I've been trying to get this to work for awhile now, but I can't seem to figure it out, and hours of Googling has yet to reveal any useful results.

I have an array of 32-bit pixels in RGBA order, and I want to create a device-independent bitmap from them and place it on the clipboard using SetClipboardData(CF_DIBV5, dib) or similar (ideally, I want to preserve the alpha channel). Registering a custom clipboard type is not an option, since the point of putting it on the clipboard is so that it can be pasted into another program. Bonus points if I don't have to manually convert my pixel data into some other format (such as planar BGRA).

My current code goes like this (it's all within a set_clipboard_img function):

if(!OpenClipboard(hwnd)) return;
BITMAPV5HEADER* info = (BITMAPV5HEADER*) GlobalAlloc(GMEM_MOVEABLE, sizeof(BITMAPV5HEADER));
info->bV5Size = sizeof(BITMAPV5HEADER);
info->bV5Width = img_width;
info->bV5Height = -img_height;
info->bV5Planes = 1; // The docs say this is the only valid value here.
info->bV5BitCount = 32;
info->bV5Compression = BI_BITFIELDS;
info->bV5SizeImage = img_width * img_height * 4;
info->bV5RedMask   = 0xff000000;
info->bV5GreenMask = 0x00ff0000;
info->bV5BlueMask  = 0x0000ff00;
info->bV5AlphaMask = 0x000000ff;
unsigned char* buf;
// One of the sources I found said that I can pass a BITMAPV5HEADER in place of the BITMAPINFO, hence the first reinterpret_cast.
HBITMAP dib = CreateDIBSection(NULL, reinterpret_cast<BITMAPINFO*>(info), DIB_RGB_COLORS, reinterpret_cast<void**>(&buf), NULL, 0);
if(dib == NULL) {
    CloseClipboard();
    return;
}
// img_pixels_ptr is a unsigned char* to the pixels in non-planar RGBA format
std::copy_n(img_pixels_ptr, info->bV5SizeImage, buf);
EmptyClipboard();
auto result = SetClipboardData(CF_DIBV5, dib);
if(result == NULL) {
    char str[256];
    str[255] = 0;
    FormatMessageA(FORMAT_MESSAGE_FROM_SYSTEM, NULL, GetLastError(), 0, str, 255, NULL);
    std::cerr << "Error setting clipboard: " << str << std::endl;
    // Here I get "handle not valid". I have no idea _why_ it's not valid, though.
}
CloseClipboard();

Ultimately, I'll also need to be able to reverse the process (getting a potentially-transparent bitmap off the clipboard), but one thing at a time.

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You cannot pass an HBITMAP to SetClipboardData(). It requires an HGLOBAL from GlobalAlloc() instead. That is why SetClipboardData() is failing with an ERROR_INVALID_HANDLE error.

You need to put your BITMAPV5HEADER and pixel data directly into the allocated HGLOBAL and put it as-is onto the clipboard, forget using CreateDIBSection() at all:

Standard Clipboard Formats

CF_DIBV5
17
A memory object containing a BITMAPV5HEADER structure followed by the bitmap color space information and the bitmap bits.

Try something more like this:

void printErr(const char *msg)
{
    char str[256] = {0};
    FormatMessageA(FORMAT_MESSAGE_FROM_SYSTEM, NULL, GetLastError(), 0, str, 255, NULL);
    std::cerr << msg << ": " << str << std::endl;
}

...

DWORD size_pixels = img_width * img_height * 4;

HGLOBAL hMem = GlobalAlloc(GHND, sizeof(BITMAPV5HEADER) + size_pixels);
if (!hMem)
{
    printErr("Error allocating memory for bitmap data");
    return;
}

BITMAPV5HEADER* hdr = (BITMAPV5HEADER*) GlobalLock(hMem);
if (!hdr)
{
    printErr("Error accessing memory for bitmap data");
    GlobalFree(hMem);
    return;
}

hdr->bV5Size = sizeof(BITMAPV5HEADER);
hdr->bV5Width = img_width;
hdr->bV5Height = -img_height;
hdr->bV5Planes = 1;
hdr->bV5BitCount = 32;
hdr->bV5Compression = BI_BITFIELDS;
hdr->bV5SizeImage = size_pixels;
hdr->bV5RedMask   = 0xff000000;
hdr->bV5GreenMask = 0x00ff0000;
hdr->bV5BlueMask  = 0x0000ff00;
hdr->bV5AlphaMask = 0x000000ff;

// img_pixels_ptr is a unsigned char* to the pixels in non-planar RGBA format
CopyMemory(hdr+1, img_pixels_ptr, size_pixels);
GlobalUnlock(hMem);

if (!OpenClipboard(hwnd))
{
    printErr("Error opening clipboard");
}
else
{
    if (!EmptyClipboard())
        printErr("Error emptying clipboard");

    else if (!SetClipboardData(CF_DIBV5, hMem))
        printErr("Error setting bitmap on clipboard");

    else
        hMem = NULL; // clipboard now owns the memory

    CloseClipboard();
}

if (hMem)
    GlobalFree(hMem);