UV---DPI-(variable-or-homogeneous).md

some assumptions about the whole thing:

• square image
• you use Meters of Blender Units. (Else the texture_dpi function changes a little)
• you pass the correct image name (or image of equivalent dimensions)
• you have an active uvmap
• you are in edit mode.

Insight can also be found at TextEditor -> Templates -> Python -> Operator Mesh UV

import math

import bpy
import bmesh
from mathutils import Vector


def texture_dpi(polygon_area, uv_area, image_dim):
    """
    polygon_area:   in (meters or BU)
    uv_area:        in ratio (0..1)
    image_dim:      either width or height of image, this assumes
                    square images anyway, else none of this makes sense
    """

    l1 = math.sqrt(polygon_area)
    l2 = math.sqrt(uv_area)

    # assume the units are BU or meter.
    inches = l1 * 39.3701
    pixels = int(l2 * image_dim)
    return int(pixels / inches)


def calc_area_from_2d_vectorlist(v):
    # http://www.mathopenref.com/coordpolygonarea.html
    sum = 0
    n = len(v)
    for i in range(n - 1):
        sum += ((v[i].x * v[i + 1].y) - (v[i].y * v[i + 1].x))
    sum += ((v[n - 1].x * v[0].y) - (v[n - 1].y * v[0].x))
    return abs(sum / 2)


def get_bm_from_edit_object(image_name):
    obj = bpy.context.edit_object
    me = obj.data
    bm = bmesh.from_edit_mesh(me)

    uv_layer = bm.loops.layers.uv.verify()
    bm.faces.layers.tex.verify()

    totals = []
    for f in bm.faces:
        vl = [l[uv_layer].uv for l in f.loops]
        fa = calc_area_from_2d_vectorlist(vl)  # 2d area of uv loop
        totals.append([f.calc_area(), fa])     # 2d area of face (local size)
        break  # if homogeneous  , else comment it out.

    image_dim = bpy.data.images[image_name].size[0]
    for polygon_area, uv_area in totals:
        dpi = texture_dpi(polygon_area, uv_area, image_dim)
        print(dpi)

get_bm_from_edit_object('some_texture.png')

on this line break # if homogeneous , else comment it out. I've left the break statement to stop iteration and just use the first polygon. The assumption is that all your polygons have the same amount of area per pixel, and you can calculate DPI once and the value will be the same for all other polygons.

Sometimes you might have textures and uvmaps that intentionally rescale certain uv_islands to get more pixels in a smaller space, these islands can be calculated independently or simply by the index of one of the faces of the island - exercise for the reader.