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I am currently studying shadow mapping, and my biggest issue right now is the transformations between spaces. This is my current working theory/steps.
Pass 1:
Get depth of pixel from camera, store in depth buffer
Get depth of pixel from light, store in another buffer
Pass 2:
Use texture coordinate to sample camera's depth buffer at current pixel
Convert that depth to a view space position by multiplying the projection coordinate with invProj matrix. (also do a perspective divide).
Take that view position and multiply by invV (camera's inverse view) to get a world space position
Multiply world space position by light's viewProjection matrix.
Perspective divide that projection-space coordinate, and manipulate into [0..1] to sample from light depth buffer.
Get current depth from light and closest (sampled) depth, if current depth > closest depth, it's in shadow.
Shader Code
Pass1:
PS_INPUT vs(VS_INPUT input) {
output.pos = mul(input.vPos, mvp);
output.cameraDepth = output.pos.zw;
..
float4 vPosInLight = mul(input.vPos, m);
vPosInLight = mul(vPosInLight, light.viewProj);
output.lightDepth = vPosInLight.zw;
}
PS_OUTPUT ps(PS_INPUT input){
float cameraDepth = input.cameraDepth.x / input.cameraDepth.y;
//Bundle cameraDepth in alpha channel of a normal map.
output.normal = float4(input.normal, cameraDepth);
//4 Lights in total -- although only 1 is active right now. Going to use r/g/b/a for each light depth.
output.lightDepths.r = input.lightDepth.x / input.lightDepth.y;
}
Pass 2 (Screen Quad):
float4 ps(PS_INPUT input) : SV_TARGET{
float4 pixelPosView = depthToViewSpace(input.texCoord);
..
float4 pixelPosWorld = mul(pixelPosView, invV);
float4 pixelPosLight = mul(pixelPosWorld, light.viewProj);
float shadow = shadowCalc(pixelPosLight);
//For testing / visualisation
return float4(shadow,shadow,shadow,1);
}
float4 depthToViewSpace(float2 xy) {
//Get pixel depth from camera by sampling current texcoord.
//Extract the alpha channel as this holds the depth value.
//Then, transform from [0..1] to [-1..1]
float z = (_normal.Sample(_sampler, xy).a) * 2 - 1;
float x = xy.x * 2 - 1;
float y = (1 - xy.y) * 2 - 1;
float4 vProjPos = float4(x, y, z, 1.0f);
float4 vPositionVS = mul(vProjPos, invP);
vPositionVS = float4(vPositionVS.xyz / vPositionVS.w,1);
return vPositionVS;
}
float shadowCalc(float4 pixelPosL) {
//Transform pixelPosLight from [-1..1] to [0..1]
float3 projCoords = (pixelPosL.xyz / pixelPosL.w) * 0.5 + 0.5;
float closestDepth = _lightDepths.Sample(_sampler, projCoords.xy).r;
float currentDepth = projCoords.z;
return currentDepth > closestDepth; //Supposed to have bias, but for now I just want shadows working haha
}
CPP Matrices
// (Position, LookAtPos, UpDir)
auto lightView = XMMatrixLookAtLH(XMLoadFloat4(&pos4), XMVectorSet(0,0,0,1), XMVectorSet(0,1,0,0));
// (FOV, AspectRatio (1000/680), NEAR, FAR)
auto lightProj = XMMatrixPerspectiveFovLH(1.57f , 1.47f, 0.01f, 10.0f);
XMStoreFloat4x4(&_cLightBuffer.light.viewProj, XMMatrixTranspose(XMMatrixMultiply(lightView, lightProj)));
Current Outputs
White signifies that a shadow should be projected there. Black indicates no shadow.
CameraPos (0, 2.5, -2)
CameraLookAt (0, 0, 0)
CameraFOV (1.57)
CameraNear (0.01)
CameraFar (10.0)
LightPos (0, 2.5, -2)
LightLookAt (0, 0, 0)
LightFOV (1.57)
LightNear (0.01)
LightFar (10.0)
If I change the CameraPosition to be (0, 2.5, 2), basically just flipped on the Z axis, this is the result.
Obviously a shadow shouldn't change its projection depending on where the observer is, so I think I'm making a mistake with the invV. But I really don't know for sure. I've debugged the light's projView matrix, and the values seem correct - going from CPU to GPU. It's also entirely possible I've misunderstood some theory along the way because this is quite a tricky technique for me.
Aha! Found my problem. It was a silly mistake, I was calculating the depth of pixels from each light, but storing them in a texture that was based on the view of the camera. The following image should explain my mistake better than I can with words.
For future reference, the solution I decided was to scrap my idea for storing light depths in texture channels. Instead, I basically make a new pass for each light, and bind a unique depth-stencil texture to render the geometry to. When I want to do light calculations, I bind each of the depth textures to a shader resource slot and go from there. Obviously this doesn't scale well with many lights, but for my student project where I'm only required to have 2 shadow casters, it suffices.
_context->DrawIndexed(indexCount, 0, 0); //Draw to regular render target
_sunlight->use(1, _context); //Use sunlight shader (basically just runs a Vertex Shader & Null Pixel shader so depth can be written to depth map)
_sunlight->bindDSVSetNullRenderTarget(_context);
_context->DrawIndexed(indexCount, 0, 0); //Draw to sunlight depth target
bindDSVSetNullRenderTarget(ctx){
ID3D11RenderTargetView* nullrv = { nullptr };
ctx->OMSetRenderTargets(1, &nullrv, _sunlightDepthStencilView);
}
//The purpose of setting a null render target before doing the draw call is
//that a draw call with only a depth target bound is much faster.
//(At least I believe so, from my reading online)
I'm trying to write a shader to colorize a custom geometry in SceneKit. I want to set the colors so that horizontal surfaces that are facing up are white, horizontal surfaces that are facing downward are black, and all other surfaces in between are shades of gray based on their orientation. I used the material's surface entry point to call the following shader
vec4 normal = vec4(_surface.normal, 1.0);
// Assume value is [-1, 1], scale to [0, 1]
float color = normal.z * 0.5 + 0.5;
_surface.diffuse = vec4(color, color, color, 1.0);
It appears that the normal.z is relative to the camera (or view). I assume I need to transform the value, so that it's in another space. I tried multiple transforms (and combinations of transforms) such as u_inverseViewTransform, but the results all seem to be in view space. Does anyone know how to colorize a geometry based on the orientation of its surfaces?
Since _surface.normal is a vector in view space, you have to transform the vector to world space.
The transformation of a point form world space to view space is done by u_viewTransform, so the inverse operation (from view space to world space) can be done by u_inverseViewTransform.
_surface.normal is a direction vector, but not a point. A vector has to be transformed by the normal matrix, which is the transposed, inverse of the upper left 3*3 matrix of a 4*4 matrix:
transpose(inverse(mat3(u_viewTransform)))
See Why is the transposed inverse of the model view matrix used to transform the normal vectors?, Why transforming normals with the transpose of the inverse of the modelview matrix?
But since u_viewTransform and u_inverseViewTransform are Orthogonal matrices the transposed, inverse can be skipped, because the inverse matrix and the transposed matrix are equal. See In which cases is the inverse matrix equal to the transpose?.
This follows you have to transform by mat3(u_inverseViewTransform):
vec3 normal = mat3(u_inverseViewTransform) * _surface.normal;
float color = normal.z * 0.5 + 0.5;
_surface.diffuse = vec4(color, color, color, 1.0);
Updated with more explanation around my confusion
(This is how a non-graphics developer imagines the rendering process!)
I specify a 2x2 sqaure to be drawn in by way of two triangles. I'm going to not talk about the triangle anymore. Square is a lot better. Let's say the square gets drawn in one piece.
I have not specified any units for my drawing. The only places in my code that I do something like that is: canvas size (set to 1x1 in my case) and the viewport (i always set this to the dimensions of my output texture).
Then I call draw().
What happens is this: that regardless of the size of my texture (being 1x1 or 10000x10000) all my texels are filled with data (color) that I returned from my frag shader. This is working each time perfectly.
So now I'm trying to explain this to myself:
The GPU is only concerned with coloring the pixels.
Pixel is the smallest unit that the GPU deals with (colors).
Depending on how many pixels my 2x2 square is mapped to, I should be running into one of the following 3 cases:
The number of pixels (to be colored) and my output texture dims match one to one: In this ideal case, for each pixel, there would be one value assigned to my output texture. Very clear to me.
The number of pixels are fewer than my output texture dims. In this case, I should expect that some of the output texels to have exact same value (which is the color of the pixel the fall under). For instance if the GPU ends up drawing 16x16 pixels and my texture is 64x64 then I'll have blocks of 4 texel which get the same value. I have not observed such case regardless of the size of my texture. Which means there is never a case where we end up with fewer pixels (really hard to imagine -- let's keep going)
The number of pixels end up being more than the number of texels. In this case, the GPU should decide which value to assign to my texel. Would it average out the pixel colors? If the GPU is coloring 64x64 pixels and my output texture is 16x16 then I should expect that each texel gets an average color of the 4x4 pixels it contains. Anyway, in this case my texture should be completely filled with values I didn't intend specifically for them (like averaged out) however this has not been the case.
I didn't even talk about how many times my frag shader gets called because it didn't matter. The results would be deterministic anyway.
So considering that I have never run into 2nd and 3rd case where the values in my texels are not what I expected them the only conclusion I can come up with is that the whole assumption of the GPU trying to render pixels is actually wrong. When I assign an output texture to it (which is supposed to stretch over my 2x2 square all the time) then the GPU will happily oblige and for each texel will call my frag shader. Somewhere along the line the pixels get colored too.
But the above lunatistic explanation also fails to answer why I end up with no values in my texels or incorrect values if I stretch my geometry to 1x1 or 4x4 instead of 2x2.
Hopefully the above fantastic narration of the GPU coloring process has given you clues as to where I'm getting this wrong.
Original Post:
We're using WebGL for general computation. As such we create a rectangle and draw 2 triangles in it. Ultimately what we want is the data inside the texture mapped to this geometry.
What I don't understand is if I change the rectangle from (-1,-1):(1,1) to say (-0.5,-0.5):(0.5,0.5) suddenly data is dropped from the texture bound to the framebuffer.
I'd appreciate if someone makes me understand the correlations. The only places that real dimensions of the output texture come into play are the call to viewPort() and readPixels().
Below are relevant pieces of code for you to see what I'm doing:
... // canvas is created with size: 1x1
... // context attributes passed to canvas.getContext()
contextAttributes = {
alpha: false,
depth: false,
antialias: false,
stencil: false,
preserveDrawingBuffer: false,
premultipliedAlpha: false,
failIfMajorPerformanceCaveat: true
};
... // default geometry
// Sets of x,y,z (for rectangle) and s,t coordinates (for texture)
return new Float32Array([
-1.0, 1.0, 0.0, 0.0, 1.0, // upper left
-1.0, -1.0, 0.0, 0.0, 0.0, // lower left
1.0, 1.0, 0.0, 1.0, 1.0, // upper right
1.0, -1.0, 0.0, 1.0, 0.0 // lower right
]);
...
const geometry = this.createDefaultGeometry();
gl.bindBuffer(gl.ARRAY_BUFFER, buffer);
gl.bufferData(gl.ARRAY_BUFFER, geometry, gl.STATIC_DRAW);
... // binding to the vertex shader attribs
gl.vertexAttribPointer(positionHandle, 3, gl.FLOAT, false, 20, 0);
gl.vertexAttribPointer(textureCoordHandle, 2, gl.FLOAT, false, 20, 12);
gl.enableVertexAttribArray(positionHandle);
gl.enableVertexAttribArray(textureCoordHandle);
... // setting up framebuffer; I set the viewport to output texture dimensions (I think this is absolutely needed but not sure)
gl.bindTexture(gl.TEXTURE_2D, texture);
gl.bindFramebuffer(gl.FRAMEBUFFER, this.framebuffer);
gl.framebufferTexture2D(
gl.FRAMEBUFFER, // The target is always a FRAMEBUFFER.
gl.COLOR_ATTACHMENT0, // We are providing the color buffer.
gl.TEXTURE_2D, // This is a 2D image texture.
texture, // The texture.
0); // 0, we aren't using MIPMAPs
gl.viewport(0, 0, width, height);
... // reading from output texture
gl.bindTexture(gl.TEXTURE_2D, texture);
gl.framebufferTexture2D(
gl.FRAMEBUFFER, gl.COLOR_ATTACHMENT0, gl.TEXTURE_2D, texture,
0);
gl.readPixels(0, 0, width, height, gl.FLOAT, gl.RED, buffer);
new answer
I'm just saying the same thing yet again (3rd time?)
Copied from below
WebGL is destination based. That means it's going to iterate over the pixels of the line/point/triangle it's drawing and for each point call the fragment shader and ask 'what value should I store here`?
It's destination based. It's going to draw each pixel exactly once. For that pixel it's going to ask "what color should I make this"
destination based loop
for (let i = start; i < end; ++i) {
fragmentShaderFunction(); // must set gl_FragColor
destinationTextureOrCanvas[i] = gl_FragColor;
You can see in the loop above there is no setting any random destination. There is no setting any part of destination twice. It's just going to run from start to end and exactly once for each pixel in the destination between start and end ask what color it should make that pixel.
How to do you set start and end? Again, to make it simple let's assume a 200x1 texture so we can ignore Y. It works like this
vertexShaderFunction(); // must set gl_Position
const start = clipspaceToArrayspaceViaViewport(viewport, gl_Position.x);
vertexShaderFunction(); // must set gl_Position
const end = clipspaceToArrayspaceViaViewport(viewport, gl_Position.x);
for (let i = start; i < end; ++i) {
fragmentShaderFunction(); // must set gl_FragColor
texture[i] = gl_FragColor;
}
see below for clipspaceToArrayspaceViaViewport
What is viewport? viewport is what you set when you called `gl.viewport(x, y, width, height)
So, set gl_Position.x to -1 and +1, viewport.x to 0 and viewport.width = 200 (the width of the texture) then start will be 0, end will be 200
set gl_Position.x to .25 and .75, viewport.x to 0 and viewport.width = 200 (the width of the texture). The start will be 125 and end will be 175
I honestly feel like this answer is leading you down the wrong path. It's not remotely this complicated. You don't have to understand any of this to use WebGL IMO.
The simple answer is
You set gl.viewport to the sub rectangle you want to affect in your destination (canvas or texture it doesn't matter)
You make a vertex shader that somehow sets gl_Position to clip space coordinates (they go from -1 to +1) across the texture
Those clip space coordinates get converted to the viewport space. It's basic math to map one range to another range but it's mostly not important. It's seems intuitive that -1 will draw to the viewport.x pixel and +1 will draw to the viewport.x + viewport.width - 1 pixel. That's what "maps from clip space to the viewport settings means".
It's most common for the viewport settings to be (x = 0, y = 0, width = width of destination texture or canvas, height = height of destination texture or canvas)
So that just leaves what you set gl_Position to. Those values are in clip space just like it explains in this article.
You can make it simple by doing if you want by converting from pixel space to clip space just like it explains in this article
zeroToOne = someValueInPixels / destinationDimensions;
zeroToTwo = zeroToOne * 2.0;
clipspace = zeroToTwo - 1.0;
gl_Position = clipspace;
If you continue the articles they'll also show adding a value (translation) and multiplying by a value (scale)
Using just those 2 things and a unit square (0 to 1) you can choose any rectangle on the screen. Want to effect 123 to 127. That's 5 units so scale = 5, translation = 123. Then apply the math above to convert from pixels to clips space and you'll get the rectangle you want.
If you continue further though those articles you'll eventually get the point where that math is done with matrices but you can do that math however you want. It's like asking "how do I compute the value 3". Well, 1 + 1 + 1, or 3 + 0, or 9 / 3, or 100 - 50 + 20 * 2 / 30, or (7^2 - 19) / 10, or ????
I can't tell you how to set gl_Position. I can only tell you make up whatever math you want and set it to *clip space* and then give an example of converting from pixels to clipspace (see above) as just one example of some possible math.
old answer
I get that this might not be clear I don't know how to help. WebGL draws lines, points, or triangles two a 2D array. That 2D array is either the canvas, a texture (as a framebuffer attachment) or a renderbuffer (as a framebuffer attachment).
The size of the area is defined by the size of the canvas, texture, renderbuffer.
You write a vertex shader. When you call gl.drawArrays(primitiveType, offset, count) you're telling WebGL to call your vertex shader count times. Assuming primitiveType is gl.TRIANGLES then for every 3 vertices generated by your vertex shader WebGL will draw a triangle. You specify that triangle by setting gl_Position in clip space.
Assuming gl_Position.w is 1, Clip space goes from -1 to +1 in X and Y across the destination canvas/texture/renderbuffer. (gl_Position.x and gl_Position.y are divided by gl_Position.w) which is not really important for your case.
To convert back to actually pixels your X and Y are converted based on the settings of gl.viewport. Let's just do X
pixelX = ((clipspace.x / clipspace.w) * .5 + .5) * viewport.width + viewport.x
WebGL is destination based. That means it's going to iterate over the pixels of the line/point/triangle it's drawing and for each point call the fragment shader and ask 'what value should I store here`?
Let's translate that to JavaScript in 1D. Let's assume you have an 1D array
const dst = new Array(100);
Let's make a function that takes a start and end and sets values between
function setRange(dst, start, end, value) {
for (let i = start; i < end; ++i) {
dst[i] = value;
}
}
You can fill the entire 100 element array with 123
const dst = new Array(100);
setRange(dst, 0, 99, 123);
To set the last half of the array to 456
const dst = new Array(100);
setRange(dst, 50, 99, 456);
Let's change that to use clip space like coordinates
function setClipspaceRange(dst, clipStart, clipEnd, value) {
const start = clipspaceToArrayspace(dst, clipStart);
const end = clipspaceToArrayspace(dst, clipEnd);
for (let i = start; i < end; ++i) {
dst[i] = value;
}
}
function clipspaceToArrayspace(array, clipspaceValue) {
// convert clipspace value (-1 to +1) to (0 to 1)
const zeroToOne = clipspaceValue * .5 + .5;
// convert zeroToOne value to array space
return Math.floor(zeroToOne * array.length);
}
This function now works just like the previous one except takes clip space values instead of array indices
// fill entire array with 123
const dst = new Array(100);
setClipspaceRange(dst, -1, +1, 123);
Set the last half of the array to 456
setClipspaceRange(dst, 0, +1, 456);
Now abstract one more time. Instead of using the array's length use a setting
// viewport looks like `{ x: number, width: number} `
function setClipspaceRangeViaViewport(dst, viewport, clipStart, clipEnd, value) {
const start = clipspaceToArrayspaceViaViewport(viewport, clipStart);
const end = clipspaceToArrayspaceViaViewport(viewport, clipEnd);
for (let i = start; i < end; ++i) {
dst[i] = value;
}
}
function clipspaceToArrayspaceViaViewport(viewport, clipspaceValue) {
// convert clipspace value (-1 to +1) to (0 to 1)
const zeroToOne = clipspaceValue * .5 + .5;
// convert zeroToOne value to array space
return Math.floor(zeroToOne * viewport.width) + viewport.x;
}
Now to fill the entire array with 123
const dst = new Array(100);
const viewport = { x: 0, width: 100; }
setClipspaceRangeViaViewport(dst, viewport, -1, 1, 123);
Set the last half of the array to 456 there are now 2 ways. Way one is just like the previous using 0 to +1
setClipspaceRangeViaViewport(dst, viewport, 0, 1, 456);
You can also set the viewport to start half way through the array
const halfViewport = { x: 50, width: 50; }
setClipspaceRangeViaViewport(dst, halfViewport, -1, +1, 456);
I don't know if that was helpful or not.
The only other thing to add is instead of value replace that with a function that gets called every iteration to supply value
function setClipspaceRangeViaViewport(dst, viewport, clipStart, clipEnd, fragmentShaderFunction) {
const start = clipspaceToArrayspaceViaViewport(viewport, clipStart);
const end = clipspaceToArrayspaceViaViewport(viewport, clipEnd);
for (let i = start; i < end; ++i) {
dst[i] = fragmentShaderFunction();
}
}
Note this is the exact same thing that is said in this article and clearified somewhat in this article.
I am using a custom shader to create a sprite in SpriteKit.
The main part of the shader does this...
vec4 col = mix(baseColor, overlayColor, overlayColor.a);
The colours I have are something like...
baseColor = UIColor(red:0.51, green:0.71, blue:0.88, alpha:1.0)
and...
overlay = UIColor(red: 1.0, green: 1.0, blue: 1.0, alpha: 0.5)
According to everywhere on the internet (links to follow) the blend function I'm using above is the same as a Normal blend mode in Photoshop, Pixelmator, Sketch, etc... this should result in the colour...
col = UIColor(red:0.75, green:0.85, blue:0.95, alpha:1.00)
Which is a bright blue colour. However, what I'm getting is...
col = UIColor(red:0.51, green:0.61, blue:0.69, alpha:1.00)
Which is a murky grey colour.
You can see what it should look like here... https://thebookofshaders.com/glossary/?search=mix
If you enter the code...
#ifdef GL_ES
precision mediump float;
#endif
uniform vec2 u_resolution;
uniform float u_time;
vec4 colorA = vec4(0.5, 0.7, 0.9, 1.0);
vec4 colorB = vec4(1.0, 1.0, 1.0, 0.5);
void main() {
vec4 color = vec4(0.0);
// Mix uses pct (a value from 0-1) to
// mix the two colors
color = mix(colorA, colorB, colorB.a);
color.a = 1.0;
gl_FragColor = color;
}
The ideal output colour looks like this...
But it looks like this...
I’m gonna investigate this more tomorrow. I wish I knew why the output was completely different than everywhere else says it should be.
OK, thanks to #Reaper's comment I started out on a full investigation of what was going wrong with this.
When mixing the hard coded colours in our shader the colour was actually correct.
So it lead me to look at the texture images we were using.
The one that had the white with 50% alpha was definitely white. (not grey).
But... (quirk in the system?) open GL was picking it up as 50% grey with 50% alpha.
And so the mix wasn't actually mixing the correct colours in the first place.
We fixed this by using a 100% alpha image for the colours and a 100% image for the alpha map (black -> white).
By doing this it fixed the problem we were having.
I have a texture image that I am using with GLKit. If I use GL_MODULATE on the texture and have vertex RGBA (1.0, 1.0, 1.0, 1.0) then the texture shows up entirely as it would do in GL_REPLACE. Fully opaque.
Then if I use Red (1.0, 0.0, 0.0, 1.0) for vertex RGB the texture shows up again as Red modulating the texture.
So far so good.
But when I change the transparency in the vertex color and I use RGBA(1.0, 0.0, 0.0, 0.5), then only a light red color is seen and the texture is not visible, so the color is replacing the texture entirely.
The texture itself has no alpha, it is RGB565 texture.
I am using GLKit with GLKTextureEnvModeModulate.
self.effect.texture2d0.envMode = GLKTextureEnvModeModulate;
Any help on why the texture would disappear, when I specify the alpha?
Adding snapshots:
This is the original texture
RGBA (1.0, 1.0, 1.0, 1.0) - white color , no premultiplication, opaque, texture visible
RGBA (1.0, 1.0, 1.0, 0.5) - white color, no premultiplication, alpha = 0.5, texture lost
RGBA (1.0, 0, 0, 1.0) - red color , no premultiplication, opaque, texture visible
RGBA (1.0, 0, 0, 0.5) - red color, no premultiplication, alpha = 0.5, texture lost
RGBA (0.5, 0, 0, 0.5) - red color, premultiplication, alpha = 0.5 per #andon, texture visible, but you may need to magnify to see it
RGBA (0.1, 0, 0, 0.1) - red color, premultiplication, alpha = 0.1 per #andon, texture lost, probably because not enough contrast is there
RGBA (0.9, 0, 0, 0.9) - red color, premultiplication, alpha = 0.9 per #andon, texture visible, but you may need to magnify to see it
The texture itself has no alpha, it is RGB565 texture
RGB565 implicitly has constant alpha (opaque -> 1.0). That may not sound important, but modulating vertex color with texture color does a component-wise multiplication and that would not work at all if alpha were not 1.0.
My blend function is for pre-multiplied - One, One - Src.
This necessitates pre-multiplying the RGB components of vertex color by the A component. All colors must be pre-multiplied, this includes texels and vertex colors.
You can see why below:
Vtx = (1.0, 0.0, 0.0, 0.5)
Tex = (R, G, B, 1.0)
// Modulate Vertex and Tex
Src = Vtx * Tex = (R, 0, 0, 0.5)
// Pre-multiplied Alpha Blending (done incorrectly)
Blend_RGB = Src * 1 + (1 - Src.a) * Dst
= Src + Dst / 2.0
= (R, 0, 0) + Dst / 2.0
The only thing this does is divide the destination color by 2 and add the unaltered source color to it. It is supposed to resemble linear interpolation (a * c + (1 - c) * b).
Proper blending should look like this:
// Traditional Blending
Blend_RGB = Src * Src.a + (1 - Src.a) * Dst
= (0.5R, 0, 0) + Dst / 2.0
This can be accomplished using the original blend function if you multiply the RGB part of the vertex color by A.
Correct pre-multiplied alpha blending (by pre-multiplying vertex color):
Vtx = (0.5, 0.0, 0.0, 0.5) // Pre-multiply: RGB *= A
Tex = (R, G, B, 1.0)
// Modulate Vertex and Tex
Src = Vtx * Tex = (0.5R, 0, 0, 0.5)
// Pre-multiplied Alpha Blending (done correctly)
Blend_RGB = Src * 1 + (1 - Src.a) * Dst
= (0.5R, 0, 0) + Dst / 2.0