Calculate Vector

[justin hidair]

========
*See the joint file*

Ho do I get the flashy green and red arrows (by arrows i mean vectors) from that one vector (Face Normal from maya) ? I can't wrap my head around that... Cross product only works if you know two vectors..

so how I can manage to determine these two from a face normal , with of course the right orientation ?? thanks in advance

[Kyle Burris]

You could get the positions of two vertices that form one of the edges, make a vector from that, and get the mid point. Then use that vector to use in your cross

[Paul Molodowitch]

It's a little unclear what the red and green arrows are supposed to represent.  Ate they pointing to the midpoints of edges? Are they supposed to be perpendicular to each other? Are they supposed to be aligned to u (or v)?

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[justin hidair]

green and red arrows are vectors, it's like "axis" , secretly they are binormal and tangent vector, but how do I get them ?

[justin hidair]

Imagine a rotated ngon like a flat disk , in this one case, the technique you suggested fails

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[Alok Gandhi]

Given a surface normal, the choice for a tangent vector is arbitrary for a flat surface. You have the freedom to decide the direction of the tangent vector. In your case, the tangent vector can be defined from the base point of the normal to any arbitrary point on the polygon, this can be the mid-point of an edge or even can be one of the vertices. The choice is yours. Calculating the bitangent, then, is trivial. It is the result of the cross product between the normal and tangent.

The technique would be:

1. Get the tangent (this is arbitrary - it could be an edge or a vector between the mid-point of edges and the base of the normal etc.- any vector  that lies on the surface meaning you just need two points on the surface, does not matter where - this works only for flat surfaces which I assume you already have.)

2. Cross the normal and the tangent to the bitangent.

You can find some reference here

- Alok

[Alok Gandhi]

erratum:

2. Cross the normal and the tangent to *obtain the bitangent.

[Leonardo Bruni]

If you have the normal,you could use an arbitrary vector that i'll call worldUp for the first cross actually.
In something like a pseudocode, i suppose that you get "mynormal", and i'll call the variable red and green like in your image.

vector N = normalize(mynormal)
vector worldUp = [0,1,0] 
vector red = normalize(N ^ worldUp) 
vector green = normalize(red ^ N)

With 2 cross you can be sure that the matrix that you'll build will be orthogonal
Now you should have the result that you posted in your image

2017-04-02 5:53 GMT+02:00 Alok Gandhi <alok.ga...@gmail.com>:

erratum:

2. Cross the normal and the tangent to *obtain the bitangent.

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[justin hidair]

Thanks Alok !

[Rémi Deletrain]

I make this code for create matrix from mesh face

def get_matrix_from_face(mfn_mesh, point, face_id):

    """

    !@Brief Get matrix from point position and face id.

            Take normal, tangent, binormal of all face vertex and average it.

    @type mfn_mesh: OpenMaya.MFnMesh

    @param mfn_mesh: MFnMesh for get point orientation

    @type point: MFloatPoint

    @param point: Position on face.

    @type face_id: int

    @param face_id: Face id

    @rtype: pymel.Core.datatypes.Matrix

    @return: Matrix found

    """

    #   Get normal

    normals = OpenMaya.MFloatVectorArray()

    mfn_mesh.getFaceVertexNormals(face_id, normals)

    normal = average_vector_array(normals)

    #   Get tangent

    tangents = OpenMaya.MFloatVectorArray()

    mfn_mesh.getFaceVertexTangents(face_id, tangents)

    tangent = average_vector_array(tangents)

    #   Get binormal

    binormal = tangent ^ normal

    binormal.normalize()

    #   Force normal perpendicalary

    normal = binormal ^ tangent

    normal.normalize()

    #   Create matrix

    from pymel import core as pmc

    matrix = pmc.datatypes.Matrix(

        [tangent.x, tangent.y, tangent.z, 0.0],

        [normal.x, normal.y, normal.z, 0.0],

        [binormal.x, binormal.y, binormal.z, 0.0],

        [point.x, point.y, point.z, 1.0]

    )

    return matrix

def average_vector_array(vector_array):

    """

    !@Brief Average MVector array

    @type vector_array: OpenMaya.MVectorArray / OpenMaya.MFloatVectorArray

    :param vector_array: Vector array to average

    @rtype: OpenMaya.MVector

    @return: Vector average

    """

    if not isinstance(vector_array, (OpenMaya.MVectorArray, OpenMaya.MFloatVectorArray)):

        raise BaseException("Invalid argument !!!\n\tArgument must be a MVectorArray.")

    m_vector = OpenMaya.MVector()

    for idx in xrange(vector_array.length()):

        m_vector += OpenMaya.MVector(vector_array[idx])

    m_vector /= vector_array.length()

    m_vector.normalize()

    return m_vector