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Can someone pls explain about barycentric coords

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I am getting the newly created vertices from the fixed function tessellator, they are using barycentric UVW coords.
This is supposed to transform patch space vertices to clip space. The code works but I want to understand how its done.
the tessCoord is supposedly the new position of the generated vertex and the gl_in.pos variables are the original control points of the patch.

vec4 p0 = gl_TessCoord.x * gl_in[0].gl_Position;
vec4 p1 = gl_TessCoord.y * gl_in[1].gl_Position;
vec4 p2 = gl_TessCoord.z * gl_in[2].gl_Position;
vec4 position = p0 + p1 + p2;

position *= WVP; //To clip space

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