XMVectorBaryCentric

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

Syntax

XMVECTOR XMVectorBaryCentric(
         XMVECTOR Position0,
         XMVECTOR Position1,
         XMVECTOR Position2,
         float f,
         float g
)  

Parameters

Position0
Type: XMVECTOR 

First position.

Position1
Type: XMVECTOR 

Second position.

Position2
Type: XMVECTOR 

Third position.

f
Type: float 

Weighting factor. See the remarks.

g
Type: float 

Weighting factor. See the remarks.

Return value

Type: XMVECTOR 

Returns the Barycentric coordinates.

Remarks

This function provides a way to understand points in and around a triangle, independent of where the triangle is located. This function returns the resulting point by using the following equation: Position0> + f>(Position1-Position0>) + g>(Position2-Position0>).

Any point in the plane Position0>Position1>Position2> can be represented by the Barycentric coordinate (f>,g>), where f> controls how much Position1> gets weighted into the result, and g> controls how much Position2> gets weighted into the result. Lastly, 1-f>-g> controls how much Position0> gets weighted into the result.

Note the following relations.

• If (f>=0 && g>=0 && 1-f-g>=0), the point is inside the triangle Position0>Position1>Position2>.
  
• If (f==0 && g>=0 && 1-f-g>=0), the point is on the line Position0>Position2>.
  
• If (f>=0 && g==0 && 1-f-g>=0), the point is on the line Position0>Position1>.
  
• If (f>=0 && g>=0 && 1-f-g==0), the point is on the line Position1>Position2>.
  

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.

Requirements

Header: Declared in directxmath.h.