Is it possible to draw a circle made up of triangles with DirectX 3D 11?

Question

Is there a way to create a circle out of 16 triangles with DirectX 3D 11; kind of like a unit circle? I am currently using the Direct3D 11 Tutorial 02: Rendering a Triangle from the DirectX Sample Browser (June 2010) and modified it a bit to draw the triangle in the center, but I now want to draw a circle using that triangle.

Would I have to create 48 vertices to create it, or is there a easier way? Like using a for loop.

I am also new to C++, and am just learning and getting used to it and DirectX basics.

This is the code for the Tutorial02.cpp:

//--------------------------------------------------------------------------------------
// File: Tutorial02.cpp
//
// This application displays a triangle using Direct3D 11
//
// Copyright (c) Microsoft Corporation. All rights reserved.
//--------------------------------------------------------------------------------------
#include <windows.h>
#include <d3d11.h>
#include <d3dx11.h>
#include <d3dcompiler.h>
#include <xnamath.h>
#include "resource.h"


//--------------------------------------------------------------------------------------
// Structures
//--------------------------------------------------------------------------------------
struct SimpleVertex
{
    XMFLOAT3 Pos;
};


//--------------------------------------------------------------------------------------
// Global Variables
//--------------------------------------------------------------------------------------
HINSTANCE               g_hInst = NULL;
HWND                    g_hWnd = NULL;
D3D_DRIVER_TYPE         g_driverType = D3D_DRIVER_TYPE_NULL;
D3D_FEATURE_LEVEL       g_featureLevel = D3D_FEATURE_LEVEL_11_0;
ID3D11Device*           g_pd3dDevice = NULL;
ID3D11DeviceContext*    g_pImmediateContext = NULL;
IDXGISwapChain*         g_pSwapChain = NULL;
ID3D11RenderTargetView* g_pRenderTargetView = NULL;
ID3D11VertexShader*     g_pVertexShader = NULL;
ID3D11PixelShader*      g_pPixelShader = NULL;
ID3D11InputLayout*      g_pVertexLayout = NULL;
ID3D11Buffer*           g_pVertexBuffer = NULL;


//--------------------------------------------------------------------------------------
// Forward declarations
//--------------------------------------------------------------------------------------
HRESULT InitWindow( HINSTANCE hInstance, int nCmdShow );
HRESULT InitDevice();
void CleanupDevice();
LRESULT CALLBACK    WndProc( HWND, UINT, WPARAM, LPARAM );
void Render();


//--------------------------------------------------------------------------------------
// Entry point to the program. Initializes everything and goes into a message processing 
// loop. Idle time is used to render the scene.
//--------------------------------------------------------------------------------------
int WINAPI wWinMain( HINSTANCE hInstance, HINSTANCE hPrevInstance, LPWSTR lpCmdLine, int nCmdShow )
{
    UNREFERENCED_PARAMETER( hPrevInstance );
    UNREFERENCED_PARAMETER( lpCmdLine );

    if( FAILED( InitWindow( hInstance, nCmdShow ) ) )
        return 0;

    if( FAILED( InitDevice() ) )
    {
        CleanupDevice();
        return 0;
    }

    // Main message loop
    MSG msg = {0};
    while( WM_QUIT != msg.message )
    {
        if( PeekMessage( &msg, NULL, 0, 0, PM_REMOVE ) )
        {
            TranslateMessage( &msg );
            DispatchMessage( &msg );
        }
        else
        {
            Render();
        }
    }

    CleanupDevice();

    return ( int )msg.wParam;
}


//--------------------------------------------------------------------------------------
// Register class and create window
//--------------------------------------------------------------------------------------
HRESULT InitWindow( HINSTANCE hInstance, int nCmdShow )
{
    // Register class
    WNDCLASSEX wcex;
    wcex.cbSize = sizeof( WNDCLASSEX );
    wcex.style = CS_HREDRAW | CS_VREDRAW;
    wcex.lpfnWndProc = WndProc;
    wcex.cbClsExtra = 0;
    wcex.cbWndExtra = 0;
    wcex.hInstance = hInstance;
    wcex.hIcon = LoadIcon( hInstance, ( LPCTSTR )IDI_TUTORIAL1 );
    wcex.hCursor = LoadCursor( NULL, IDC_ARROW );
    wcex.hbrBackground = ( HBRUSH )( COLOR_WINDOW + 1 );
    wcex.lpszMenuName = NULL;
    wcex.lpszClassName = L"TutorialWindowClass";
    wcex.hIconSm = LoadIcon( wcex.hInstance, ( LPCTSTR )IDI_TUTORIAL1 );
    if( !RegisterClassEx( &wcex ) )
        return E_FAIL;

    // Create window
    g_hInst = hInstance;
    RECT rc = { 0, 0, 640, 480 };
    AdjustWindowRect( &rc, WS_OVERLAPPEDWINDOW, FALSE );
    g_hWnd = CreateWindow( L"TutorialWindowClass", L"Direct3D 11 Tutorial 2: Rendering a Triangle",
                           WS_OVERLAPPEDWINDOW,
                           CW_USEDEFAULT, CW_USEDEFAULT, rc.right - rc.left, rc.bottom - rc.top, NULL, NULL, hInstance,
                           NULL );
    if( !g_hWnd )
        return E_FAIL;

    ShowWindow( g_hWnd, nCmdShow );

    return S_OK;
}


//--------------------------------------------------------------------------------------
// Helper for compiling shaders with D3DX11
//--------------------------------------------------------------------------------------
HRESULT CompileShaderFromFile( WCHAR* szFileName, LPCSTR szEntryPoint, LPCSTR szShaderModel, ID3DBlob** ppBlobOut )
{
    HRESULT hr = S_OK;

    DWORD dwShaderFlags = D3DCOMPILE_ENABLE_STRICTNESS;
#if defined( DEBUG ) || defined( _DEBUG )
    // Set the D3DCOMPILE_DEBUG flag to embed debug information in the shaders.
    // Setting this flag improves the shader debugging experience, but still allows 
    // the shaders to be optimized and to run exactly the way they will run in 
    // the release configuration of this program.
    dwShaderFlags |= D3DCOMPILE_DEBUG;
#endif

    ID3DBlob* pErrorBlob;
    hr = D3DX11CompileFromFile( szFileName, NULL, NULL, szEntryPoint, szShaderModel, 
        dwShaderFlags, 0, NULL, ppBlobOut, &pErrorBlob, NULL );
    if( FAILED(hr) )
    {
        if( pErrorBlob != NULL )
            OutputDebugStringA( (char*)pErrorBlob->GetBufferPointer() );
        if( pErrorBlob ) pErrorBlob->Release();
        return hr;
    }
    if( pErrorBlob ) pErrorBlob->Release();

    return S_OK;
}


//--------------------------------------------------------------------------------------
// Create Direct3D device and swap chain
//--------------------------------------------------------------------------------------
HRESULT InitDevice()
{
    HRESULT hr = S_OK;

    RECT rc;
    GetClientRect( g_hWnd, &rc );
    UINT width = rc.right - rc.left;
    UINT height = rc.bottom - rc.top;

    UINT createDeviceFlags = 0;
#ifdef _DEBUG
    createDeviceFlags |= D3D11_CREATE_DEVICE_DEBUG;
#endif

    D3D_DRIVER_TYPE driverTypes[] =
    {
        D3D_DRIVER_TYPE_HARDWARE,
        D3D_DRIVER_TYPE_WARP,
        D3D_DRIVER_TYPE_REFERENCE,
    };
    UINT numDriverTypes = ARRAYSIZE( driverTypes );

    D3D_FEATURE_LEVEL featureLevels[] =
    {
        D3D_FEATURE_LEVEL_11_0,
        D3D_FEATURE_LEVEL_10_1,
        D3D_FEATURE_LEVEL_10_0,
    };
    UINT numFeatureLevels = ARRAYSIZE( featureLevels );

    DXGI_SWAP_CHAIN_DESC sd;
    ZeroMemory( &sd, sizeof( sd ) );
    sd.BufferCount = 1;
    sd.BufferDesc.Width = width;
    sd.BufferDesc.Height = height;
    sd.BufferDesc.Format = DXGI_FORMAT_R8G8B8A8_UNORM;
    sd.BufferDesc.RefreshRate.Numerator = 60;
    sd.BufferDesc.RefreshRate.Denominator = 1;
    sd.BufferUsage = DXGI_USAGE_RENDER_TARGET_OUTPUT;
    sd.OutputWindow = g_hWnd;
    sd.SampleDesc.Count = 1;
    sd.SampleDesc.Quality = 0;
    sd.Windowed = TRUE;

    for( UINT driverTypeIndex = 0; driverTypeIndex < numDriverTypes; driverTypeIndex++ )
    {
        g_driverType = driverTypes[driverTypeIndex];
        hr = D3D11CreateDeviceAndSwapChain( NULL, g_driverType, NULL, createDeviceFlags, featureLevels, numFeatureLevels,
                                            D3D11_SDK_VERSION, &sd, &g_pSwapChain, &g_pd3dDevice, &g_featureLevel, &g_pImmediateContext );
        if( SUCCEEDED( hr ) )
            break;
    }
    if( FAILED( hr ) )
        return hr;

    // Create a render target view
    ID3D11Texture2D* pBackBuffer = NULL;
    hr = g_pSwapChain->GetBuffer( 0, __uuidof( ID3D11Texture2D ), ( LPVOID* )&pBackBuffer );
    if( FAILED( hr ) )
        return hr;

    hr = g_pd3dDevice->CreateRenderTargetView( pBackBuffer, NULL, &g_pRenderTargetView );
    pBackBuffer->Release();
    if( FAILED( hr ) )
        return hr;

    g_pImmediateContext->OMSetRenderTargets( 1, &g_pRenderTargetView, NULL );

    // Setup the viewport
    D3D11_VIEWPORT vp;
    vp.Width = (FLOAT)width;
    vp.Height = (FLOAT)height;
    vp.MinDepth = 0.0f;
    vp.MaxDepth = 1.0f;
    vp.TopLeftX = 0;
    vp.TopLeftY = 0;
    g_pImmediateContext->RSSetViewports( 1, &vp );

    // Compile the vertex shader
    ID3DBlob* pVSBlob = NULL;
    hr = CompileShaderFromFile( L"Tutorial02.fx", "VS", "vs_4_0", &pVSBlob );
    if( FAILED( hr ) )
    {
        MessageBox( NULL,
                    L"The FX file cannot be compiled.  Please run this executable from the directory that contains the FX file.", L"Error", MB_OK );
        return hr;
    }

    // Create the vertex shader
    hr = g_pd3dDevice->CreateVertexShader( pVSBlob->GetBufferPointer(), pVSBlob->GetBufferSize(), NULL, &g_pVertexShader );
    if( FAILED( hr ) )
    {   
        pVSBlob->Release();
        return hr;
    }

    // Define the input layout
    D3D11_INPUT_ELEMENT_DESC layout[] =
    {
        { "POSITION", 0, DXGI_FORMAT_R32G32B32_FLOAT, 0, 0, D3D11_INPUT_PER_VERTEX_DATA, 0 },
    };
    UINT numElements = ARRAYSIZE( layout );

    // Create the input layout
    hr = g_pd3dDevice->CreateInputLayout( layout, numElements, pVSBlob->GetBufferPointer(),
                                          pVSBlob->GetBufferSize(), &g_pVertexLayout );
    pVSBlob->Release();
    if( FAILED( hr ) )
        return hr;

    // Set the input layout
    g_pImmediateContext->IASetInputLayout( g_pVertexLayout );

    // Compile the pixel shader
    ID3DBlob* pPSBlob = NULL;
    hr = CompileShaderFromFile( L"Tutorial02.fx", "PS", "ps_4_0", &pPSBlob );
    if( FAILED( hr ) )
    {
        MessageBox( NULL,
                    L"The FX file cannot be compiled.  Please run this executable from the directory that contains the FX file.", L"Error", MB_OK );
        return hr;
    }

    // Create the pixel shader
    hr = g_pd3dDevice->CreatePixelShader( pPSBlob->GetBufferPointer(), pPSBlob->GetBufferSize(), NULL, &g_pPixelShader );
    pPSBlob->Release();
    if( FAILED( hr ) )
        return hr;

    // Create vertex buffer
    SimpleVertex vertices[] =
    {
        XMFLOAT3(-0.1f, 0.8f, 0.5f),
        XMFLOAT3(0.1f, 0.8f, 0.5f),
        XMFLOAT3(0.0f, 0.0f, 0.5f),
    };
    D3D11_BUFFER_DESC bd;
    ZeroMemory( &bd, sizeof(bd) );
    bd.Usage = D3D11_USAGE_DEFAULT;
    bd.ByteWidth = sizeof( SimpleVertex ) * 3;
    bd.BindFlags = D3D11_BIND_VERTEX_BUFFER;
    bd.CPUAccessFlags = 0;
    D3D11_SUBRESOURCE_DATA InitData;
    ZeroMemory( &InitData, sizeof(InitData) );
    InitData.pSysMem = vertices;
    hr = g_pd3dDevice->CreateBuffer( &bd, &InitData, &g_pVertexBuffer );
    if( FAILED( hr ) )
        return hr;

    // Set vertex buffer
    UINT stride = sizeof( SimpleVertex );
    UINT offset = 0;
    g_pImmediateContext->IASetVertexBuffers( 0, 1, &g_pVertexBuffer, &stride, &offset );

    // Set primitive topology
    g_pImmediateContext->IASetPrimitiveTopology( D3D11_PRIMITIVE_TOPOLOGY_TRIANGLELIST );

    return S_OK;
}


//--------------------------------------------------------------------------------------
// Clean up the objects we've created
//--------------------------------------------------------------------------------------
void CleanupDevice()
{
    if( g_pImmediateContext ) g_pImmediateContext->ClearState();

    if( g_pVertexBuffer ) g_pVertexBuffer->Release();
    if( g_pVertexLayout ) g_pVertexLayout->Release();
    if( g_pVertexShader ) g_pVertexShader->Release();
    if( g_pPixelShader ) g_pPixelShader->Release();
    if( g_pRenderTargetView ) g_pRenderTargetView->Release();
    if( g_pSwapChain ) g_pSwapChain->Release();
    if( g_pImmediateContext ) g_pImmediateContext->Release();
    if( g_pd3dDevice ) g_pd3dDevice->Release();
}


//--------------------------------------------------------------------------------------
// Called every time the application receives a message
//--------------------------------------------------------------------------------------
LRESULT CALLBACK WndProc( HWND hWnd, UINT message, WPARAM wParam, LPARAM lParam )
{
    PAINTSTRUCT ps;
    HDC hdc;

    switch( message )
    {
        case WM_PAINT:
            hdc = BeginPaint( hWnd, &ps );
            EndPaint( hWnd, &ps );
            break;

        case WM_DESTROY:
            PostQuitMessage( 0 );
            break;

        default:
            return DefWindowProc( hWnd, message, wParam, lParam );
    }

    return 0;
}


//--------------------------------------------------------------------------------------
// Render a frame
//--------------------------------------------------------------------------------------
void Render()
{
    // Clear the back buffer 
    float ClearColor[4] = { 0.0f, 0.125f, 0.3f, 1.0f }; // red,green,blue,alpha
    g_pImmediateContext->ClearRenderTargetView( g_pRenderTargetView, ClearColor );

    // Render a triangle
    g_pImmediateContext->VSSetShader( g_pVertexShader, NULL, 0 );
    g_pImmediateContext->PSSetShader( g_pPixelShader, NULL, 0 );
    g_pImmediateContext->Draw( 3, 0 );

    // Present the information rendered to the back buffer to the front buffer (the screen)
    g_pSwapChain->Present( 0, 0 );
}

Answer 1

If you want to draw a circle using 16 triangles, you need 17 vertices; one for each corner of your circle and one for the center. Then you have to use 48 indices to tell D3D how it should connect those vertices. Then you can call DrawIndexed to draw the triangles. You can also use a triangle strip which is a different primitive topology and uses slightly less indices. See this tutorial on how to create vertex and index buffers.

Answer 2

Use a for loop, as you say. Let's say you want 10 triangles. There are 2pi radians in a circle, so 2pi/10 is the angle for each triangle. Let's calculate:

int n = 10; // number of triangles
SimpleVertex* vertices = malloc(sizeof(SimpleVertex) * 10 * 3); // 10 triangles, 3 verticies per triangle
float deltaTheta = 2*pi / n; // Change in theta for each vertex
for( int i = 0; i < n; i++ ) {
    int theta = i * deltaTheta; // Theta is the angle for that triangle
    int index = 3 * i;
    vertices[index + 0] = SimpleVertex(0, 0, 0);
    // Given an angle theta, cosine [cos] will give you the x coordinate,
    // and sine [sin] will give you the y coordinate.
    // #include <math.h>
    vertices[index + 1] = SimpleVertex(cos(theta), sin(theta), 0);
    vertices[index + 2] = SimpleVertex(cos(theta + deltaTheta), sin(theta + deltaTheta), 0);
}

Note:

As you can imagine, many of the vertices will overlap. (0, 0, 0) is always the same, and the last vertex of one triangle equals the 2nd vertical of the next triangle. I'll leave you up to the optimization, first get it working so you understand what's happening. If you aren't familiar with trig, look up the unit circle. Or just accept that cos/sin are defined to be the x and y coordinates of a circle given degrees (Or rather, radians). You will have to wait until your tutorial goes over how to specify what vertices each triangle uses first.