normcore.py

'''
Created on Oct 1, 2015

Functions for the creation and manipulation of normal vectors.

@author: Julia M. Winchester
'''

from numpy import cross, array, sqrt, column_stack, spacing, zeros, isnan, mean, sum

def normal(plane):
    """Given triangle vertices, returns normal vector for triangle as XYZ coordinates."""
    
    a = plane[0]
    b = plane[1]
    c = plane[2]

    ab = [(b[0]-a[0]),(b[1]-a[1]),(b[2]-a[2])]
    ac = [(c[0]-a[0]),(c[1]-a[1]),(c[2]-a[2])]
    
    return cross(ab,ac)

def normalmap(varray,farray): 
    """Given a list of vertices and polygons, returns array of polygon normal vectors."""
    return array([normal(varray[verts]) for verts in farray])

def normalize(vects):
    """Normalizes (sets magnitude to 1) given vectors."""
    d = sqrt((vects**2).sum(axis=1)) # Square roots of sums of squares of normal vectors, i.e. magnitudes of normal vectors
    d = [1 if m < spacing(1) else m for m in d]
    return vects/column_stack((d,d,d)) # each face has its normal vector XYZ divided by that vector's magnitude. this normalizes the vector, i.e. gives it a magnitude of 1.   

def computenormal(varray, faceindex, fvarray, vfarray):
    """Given a polygonal mesh, returns unit normals for polygons and unit normals of vertices (approximated as average of associated polygon normals)."""
    nvert = len(varray)
    
    fnormal = normalmap(varray,faceindex)
    # normalize face normals
    fnormal4 = normalize(fnormal)
    
    # unit normals of vertices    
    vnormal = zeros([nvert,3],float)
    for vindex, faces in vfarray.iteritems():
        vnormal[vindex] = sum(fnormal4[faces], axis=0)
        if isnan(fnormal4[faces]).any(): print "nan found during vertex normal creation at vertex #: " + str(vindex)    
     
    # normalize vertex normals
    vnormal4 = normalize(vnormal)
    
    # check for nan values in vnormal4
    for i, norm in enumerate(vnormal4):
        if isnan(norm).any():
            print "nan vnormal 4 entry found"
            print "corresponding vnormal entry:"
            print norm
    
    # enforce that normals are outward
    mvertex = mean(varray,1)    
    repmvertex = column_stack((mvertex,mvertex,mvertex))            
    v = varray - repmvertex
    s = sum((v*vnormal4),0)
    s2 = 0
    s3 = 0
    
    for i in s:
        if i > 0:
            s2 += 1
        if i < 0:
            s3 += 1
    if s2 < s3:
        print 'Outward normal flipping has occurred'
        vnormal4 = -vnormal4
        fnormal4 = -fnormal4

    return [vnormal4, fnormal4]