Color Only Non-Planar Faces

Question

Is there a technique to visualize the non-planar faces on a mesh. Similar to how the overlays panel allows an option to see "face orientation" in red or blue?

Answer 1

I don't think you can get that with standard tools. I would use a script to highlight (select in edit-mode) non coplanar faces:

import bpy
import bmesh

obj = bpy.context.active_object  # Get selected object

if obj:
    bpy.ops.object.mode_set(mode='EDIT')  # Go into edit mode
    bpy.ops.mesh.select_all(action='DESELECT')  # Deselect everything

    bm = bmesh.from_edit_mesh(obj.data)  # Create bmesh object for easy mesh evaluation

    for f in bm.faces:  # Check all the faces
        # 3 points will always define a unique plane. We define its coordinates.
        A = f.verts[0]
        B = f.verts[1]
        C = f.verts[2]
        a1 = B.co.x - A.co.x
        b1 = B.co.y - A.co.y 
        c1 = B.co.z - A.co.z 
        a2 = C.co.x - A.co.x
        b2 = C.co.y - A.co.y
        c2 = C.co.z - A.co.z
        a = b1 * c2 - b2 * c1 
        b = a2 * c1 - a1 * c2 
        c = a1 * b2 - b1 * a2 
        d = (- a * A.co.x - b * A.co.y - c * A.co.z)
        # Check if any point after the third one is a part of this plane (ie the distance to the plane is == 0)
        if len(f.verts) > 3:
            for v in f.verts[3::]:
                if a * v.co.x + b * v.co.y + c * v.co.z + d != 0:
                    f.select_set(True)  # If this vertex is not part of the base plane, select the face and break
                    break

    bmesh.update_edit_mesh(obj.data)

Illustration :

Also, if you want faces to highlight only if the vertices deviate from a certain threshold to to the base plane, you could insert it in the code :

Replace

if a * v.co.x + b * v.co.y + c * v.co.z + d != 0:

With

if abs(a * v.co.x + b * v.co.y + c * v.co.z + d) > 2 :  # Threshold

Note that this is not deterministic and could change depending on which vertices get evaluated to define the plane coordinates.

Further and further reading.

Answer 2

Similarly

https://blender.stackexchange.com/a/53976/15543

4 points are coplanar if the volume created by the points is 0. If any three points determine a plane then additional points can be checked for coplanarity by measuring the distance of the points from the plane, if the distance is 0 then the point is coplanar

Below uses 3 verts to compute the face normal.

Vert 0 (v0, the coordinate of Vert 0) is a point on plane. The cross product (v1 - v0).cross(v2 - v0) defines the normal.

Feeding the rest of verts into mathutils.geometry.distance_point_to_plane determines if a face does not have coplanar vertices if any distance is not 0. A small tolerance is used.

See other example in link re creating a convex hull from the face and testing it has zero volume.

import bpy
import bmesh
from mathutils.geometry import distance_point_to_plane as dp2p
TOL = 1e-6
context = bpy.context
ob = context.edit_object #  run in edit mode
me = ob.data
bm = bmesh.from_edit_mesh(me)
for f in bm.faces:
if len(f.verts) == 3: #  tri
    f.select_set(False)
    continue
v1 = f.verts[1].co - f.verts[0].co
v2 = f.verts[2].co - f.verts[0].co
norm = v1.cross(v2)
f.select_set(
    any(
        abs(dp2p(
            v.co, 
            f.verts[0].co, 
            norm)
            ) > TOL for v in f.verts[3:]
        )
    )

bmesh.update_edit_mesh(me)

Answer 3

In edit mode, open the "Viewport Overlays" panel in the top right corner, check the "Mesh Analysis" box, and change the type dropdown to "Distortion":

(Credit to original comment: Color Only Non-Planar Faces)