Vector2.BaryCentric Method

Language:

Returns a point in barycentric coordinates, using specified 2-D vectors.

Definition

Visual Basic Public Shared Function BaryCentric( _
    ByVal v1 As Vector2, _
    ByVal v2 As Vector2, _
    ByVal v3 As Vector2, _
    ByVal f As Single, _
    ByVal g As Single _
) As Vector2

C# public static Vector2 BaryCentric(
    Vector2 v1,
    Vector2 v2,
    Vector2 v3,
    float f,
    float g
);

C++ public:
static Vector2 BaryCentric(
    Vector2 v1,
    Vector2 v2,
    Vector2 v3,
    float f,
    float g
);

JScript public static function BaryCentric(
    v1 : Vector2,
    v2 : Vector2,
    v3 : Vector2,
    f : float,
    g : float
) : Vector2;

Visual Basic	Public Shared Function BaryCentric( _ ByVal v1 As Vector2, _ ByVal v2 As Vector2, _ ByVal v3 As Vector2, _ ByVal f As Single, _ ByVal g As Single _ ) As Vector2
C#	public static Vector2 BaryCentric( Vector2 v1, Vector2 v2, Vector2 v3, float f, float g );
C++	public: static Vector2 BaryCentric( Vector2 v1, Vector2 v2, Vector2 v3, float f, float g );
JScript	public static function BaryCentric( v1 : Vector2, v2 : Vector2, v3 : Vector2, f : float, g : float ) : Vector2;

Parameters

v1 Microsoft.DirectX.Vector2
Source Vector2 structure.

v2 Microsoft.DirectX.Vector2
Source Vector2 structure.

v3 Microsoft.DirectX.Vector2
Source Vector2 structure.

f System.Single
Weighting factor. See Remarks.

g System.Single
Weighting factor. See Remarks.

Return Value

Microsoft.DirectX.Vector2
A Vector2 structure in barycentric coordinates.

Remarks

The BaryCentric method provides a way to understand points in and around a triangle, regardless of its actual location. 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 also holds true for barycentric coordinates.

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v1	Microsoft.DirectX.Vector2 Source Vector2 structure.
v2	Microsoft.DirectX.Vector2 Source Vector2 structure.
v3	Microsoft.DirectX.Vector2 Source Vector2 structure.
f	System.Single Weighting factor. See Remarks.
g	System.Single Weighting factor. See Remarks.