Vector4.BaryCentric Method

Language:

Returns a point in barycentric coordinates, using the specified 4-D vectors.

Definition

Visual Basic Public Shared Function BaryCentric( _
    ByVal v1 As Vector4, _
    ByVal v2 As Vector4, _
    ByVal v3 As Vector4, _
    ByVal f As Single, _
    ByVal g As Single _
) As Vector4

C# public static Vector4 BaryCentric(
    Vector4 v1,
    Vector4 v2,
    Vector4 v3,
    float f,
    float g
);

C++ public:
static Vector4 BaryCentric(
    Vector4 v1,
    Vector4 v2,
    Vector4 v3,
    float f,
    float g
);

JScript public static function BaryCentric(
    v1 : Vector4,
    v2 : Vector4,
    v3 : Vector4,
    f : float,
    g : float
) : Vector4;

Visual Basic	Public Shared Function BaryCentric( _ ByVal v1 As Vector4, _ ByVal v2 As Vector4, _ ByVal v3 As Vector4, _ ByVal f As Single, _ ByVal g As Single _ ) As Vector4
C#	public static Vector4 BaryCentric( Vector4 v1, Vector4 v2, Vector4 v3, float f, float g );
C++	public: static Vector4 BaryCentric( Vector4 v1, Vector4 v2, Vector4 v3, float f, float g );
JScript	public static function BaryCentric( v1 : Vector4, v2 : Vector4, v3 : Vector4, f : float, g : float ) : Vector4;

Parameters

v1 Microsoft.DirectX.Vector4
Source Vector4 structure.

v2 Microsoft.DirectX.Vector4
Source Vector4 structure.

v3 Microsoft.DirectX.Vector4
Source Vector4 structure.

f System.Single
Weighting factor. See Remarks.

g System.Single
Weighting factor. See Remarks.

Return Value

Microsoft.DirectX.Vector4
A Vector4 structure in barycentric coordinates.

Remarks

The Vector4.BaryCentric method provides a way to understand points in and around a triangle, regardless of where the triangle is actually located. This method 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 coordinates (f, g). The f parameter controls the extent to which v2 gets weighted into the result, and the f parameter controls the extent to which v3 gets weighted into the result. Lastly, (1 - f - g) controls the extent to which 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 them represents a change in coordinate systems. What holds true for Cartesian coordinates holds true for barycentric coordinates.

Feedback? Please provide us with your comments on this topic.
For more help, visit the DirectX Developer Center

v1	Microsoft.DirectX.Vector4 Source Vector4 structure.
v2	Microsoft.DirectX.Vector4 Source Vector4 structure.
v3	Microsoft.DirectX.Vector4 Source Vector4 structure.
f	System.Single Weighting factor. See Remarks.
g	System.Single Weighting factor. See Remarks.