# D3DXVec3BaryCentric function

Returns a point in Barycentric coordinates, using the specified 3D vectors.

## Syntax

```
D3DXVECTOR3* D3DXVec3BaryCentric(
_Out_  D3DXVECTOR3 *pOut,
_In_   const D3DXVECTOR3 *pV1,
_In_   const D3DXVECTOR3 *pV2,
_In_   const D3DXVECTOR3 *pV3,
_In_   FLOAT f,
_In_   FLOAT g
);

```

## Parameters

pOut [out]

Type: D3DXVECTOR3*

Pointer to the D3DXVECTOR3 structure that is the result of the operation.

pV1 [in]

Type: const D3DXVECTOR3*

Pointer to a source D3DXVECTOR3 structure.

pV2 [in]

Type: const D3DXVECTOR3*

Pointer to a source D3DXVECTOR3 structure.

pV3 [in]

Type: const D3DXVECTOR3*

Pointer to a source D3DXVECTOR3 structure.

f [in]

Type: FLOAT

Weighting factor. See Remarks.

g [in]

Type: FLOAT

Weighting factor. See Remarks.

## Return value

Type: D3DXVECTOR3*

Pointer to a D3DXVECTOR3 structure in Barycentric coordinates.

## Remarks

The D3DXVec3BaryCentric function provides a way to understand points in and around a triangle, independent of where the triangle is actually located. This function returns the resulting point by using the following equation: V1 + f(V2-V1) + g(V3-V1).

Any point in the plane V1V2V3 can be represented by the Barycentric coordinate (f,g).The parameter f controls how much V2 gets weighted into the result and the parameter g controls how much V3 gets weighted into the result. Lastly, 1-f-g controls how much V1 gets weighted into the result.

Note the following relations.

• If (f>=0 &, & g>=0 &, & 1-f-g>=0), the point is inside the triangle V1V2V3.
• If (f==0 &, & g>=0 &, & 1-f-g>=0), the point is on the line V1V3.
• If (f>=0 &, & g==0 &, & 1-f-g>=0), the point is on the line V1V2.
• If (f>=0 &, & g>=0 &, & 1-f-g==0), the point is on the line V2V3.

Barycentric coordinates are a form of general coordinates. In this context, using Barycentric coordinates represents a change in coordinate systems. What holds true for Cartesian coordinates holds true for Barycentric coordinates.

The return value for this function is the same value returned in the pOut parameter. In this way, the D3DXVec3BaryCentric function can be used as a parameter for another function.

Barycentric coordinates define a point inside a triangle in terms of the triangle's vertices. For a more in-depth description of barycentric coordinates, see Mathworld's Barycentric Coordinates Description.