Setting Up a World Matrix

Like any other transformation, you create the world transformation by concatenating a series of transformation matrices into a single matrix that contains the sum total of their effects. In the simplest case, when a model is at the world origin and its local coordinate axes are oriented the same as world space, the world matrix is the identity matrix. More commonly, the world matrix is a combination of a translation into world space, and possibly one or more rotations to "turn" the model as needed.

The following example, from a fictitious 3-D model class, uses the helper functions in the D3dutil.cpp and D3dmath.cpp files (included with the DirectX SDK) to create a world matrix that includes three rotations to orient a model and a translation to relocate it relative to its position in world space.

/*
 * For the purposes of this example, the following variables
 * assumed to be valid and initialized.
 *
 * The m_vPos variable is a D3DVECTOR that contains the model's
 * location in world coordinates.
 *
 * The m_fPitch, m_fYaw, and m_fRoll variables are D3DVALUEs that 
 * contain the model's orientation in terms of pitch, yaw, and roll
 * angles (in radians).
 */
 
D3DMATRIX C3DModel::MakeWorldMatrix(void)
{
    D3DMATRIX matWorld, // World matrix being constructed.
              matTemp,  // Temp matrix for rotations.
              matRot;   // Final rotation matrix (applied to matWorld).
 
    // Using the right-to-left order of matrix concatenation,
    // apply the translation to the object's world position
    // before applying the rotations.
    D3DUtil_SetTranslateMatrix(matWorld, m_vPos);
    D3DUtil_SetIdentityMatrix(matRot);
 
    //
    // Now, apply the orientation variables into the 
    // world matrix
    //
    if(m_fPitch || m_fYaw || m_fRoll)
    {
        // Produce and combine the rotation matrices.
        D3DUtil_SetRotateXMatrix(matTemp, m_fPitch);    // pitch
        D3DMath_MatrixMultiply(matRot,matRot,matTemp);
        D3DUtil_SetRotateYMatrix(matTemp, m_fYaw);      // yaw
        D3DMath_MatrixMultiply(matRot,matRot,matTemp);
        D3DUtil_SetRotateZMatrix(matTemp, m_fRoll);     // roll
        D3DMath_MatrixMultiply(matRot,matRot,matTemp);
 
        // Apply the rotation matrices to complete the world matrix.
        D3DMath_MatrixMultiply(matWorld, matWorld, matRot);
    }
    return (matWorld);
} 
 

After you prepare the world transformation matrix, call the IDirect3DDevice3::SetTransform method to set it, specifying the D3DTRANSFORMSTATE_WORLD flag in the first parameter. For more information, see Setting Transformations.

Performance Optimization  Direct3D uses the world and view matrices that you set through IDirect3DDevice3::SetTransform to configure several of its internal data structures. Each time you set a new world or view matrix, the system recalculates the associated internal structures. Setting these matrices frequently—for example, thousands of times per frame—is computationally expensive. You can minimize the number of required calculations by concatenating your world and view matrices into a proverbial "world-view" matrix that you set as the world matrix, then set the view matrix to the identity. Keep cached copies of individual world and view matrices that you can modify, concatenate, and reset the world matrix as needed. (For clarity, Direct3D samples rarely employ this optimization.)