline state"; m_pDev->CreatePipelineState(PSODesc, &m_pPSO); When PSO object is bound to the pipeline, the engine invokes all API-specific commands to set all states specified by the object. In case of Direct3D12 this maps directly to setting the D3D12 PSO object. In case of Direct3D11, this involves setting individual state objects (such as rasterizer and blend states), shaders, input layout etc. In case of OpenGL, this requires a number of fine-grain state tweaking calls. Diligent Engine keeps track of currently bound states and only calls functions to update these states that have actually changed.
Direct3D11 and OpenGL utilize fine-grain resource binding models, where an application binds individual buffers and textures to certain shader or program resource binding slots. Direct3D12 uses a very different approach, where resource descriptors are grouped into tables, and an application can bind all resources in the table at once by setting the table in the command list. Resource binding model in Diligent Engine is designed to leverage this new method. It introduces a new object called shader resource binding that encapsulates all resource bindings required for all shaders in a certain pipeline state. It also introduces the classification of shader variables based on the frequency of expected change that helps the engine group them into tables under the hood:
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. Shader variable type must be specified during shader creation by populating an array of ShaderVariableDesc structures and initializing ShaderCreationAttribs::Desc::VariableDesc and ShaderCreationAttribs::Desc::NumVariables members (see example of shader creation above).
Static variables cannot be changed once a resource is bound to the variable. They are bound directly to the shader object. For instance, a shadow map texture is not expected to change after it is created, so it can be bound directly to the shader:
m_pPSO->CreateShaderResourceBinding(&m_pSRB); Note that an SRB is only compatible with the pipeline state it was created from. SRB object inherits all static bindings from shaders in the pipeline, but is not allowed to change them.
Mutable resources can only be set once for every instance of a shader resource binding. Such resources are intended to define specific material properties. For instance, a diffuse texture for a specific material is not expected to change once the material is defined and can be set right after the SRB object has been created:
m_pSRB->GetVariable(SHADER_TYPE_PIXEL, "tex2DDiffuse")->Set(pDiffuseTexSRV); In some cases it is necessary to bind a new resource to a variable every time a draw command is invoked. Such variables should be labeled as dynamic, which will allow setting them multiple times through the same SRB object:
m_pSRB->GetVariable(SHADER_TYPE_VERTEX, "cbRandomAttribs")->Set(pRandomAttrsCB); Under the hood, the engine pre-allocates descriptor tables for static and mutable resources when an SRB objcet is created. Space for dynamic resources is dynamically allocated at run time. Static and mutable resources are thus more efficient and should be used whenever possible.
As you can see, Diligent Engine does not expose low-level details of how resources are bound to shader variables. One reason for this is that these details are very different for various APIs. The other reason is that using low-level binding methods is extremely error-prone: it is very easy to forget to bind some resource, or bind incorrect resource such as bind a buffer to the variable that is in fact a texture, especially during shader development when everything changes fast. Diligent Engine instead relies on shader reflection system to automatically query the list of all shader variables. Grouping variables based on three types mentioned above allows the engine to create optimized layout and take heavy lifting of matching resources to API-specific resource location, register or descriptor in the table.
This post gives more details about the resource binding model in Diligent Engine.
Setting the Pipeline State and Committing Shader Resources
Before any draw or compute command can be invoked, the pipeline state needs to be bound to the context:
m_pContext->SetPipelineState(m_pPSO); Under the hood, the engine sets the internal PSO object in the command list or calls all the required native API functions to properly configure all pipeline stages.
The next step is to bind all required shader resources to the GPU pipeline, which is accomplished by IDeviceContext::CommitShaderResources() method:
m_pContext->CommitShaderResources(m_pSRB, COMMIT_SHADER_RESOURCES_FLAG_TRANSITION_RESOURCES); The method takes a pointer to the shader resource binding object and makes all resources the object holds available for the shaders. In the case of D3D12, this only requires setting appropriate descriptor tables in the command list. For older APIs, this typically requires setting all resources individually.
Next-generation APIs require the application to track the state of every resource and explicitly inform the system about all state transitions. For instance, if a texture was used as render target before, while the next draw command is going to use it as shader resource, a transition barrier needs to be executed. Diligent Engine does the heavy lifting of state tracking.  When CommitShaderResources() method is called with COMMIT_SHADER_RESOURCES_FLAG_TRANSITION_RESOURCES flag, the engine commits and transitions resources to correct states at the same time. Note that transitioning resources does introduce some overhead. The engine tracks state of every resource and it will not issue the barrier if the state is already correct. But checking resource state is an overhead that can sometimes be avoided. The engine provides IDeviceContext::TransitionShaderResources() method that only transitions resources:
m_pContext->TransitionShaderResources(m_pPSO, m_pSRB); In some scenarios it is more efficient to transition resources once and then only commit them.
Invoking Draw Command
The final step is to set states that are not part of the PSO, such as render targets, vertex and index buffers. Diligent Engine uses Direct3D11-syle API that is translated to other native API calls under the hood:
ITextureView *pRTVs[] = {m_pRTV}; m_pContext->SetRenderTargets(_countof( pRTVs ), pRTVs, m_pDSV); // Clear render target and depth buffer const float zero[4] = {0, 0, 0, 0}; m_pContext->ClearRenderTarget(nullptr, zero); m_pContext->ClearDepthStencil(nullptr, CLEAR_DEPTH_FLAG, 1.f); // 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); Different native APIs use various set of function to execute draw commands depending on command details (if the command is indexed, instanced or both, what offsets in the source buffers are used etc.). For instance, there are 5 draw commands in Direct3D11 and more than 9 commands in OpenGL with something like glDrawElementsInstancedBaseVertexBaseInstance not uncommon. Diligent Engine hides all details with single IDeviceContext::Draw() method that takes 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); For compute commands, there is IDeviceContext::DispatchCompute() method that takes DispatchComputeAttribs structure that defines compute grid dimension.
Source Code
Full engine source code is available on GitHub and is free to use. The repository contains tutorials, sample applications, asteroids performance benchmark and an example Unity project that uses Diligent Engine in native plugin.
Atmospheric scattering sample demonstrates how Diligent Engine can be used to implement various rendering tasks: loading textures from files, using complex shaders, rendering to multiple render targets, using compute shaders and unordered access views, etc.

Asteroids performance benchmark is based on this demo developed by Intel. It renders 50,000 unique textured asteroids and allows comparing performance of Direct3D11 and Direct3D12 implementations. Every asteroid is a combination of one of 1000 unique meshes and one of 10 unique textures.

Finally, there is an example project that shows how Diligent Engine can be integrated with Unity.

Future Work
The engine is under active development. It currently supports Windows desktop, Universal Windows, Linux, Android, MacOS, and iOS platforms. Direct3D11, Direct3D12, OpenGL/GLES backends are now feature complete. Vulkan backend is coming next, and Metal backend is in the plan.

• Good Evening,
I want to make a 2D game which involves displaying some debug information. Especially for collision, enemy sights and so on ...
First of I was thinking about all those shapes which I need will need for debugging purposes: circles, rectangles, lines, polygons.
I am really stucked right now because of the fundamental question:
Where do I store my vertices positions for each line (object)? Currently I am not using a model matrix because I am using orthographic projection and set the final position within the VBO. That means that if I add a new line I would have to expand the "points" array and re-upload (recall glBufferData) it every time. The other method would be to use a model matrix and a fixed vbo for a line but it would be also messy to exactly create a line from (0,0) to (100,20) calculating the rotation and scale to make it fit.
If I proceed with option 1 "updating the array each frame" I was thinking of having 4 draw calls every frame for the lines vao, polygons vao and so on.
In addition to that I am planning to use some sort of ECS based architecture. So the other question would be:
Should I treat those debug objects as entities/components?
For me it would make sense to treat them as entities but that's creates a new issue with the previous array approach because it would have for example a transform and render component. A special render component for debug objects (no texture etc) ... For me the transform component is also just a matrix but how would I then define a line?
Treating them as components would'nt be a good idea in my eyes because then I would always need an entity. Well entity is just an id !? So maybe its a component?
Regards,
LifeArtist