public static UVOrientation GetNorthEastVectors(Polygon polygon, Transform brushTransform)
{
Vertex vertex1;
Vertex vertex2;
Vertex vertex3;
// Get three vertices which will reliably give us good UV information (i.e. not collinear)
GetPrimaryPolygonDescribers(polygon, out vertex1, out vertex2, out vertex3);
// Take 3 positions and their corresponding UVs
Vector3 pos1 = brushTransform.TransformPoint(vertex1.Position);
Vector3 pos2 = brushTransform.TransformPoint(vertex2.Position);
Vector3 pos3 = brushTransform.TransformPoint(vertex3.Position);
Vector2 uv1 = vertex1.UV;
Vector2 uv2 = vertex2.UV;
Vector2 uv3 = vertex3.UV;
// Construct a matrix to map to the triangle's UV space
Matrix2x2 uvMatrix = new Matrix2x2()
{
m00 = uv2.x - uv1.x, m10 = uv3.x - uv1.x,
m01 = uv2.y - uv1.y, m11 = uv3.y - uv1.y,
};
// Invert the matrix to map from UV space
Matrix2x2 uvMatrixInverted = uvMatrix.Inverse;
// Construct a matrix to map to the triangle's world space
Matrix3x2 positionMatrix = new Matrix3x2()
{
m00 = pos2.x - pos1.x, m10 = pos3.x - pos1.x,
m01 = pos2.y - pos1.y, m11 = pos3.y - pos1.y,
m02 = pos2.z - pos1.z, m12 = pos3.z - pos1.z,
};
// Multiply the inverted UVs by the positional matrix to get the UV vectors in world space
Matrix3x2 multipliedMatrix = positionMatrix.Multiply(uvMatrixInverted);
// Extract the world vectors that correspond to UV north (0,1) and UV east (1,0). Note that these aren't
// normalized and their magnitude is the reciprocal of tiling
Vector3 eastVectorScaled = new Vector3(multipliedMatrix.m00, multipliedMatrix.m01, multipliedMatrix.m02);
Vector3 northVectorScaled = new Vector3(multipliedMatrix.m10, multipliedMatrix.m11, multipliedMatrix.m12);
return(new UVOrientation()
{
NorthVector = northVectorScaled.normalized,
EastVector = eastVectorScaled.normalized,
NorthScale = northVectorScaled.magnitude,
EastScale = eastVectorScaled.magnitude,
});
}
public Matrix3x2 Multiply(Matrix2x2 o)
{
return(new Matrix3x2()
{
m00 = this.m00 * o.m00 + this.m10 * o.m01,
m10 = this.m00 * o.m10 + this.m10 * o.m11,
m01 = this.m01 * o.m00 + this.m11 * o.m01,
m11 = this.m01 * o.m10 + this.m11 * o.m11,
m02 = this.m02 * o.m00 + this.m12 * o.m01,
m12 = this.m02 * o.m10 + this.m12 * o.m11,
});
}
