How to make all quads or ngons on your mesh planar (2d)?

Question

I want the quads in my mesh to be planar, or flat, that is, the 4 points of the quad could all be on the same plane. Or in other words, they need only x and y values to describe their "local" position.

Difficult part is if you do it to one face, the vertices shared by neighbouring faces get transformed which makes them non-planar...

Doing Mesh-> Cleanup-> Make Planar Faces on all faces doesn't work right. Every time you apply it the mesh visibly changes. If it worked the first time it wouldn't change more than once. Besides, the non-planar quads are visible to the eye.

Reason: modelling a low polygon mesh to be converted to individual flat faces in a program called Pepakura and make into a real life sculpture from flat MDF pieces.

Each quad has to be planar ("flat") so I can build this from flat MDF pieces.

Obviously the overall shape of the mesh will change, but not much.

Answer 1

This is a completely different method. It is more manual work but will give you 100% planar ngons.

In short: split all your faces. Scale each of them along their normal to 0. This will make them planar. Join them back again using booleans.

Split your mesh: Go into edit mode. Go to mesh select mode faces. Select all faces, press spacebar and type "edge split". Now you should be able to move one face without it dragging the others with it.

Set your Transform orientation to "Normal". Scale it along it's normal to 0: hit Szz0Enter. Scale it up five times or so: hit S5Enter.

Extrude it some: hit e5Enter. Recalculate normals: hit Ctrl+N. Split this box into a new object: hit P and select "Selection".

Do the same for another face but extrude it the other way.

Subtract the second from the first:

You can also use intersection:

Continue with more faces:

By now, the central crossing of these four faces have produced two vertices. If you don't want this. Slide one of them into the other.

You probably want to use the mirror modifier to reduce the work by half.

Answer 2

First thing first: How to check for non planar faces and amount of their distortion:

Second thing: How to make them planar?

There is no way to make them all planar without changing overall shape of the mesh a lot or the topology. Here is why:

To make faces planar, we need to move the vertices. So for each vertex we will see all the faces around it, get their normals, from each of these normals construct a plane and where those planes intersect store a new vertex. From all these new vertices then make a new mesh with the same topology and switch it for the old one. Very simple, but it has one catch: when a vertex has more than 3 surrounding faces, their planar intersection does not necessarily exist - it would be actually very rate if it did:

To meet them at single point, some plane translation is inevitable and depending on the angles this translation can be huge and ruin the shape of object.

So to create mesh from these intersecting planes (made from normals of faces) one would have to create a different mesh with a totally new topology, different vertex count (depending on the mesh shape) by basically chiseling a solid with these planes (would you accept this solution?).

The other solution is not exact and is an iterative approach to a solution. This solution Blender offers under Mesh > Cleanup > Make Planar Faces. We call these iterative methods to a solution Numerical methods. Each numeric method (which is an algorithm) has it's stability. Making faces planar is in general a very unstable algorithm. You may find your mesh oscillating between different shapes never closing on a solution or vertices getting very far from their original location sliding away to infinity - also never closing on a solution. What will happen depends on the mesh shape and you may actually find meshes that this approach solves and converges to a single solution.

But usually it's best to apply this operator not on the entire mesh, but only to selected parts that you know will solve. That's also why the operator has limited iterations to 200 - if it does not converge in that many steps it's very unlikely it will converge in more.

So to make a mesh from planar faces one must start from the beginning:

• Use the Bisect tool to make planar cuts.

• Use the F2 Addon to make planar faces:

  

• Rotate faces around edges to keep them planar: What's the easiest way to rotate around an edge that is not parallel to a primary axis?

• Slide vertices on edges Shift V to maintain planar face (C to extend outside face)

Answer 3

"Make planar faces" works with iterations. Each iteration only affects the non-planar faces a tiny amount.

This is with 1 iteration:

And this is with 200 iterations:

Quite a difference huh? But the cube was very distorted in the first place. I hade to apply the "Make planar faces" like 6 times before it was done.

What I think you should try is crank the iteration setting up to max. If your faces are almost planar already, it will flatten out after a while. It does for me when used on a real case (the cube was not).

Answer 4

Here is a a demo video to show how I did it.

First, you have to admit that nothing is perfect. It totally depends on how accurate you want.

As Gunslinger mentioned, there is already a build-in operation called Make Planar Faces in Mesh > Clean up menu. However, if the result is not as good as expected by taking more iterations, there is a spin-off from this post.

Here is a way to make it happen in a few minutes by using it (combined with other operations of course), not so effective, but seems to be the only affordable way to get the most accurate result:

Download the attached addon, which is the same as the one in the post above. Install. Then follow steps below:

1. Delete one side of the model, luckily this is a symetrical mesh, it is enough to edit half of it, then mirror it for the other side.
2. Select all vertices on a quad IN TURN (you have to do this right clicking on each verts instead of using tools like border select or cicle select). This first quad should be around the center of the topology structure (eye in this case, you'll realize why I recommend to do so later). Then click Coplanar by 3 Verts button in Mesh Tools panel in Tool tab. In the option below, set Reference Plane to First, which mean taking the first three selected vertices to define the reference plane.
3. Then select two vertices on either edge first, then select one adjacent quad which shares the same edge with this quad, then repeat step 2.
4. Repeat it until you finish this operation on every quad. Now, all quads should be "perfectly" planar. (Note that you have to avoid re-touching all polygons that have been tweaked, otherwise the distortion will be distributed back!)

5. To check it, there are generally three ways in Edit Mode:

   • Select all polygons then use Mesh > Clean up > Split Non-Planar Faces (or find it in Spacebar searcher), set Max Angle to 0.001 in the option panel, which is the smallest accepted value (0 means to split all quads or ngons no matter what). If no quads splitted, then congratulations.

   • In Properties sidebar (N panel), toggle Mesh Analysis panel, then set Type to Distortion. set the min angle to 0°, and the second angle to a very small degree like 0.1° (values smaller than that will not that helpful here anyway). If all quads appear as dark blue identically, then congratulations.

   • Go to File > User Preferences... > Add-ons, enable 3D Print Toolbox addon. Find 3D Printing tab in tool sidebar (T panel), click Distorted under Checks section, while keepting the degree value 0 as default. If any non-flat polygons found, You'll see the check result in Output Section Below, click that button will select all non-flat faces so you can see where further tweaks needed. If it shows 0, then congratulations. This is the most recommended way for final check.

However, not all cases can be done by this solution. Your case got some luck because:

1. it is an open mesh (not solid);
2. it is symetrical (make it more affordable for manual tweaking);
3. it has a relatively simple topology;
4. there are a few triangles, which can be used to make adjacent quads happy if you have to.

However, more tweaks have to be taken for fine tuning (mainly for avoiding distortion happening again while mirroring).

Example file:

Script used (run it in Text Editor, or save as .py file then install as addon):

bl_info = {
    "name": "Coplanar by 3 Verts",
    "author": "NirenYang[BlenderCN]",
    "version": (0, 1),
    "blender": (2, 75, 5),
    "location": "3d view - toolbar",
    "description": "Make vertices coplanar using a plane defined by the first/last three selected verts.",
    "warning": "",
    "wiki_url": "",
    "tracker_url": "",
    "category": "mesh",
}


import bpy
import bmesh
from mathutils.geometry import intersect_line_plane, distance_point_to_plane, normal

enum_ref = [( 'first', 'First', 'Defined by the first three selected verts' ),
            ( 'last', 'Last', 'Defined by the last three selected verts' )]
class MESH_OT_3points_flat_trim(bpy.types.Operator):
    """
    Manually pick three vertices to define the reference plane
    """
    bl_idname = 'mesh.3points_flat_trim'
    bl_label = 'Coplanar by 3 Verts'
    bl_options = {'REGISTER', 'UNDO'}

ref_order = bpy.props.EnumProperty(name='Refferece Plane', description='Use the first/last three selected vertices to define the reference plane', items=enum_ref, default="last")
filter_distance = bpy.props.FloatProperty(name='Filter Distance', description='Only affects vertices further than this distance', default=0.0, precision=3, min=0.0)


@classmethod
def poll(cls, context):
    obj = context.active_object
    return (obj and obj.type == 'MESH')

def execute(self, context):
    C = context
    D = bpy.data
    ob = C.active_object

    #if bpy.app.debug != True:
    #    bpy.app.debug = True
    #    if C.active_object.show_extra_indices != True:
    #        C.active_object.show_extra_indices = True

    if ob.mode == 'OBJECT':
        me = C.object.data
        bm = bmesh.new()
        bm.from_mesh(me)
    else:
        obj = C.edit_object
        me = obj.data
        bm = bmesh.from_edit_mesh(me)

    bm.select_history.validate()
    if len(bm.select_history) < 3:
        self.report({'INFO'}, 'Pick three vertices first')
        return {'CANCELLED'}

    points3Index = []
    points3 = []
    _ordering = bm.select_history if self.ref_order=="first" else list(bm.select_history)[::-1]
    for i in _ordering:
        if len(points3) >= 3:
            break
        elif isinstance(i, bmesh.types.BMVert):
            points3.append(i.co)
            points3Index.append(i.index)
    print(points3Index)
    if len(points3) < 3:
        self.report({'INFO'}, 'at least three vertices are needed to be selected')
        return {'CANCELLED'}


    points3Normal = normal(*points3)
    for v in bm.verts:
        if v.select and v.index not in points3Index:
            _move = True
            if self.filter_distance > 0.0:
                _move = abs(distance_point_to_plane(v.co, points3[0], points3Normal)) < self.filter_distance
            if _move == True:
                v.co = intersect_line_plane(v.co, v.co+points3Normal, points3[0], points3Normal)

    if ob.mode == 'OBJECT':
        bm.to_mesh(me)
        bm.free()
    else:
        bmesh.update_edit_mesh(me, True)

    return {'FINISHED'}

def menu_func_MESH_OT_3points_flat_trim(self, context):
    self.layout.operator(MESH_OT_3points_flat_trim.bl_idname,
                        text=MESH_OT_3points_flat_trim.bl_label)

def register():   
    bpy.utils.register_class(MESH_OT_3points_flat_trim) 
    bpy.types.VIEW3D_PT_tools_meshedit.append(menu_func_MESH_OT_3points_flat_trim)

def unregister():
    bpy.types.VIEW3D_PT_tools_meshedit.remove(menu_func_MESH_OT_3points_flat_trim)
    bpy.utils.unregister_class(MESH_OT_3points_flat_trim)

if __name__ == "__main__":
    register()