This image shows how you might imagine the geometry-blending process. In a single rendering call, the system takes the vertices for the banana, transforms them twice—once without modification, and once with a simple rotation—and blends the results to create a bent banana. The system blends the vertex position, as well as the vertex normal when lighting is enabled. Applications are not limited to two blending paths; Direct3D can blend geometry between as many as four world matrices, including the standard world matrix, D3DTS_WORLD.

Note  When lighting is enabled, vertex normals are transformed by a corresponding inverse world-view matrix, weighted in the same way as the vertex position computations. The system normalizes the resulting normal vector if the D3DRS_NORMALIZENORMALS render state is set to TRUE.

Without geometry blending, dynamic articulated models are often rendered in segments. For instance, consider a 3-D model of the human arm. In the simplest view, an arm has two parts: the upper arm which connects to the body, and the lower arm, which connects to the hand. The two are connected at the elbow, and the lower arm rotates at that point. An application that renders an arm might retain vertex data for the upper and lower arm, each with a separate world transformation matrix. The following code example illustrates this.

typedef struct _Arm {
    VERTEX upper_arm_verts[200];
    D3DMATRIX matWorld_Upper;
    
    VERTEX lower_arm_verts[200];
    D3DMATRIX matWorld_Lower;
} ARM, *LPARM;

ARM MyArm; // This needs to be initialized.

To render the arm, two rendering calls are made, as shown in the following code.

// Render the upper arm.
d3dDevice->SetTransform( D3DTS_WORLD, &MyArm.matWorld_Upper );
d3dDevice->DrawPrimitive( D3DPT_TRIANGLELIST, 0, numFaces );

// Render the lower arm, updating its world matrix to articulate
// the arm by pi/4 radians (45 degrees) at the elbow.
MyArm.matWorld_Lower = RotateMyArm(MyArm.matWorld, pi/4);
d3dDevice->SetTransform( D3DTS_WORLD, &MyArm.matWorld_Lower );
d3dDevice->DrawPrimitive( D3DPT_TRIANGLELIST, 0, numFaces );

The IDirect3DDevice8::SetTransform method recognizes the D3DTS_WORLD and D3DTS_WORLDn macros, which correspond to values that can be defined by the D3DTS_WORLDMATRIX macro. These macros are used to identify the matrices between which geometry will be blended.

The D3DRENDERSTATETYPE enumerated type includes the D3DRS_VERTEXBLEND render state to enable and control geometry blending. Valid values for this render state are defined by the D3DVERTEXBLENDFLAGS enumerated type. If geometry blending is enabled, the vertex format must include the appropriate number of blending weights.

Geometry blending weights are encoded in the vertex format, appearing immediately after the position for each vertex, as described in Vertex Formats. You communicate the number of blending weights in the vertex format by including one of the D3DFVF_XYZB1 through D3DFVF_XYZB5 Flexible Vertex Format Flags in the vertex description that you provide to the Microsoft® Direct3D® rendering methods.

In the preceding formula, vBlend is the output vertex, the v-elements are the vertices produced by the applied world matrix (D3DTS_WORLDn). The W elements are the corresponding weight values within the vertex format. A vertex blended between n matrices can have n–1 blending weight values, one for each blending matrix, except the last. The system automatically generates the weight for the last world matrix so that the sum of all weights is 1.0, expressed in sigma notation here. This formula can be simplified for each of the cases supported by Direct3D.