Calculate vector position

Question

I'm trying to calculate & move vertices to their average "radius" and form a circle from these new positions.

Example: I have 8 vertices selected, I have a little script in Maya that will iterate through each point, find the distance from the center of the selection to the current point in the loop. It saves these values and creates an "average distance from the center" value.

• Black = Each vertex position (X,Y,Z)
• Red = Distance between center and vertex
• Blue = Average of ALL verts from the Centerpoint (X,Y,Z) & Vertex (X,Y,Z) = integerXYZ (blue is the same distance)
• Green is the position I'm trying to find in (XYZ)

I can't figure out how to calculate the (X,Y,Z) coordinates of the green dot!

I have calculated this information with: (up to the position of the green points):

import maya.cmds as cmds
import math
sel = cmds.ls(sl=1, fl=1)
averageDistance = 0
cmds.setToolTo('Move')
oldCoordArray = []
oldDistanceArray = []
newXPos = 0
cs = cmds.manipMoveContext("Move", q=1, p=1)
for i in range(0, len(sel), 1):
    vts = cmds.xform(sel[i],q=1,ws=1,t=1)
    print vts
    x = round(float(cs[0]),2) - round(float(vts[0]),2)
    y = round(float(cs[1]),2) - round(float(vts[1]),2)
    z = round(float(cs[2]),2) - round(float(vts[2]),2)
    distanceFromCenter = math.sqrt((x * x) + (y * y) + (z * z))
    oldCoordArray += [(round(float(vts[0]),2),round(float(vts[1]),2),round(float(vts[2]),2))]
    oldDistanceArray += [(distanceFromCenter)]
    averageDistance += distanceFromCenter    
    if (i == len(sel) -1):
        averageDistance /= len(sel)
        print 'average Distance: %s' %averageDistance
        for i in range(0, len(sel), 1):
            #Calculate percentage difference between distances
            t = oldDistanceArray[i] * 100 / averageDistance
            percDiff = (t / 100) * oldCoordArray[i][0]
            newXPos -= (oldCoordArray[i][0] / percDiff) * 100     

(original image here)

Answer 1

If I understand, you have looped through the eight points $(X_i,Y_i,Z_i)$and averaged the $X,Y,Z$ coordinates to find the red coordinates, call them $(X_c,Y_c,Z_c)$ The distance of each point from the center is $d_i=\sqrt{(X_i-X_c)^2+(Y_i-Y_c)^2+(Z_i-Z_c)^2}$. If you just average all the $d_i$ the blue segments will extend past the nearer points. It is not clear to me how you choose the blue length $b$. But however you do it, the coordinates of the green points $g_i=\left(\frac b{d_i}(X_i-X_c)+X_c,\frac b{d_i}(Y_i-Y_c)+Y_c,\frac b{d_i}(Z_i-Z_c)+Z_c\right)$