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"Interesting Pattern" as Garman said.

Let's have fun and create our own procedural pattern.

The problem to solve is to create funny pattern artwork above. Originally, this is something that you would like to do using procedural tool like Houdini.

How do we create this in Blender, as procedural as possible? We will take a look step by step on how you could solve the puzzle.

NOTE: You will need Blender version 2.68 up that has "Use Modifier Stack" option for Particles.

1. BREAKING THE PATTERN ELEMENTS

Like all kind of patterns, we should be able to break it into elements that can be repeated. The above funny "pipe" pattern maybe already familiar to you. There are probably similar patterns like that in Math. 3D patterns actually interesting.

One example I could remember from top of my head is the Procedural Snakes in "Snakes On The Plane" by Cafe FX. There is some sequences showing Snakes going in motion in a complicated patterns, that's Math.

Anyway, the above patterns can be broken into 2 x Shapes like below:
Shape A

Shape B

2. PROCEDURAL CIRCLE


The above design can be created using either Poly Mesh or Curve. Any modeling technique will work.

With Curve, we can start with a circle. We just need to turn the circle into 1/4 circle, which is, actually slightly tricky because when you delete a point in Circle, Blender tends to adjust the bezier handles. You can give it a try.

See down below for Python script way to create 1/4 Curve.

I will probably do something like below to then be converted to Curve.

With Mesh, we could start right away with a Torus shape which is cut into 1/4 Circle Torus.

However, a more procedural way is to probably start with a Single Mesh Point + Screw Modifier. Which then converted into Curve, to take advantage of Blender Curve and Modifier.

Step by step:
1. Merge Cube into Single Mesh Point. Place the single Mesh point at XYZ position: 0, 1, 0.
2. Create Empty, this will be our reference point for Screw Modifier.
3. Apply Screw Modifier to the Single Mesh Point. Make sure the angle is 90 degree so we get 1/4 of Circle. You can adjust the number of steps. Assign the Empty created on Step 2 as the ObAxis, turn on Object Screw option.


We should be getting something like below.

Procedural 1/4 Circle part one.

At this stage that 1/4 Circle is pretty procedural. If you want less or more DIVISIONS for this Circle shape, you can adjust the Step on Screw Modifier. If you like to increase or decrease the RADIUS, you can do so by moving the Single Vertex in Y axis (for this setup).

Remember this technique in the future, will come in handy.

Watch also Curve Start Bevel and End Bevel, it is interesting that you can "Carve" the Curve Start and End like that. Very Houdini like.

4. Next, we want to convert this Mesh into Curve object. Why? Because Curve in Blender has interesting property that can be used to create a Pipe with hole, which Radius can be adjusted anytime as we please.


5. Now that it is a Curve, under Curve Property, we can enable the Depth and Fill of Curve.



Procedural 1/4 Circle part two.

Now, we have 1/4 Torus with adjustable Radius for our Pattern Design Element.

The only little GLITCH is that the end and start of "Torus" is not 100% tangent. But it is ok, something we can always make up in the end.

If you can suggest a better method to create 1/4 Torus, please let me know. If you don't care much with the Radius, you can always use Torus Mesh and cut it into 1/4 quarter.

Now, it's matter of duplicating, rotating and position this shape to get the 2 x Elements:


We can group them and we will use as Particle Instances.

3. PROCEDURAL GRID

The idea here is just to place the 2 x pattern elements above into a template grid that will then create the Patterns.

Can we create procedural Grid? Sure, you can, by using a Single Face and Array Modifiers.

1. I tested it with Single Vertex + Array Modifier combination, apparently it does not work. Array Modifier seems to like Edge or Face. We will start with A Single Face.


2. Assign live 2 x Array Modifier the Face in 2 Direction to create procedural grid. The Array Count can be adjusted anytime. Activate Merge so that we do not have duplicate vertices in one spot.



Procedural Grid.

4. PROCEDURAL PATTERN

Now that we have every ingredient, we can simply Copy Stamp the Instances into Particles.

I remind you again that you need Blender 2.68 that has "Use Modifier Stack" option under Particles. This is so that we can use our Procedural Grid to generate the Template for Particle Instance while keeping everything live and procedural.

Simply create Particle System using our Procedural Grid, and then activate "Use Modifier Stack". There are few settings you need to adjust under Particle System so that everything works:

IMPORTANT:
The Emission Count (Total Particles) = (Array Count X + 1) * (Array Count Y + 1)



Everything set properly, you will get the setup and our puzzle is solved.


The power of procedural will enable you to do these:

RANDOMIZATION OF PATTERN
By adjusting the Seed of Particle, you will get random patterns.





RADIUS VARIATION
Thick Radius.

Thin Radius.

GRID EXPANSION
Since the Array is still live, we can simply adjust the Grid X and Y. Remember to also adjust Particle Total Count, using the formula above.

There must be a name for this kind of Pattern.

You could generate any size of Patterns you want. Not a worry, because it is all procedural.

COLOR VARIATION
If you want to have Pipe in different color, you can do that too. Just add more Pipe in different colors to the "Group" for Particle Instances.



Everything will propagate automatically:


Feel free to experiment further with some other pattern. Blender Particles can be arranged in Grid or Hexagonal Grid. However, if you code it using Python script, you could create all kind of patterns.

Challenged and would like to do Procedural 3D Pattern? Go for it. Just add one more Array Modifier and break the pattern into element that you can duplicates in 3D. Have fun!

Convert to Mesh Edge, adding Displace Modifier + Noise to the Pattern.

Next probably shade it.

UPDATE 2013.07.23: 

PYTHON 1/4 CURVE + REFINING THE CURVE GLITCH

As soon as I posted this, Adhi Hargo posted Python way to create 1/4 Quarter Curve!
https://gist.github.com/adhihargo/6062845

Thanks Adhi, brilliant!

There is still the glitch of start and end curve not being tangent and flat like 1/4 Torus. However, if you Subdivide the Curve, enough, it should be work.



Although, I like to keep the Curve point as little and efficient as possible because eventually we probably convert it back into Mesh Edge anyway. Or you do few conversion:
Curve -> Remove Pipe -> Mesh Edge -> Remove Doubles -> Curve -> Recreate Pipe





Fly with a Speed of Light, Suzanne.
Today is 20th of July 2013, and Blender just got another update to version 2.68.

Every Blender update always brings a lot of excitements, apart from optimization in performance, the new release always comes with a lot of interesting features.

Blender Realtime Rendering (BPR) for Blender Internal Renderer, just like Blender Cycles. No one can see this coming, well I don't, but this is nice. CTRL + B to render region.


You can see the details of the updates in here:
http://www.blender.org/development/release-logs/blender-268/
http://wiki.blender.org/index.php/Dev:Ref/Release_Notes/2.68/Physics

Blender has major updates every few months. It also has quick updates built daily, for bug fixes, etc. I think the Blender development is really impressive, can't be thankful enough to Ton Roosendaal and Blender Development teams, you rocks.

THE TUBE PROJECT
When you run version 2.68, you will see the new Splash Screen from "The Tube", Blender Open Movie, which you can follow and support from their website:
http://urchn.org/post/category/blender

Splash Screen from "Tube" Open Movie Project
Some of the best Blender Artists are working on The Tube. I am definitely looking forward to the release of this short film.

In the meantime, there is one feature of Blender 2.68 that catches my eyes... "Use Modifier Stack" for Particle. In short: ability of Blender Particles to emit from Faces that are generated on-the-fly using Modifier Stack. Particles and VFX lovers, this feature will excite you.

PARTICLES: Use Modifier Stack

What is the news with the "Use Modifier Stack"? Well, you probably have done this in the past, where you use one of the "Generate" Modifiers on mesh object, then you add or stack Particle System at the end, and then you are getting a funny result.


For example, here I created an Edge mesh and then add Skin Modifier to it and then lastly stack Particle System at the end hoping for the Skin Modifier mesh to emit Particles.


However, when you see in 3D View, you are getting something like below.

Funny result.

However, from 2.68, we have "Use Modifier Stack" added to the Particle System. The option is available under Particles Property tab. It is a toggle, you can either have it ON or OFF.

TIPS: In my opinion, this cool effect should be ON by default. Remember to always turn this on next time you create Particle effect.


If you enable "Use Modifier Stack", you will now get a more expected (I say: exciting and significant) result where Particles are born from Faces of the mesh. And this is actually a Procedural/Generative effects which means Particles can be generated LIVE from mesh that is changing.

Awesome result.

This is actually really cool.

I have a feeling that Blender Particles system will start to get more development throughout until Blender version 3.0. Maybe we will even get Node Based Particles sooner? Let's keep hoping and supporting Blender Development.

BLENDER SMOKE AND FIRE SECRETLY HAS IT...

This "ability to generate X (emitting from face) with respect to Modifier Stack" feature has always been available for Blender Smoke and Fire and it is always ON by default and we all take it for granted.


Emitting Smoke and/or Fire from LIVE Skin Modifier mesh from edge, for example, has always been possible back in previous versions of Blender. 

... FINALLY IN BLENDER PARTICLE.

And now, Blender Particles finally has IT too.

Having the ability to emit Particles that respect the Modifier Stacks really allow us to do some advance Particles setup, with ease. This adds additional level of flexibility of being able to tweak and modify the mesh to update to Particles.

No longer one needs to "Apply Modifier" to the mesh object, to have it to work with Particles, we simply keep stacking the effects for Particles setup.

I guess this is a very good time to revisit some Blender Generate Modifiers and see what effects we can do with Blender Particles.

BUILD MODIFIER > PARTICLES


The Build modifier slowly (re)builds your mesh based on Face index number (which can be Sorted beforehand). It comes with option to randomly re-generate faces from whatever mesh you feed into it.

Grease Pencil > Bake to Curve
Curve > Simplify Curve > Bake to Mesh
Mesh Edge > Skin Modifier > Build Modifier > Particles

I believe at some point, when we have less baking, everything is more procedural. I like to see one day between Curve to Mesh is no longer separate. We cannot emit Particles from Curve yet, but Curve object in Blender actually has some interesting live Remeshing-ability too, which I think potentially needs to be hooked up with Particle Emission.



Next, "Mask Modifier" below is even nicer.

DYNAMIC PAINT > MASK MODIFIER > PARTICLES


Mask Modifier is one of those Generate Modifier that one can easily overlooked. I only paid attention to it when Dynamic Paint actually works together with it. Dynamic Paint generates Vertex Grouping on the fly, which is transfered into Mask Modifier that will actually Delete the Face on the fly.

Particles does not respect the Modifier back then... so this masking thing may not be too significant, however, it is super significant now.

So, Mask Modifier, can "mask" out or delete Faces on the fly. You can also inverse the effect where it will delete non selected. Very Houdini like (Group and Delete)!

Who will be the first to update and create realistic updated Burning Paper effect? :]

VFX POTENTIAL: Advance Dispersion or Dissolve effect, emit blood or dust from collision.


ARRAY MODIFIER > PARTICLES
The infamous Array Modifier needs no introduction, now this works with Particles so you could build Particles Arrays source.


PARTICLE INSTANCE MODIFIER > PARTICLES
With this stacking thing, we can now pretty much emit Particles from emitted Particles, if you know how to set it up. Not very obvious, but basically you Instance some meshes (using Instance Modifier) and then add Particle System to the object with Instance Modifier.

Make sure you have "Use Modifier Stack" turned on.

VFX POTENTIAL: Fireworks, explosions with debris, comet, meteor, arrow with fire, blood splatters, rolling puffs effect.


CONCLUSIONS

I guess that is all for this quick write up of "Use Modifier Stack". There are many other Modifiers that will work in interesting way with Particles.

Again, I have only highlighted small bits of this additional particle update called "Use Modifier Stack". However, this certainly something not to be missed. Seems small but very significant.

High in wish list is the ability for Particles to carry Color and all kind of per point attributes from Mesh Point. It is kind of there, but not really, but can be rendered somewhat.

Now it is a great time to create practical and more polished effects.

Time to think for a more interesting complex effects with Particles. With power comes responsibility, right?  Layering effects, Lighting and Rendering, and Compositing. Those are next areas I certainly have to cover. Must take the VFX to polished level Andrew Price aka Blender Guru quality.

However, with Blender Sushi philosophy, it is always a good idea to experiment and to explore time to time, especially whenever there is a new Blender updates.

Be curious, do research, study reference, write notes, and make your own original works. That is the principle you could apply in everything.

So, one more thing...

Dynamic Paint > Boids Particles

This is Blender Particles live boids that generates/eats mesh of faces on the fly.

The Love For Lattice


Lattice Modifier in Blender is another interesting modifier that people may or may not use regularly. I think the Lattice deserves a bit more love.

Oh, Lattice, why you so complicated?
NOTE: Lots of modifiers in Blender works amazingly well, although sometimes the magic is a little bit obscured. Unless you read a little bit of documentation.

CIRCULAR RAMP USING LATTICE MODIFIER
The other day, someone asked on Blender Facebook page on how to create a Semi-Circular Ramp for architecture modeling that goes 1/4 Circle. It was an interesting question, so I decided to give an answer.

My first solution is like this:
1. Draw 1/4 Circle.
I am using Poly Circle first, delete 3/4 of the Circle, and then I convert it to actual Curve object in Blender.


We can easily "Extrude" the Curve path to get actual Path, instead of just curve. I tilt the Path 90 degree so that it is more correct.

2. Apply Lattice Modifier to create Ramp.
Now, Lattice Modifier in Blender is a little bit weird because we need to create a Lattice object separately first of all, before we are able to use the Lattice Modifier.


The Lattice itself is free in 3D space. We need to edit the shape inside Edit Mode and tweak the Property under Property Panel. This is done manually to match the bounding box of our object to be influenced.


Once you get the Lattice in place, that is when we can simply reference the Lattice for Lattice Modifier.

We can choose between BSpline, Cardinal, or Linear for the Lattice Modifier to get the effect we want.


The cool thing about Blender Lattice is that we can change the division number of UVW, at any time. Really handly.

CIRCULAR RAMP USING SCREW MODIFIER (EASIER AND SUFFICIENT)
A second solution, perhaps easier way is actually just using Screw Modifier. Probably lest control, but it does a perfect ramp. Except that we probably don't have much control on the Ramp beginning and end.

1. Start by drawing a polygon edge:

2. Then apply Screw Modifier to the edge.
It goes a bit weird at first, but no worries, Modifier is LIVE so we can always tweak and modify the input and getting the right output.

3. Tweak the Screw Modifier
I like using Empty whenever we need "Object" as reference for modifier. So I created an Empty in 3D scene. Adjust the location of Empty and assign it as AxisOb (Axis Object) of Screw Modifier. From here, everything is pretty intuitive.

For the ramp, we just need 90 degree circle, actually. So this will do the job.



This should work and pretty adjustable up to certain extend. And work together with Solidify Modifier if we want thickness on the ramp.



LATTICE AND PYTHON
Now, back to our friend Lattice Deformer...

So, what is wrong with Blender Lattice Deformer? Lattice is an Object that is created separately from the Lattice Deformer. You must create Lattice and then point Lattice Deformer to it.


http://wiki.blender.org/index.php/Doc:2.6/Tutorials/Modifiers/Lattice/Shaping_a_Fork


I think the workflow is a little quirky. Lots of steps required just to setup Lattice Modifier. Why can't the Lattice be confirmed into an Object dimension for example?

Let's try to make the workflow easier using Python.

1. Start with a Cylinder that I have subdivided in height a few times, rotate in arbitrary angle




2. Next, we want Lattice that is confirming our object, which is the Cylinder in our case.

How to do this manually?
We can apply the Dimension as Scale of Lattice and apply Rotation of our object as the Rotation of Lattice. Copy position of our object to Lattice as well, we can simply copy and paste it, but only if our object origin is at center, this is not always true.

Constraint way?
We can use Rotation Constraint. Location Constraint works, but again, only if origin of our object is at the center of origin, otherwise Lattice won't be at the correct place.

Python way?
We can use Python.

My proposition is to create a Python script that does all the steps below to our selected object:
1. Create Lattice Object
2. Confirm Lattice into our object
3. Assign Lattice Deformer
4. Setup the Lattice Deformer

BLENDER SUSHI SCRIPT: Confirm Lattice Object into Selected Object as Lattice Modifier


import bpy

'''
Created by Jimmy Gunawan
Last update: 20130422
Original Source: Blender Sushi

FUNCTION:
Automatically create and confirm Lattice position to selected object as Lattice Modifier.

HOW TO USE:
1. Select a mesh that you like to be Latticed
2. Run the script
3. Select Lattice, go to Edit Mode, deform the object
4. Under Lattice Object Data Property, you also have extra options for Lattice object.

'''

object = bpy.context.active_object
object_name = object.name


# Get Rotation of active object
rotXYZ = object.rotation_euler

# Get Dimension of active object
dimensionXYZ = object.dimensions

# REFERENCE:
# http://blenderscripting.blogspot.com.au/2011/05/blender-25-python-moving-object-origin.html
# https://github.com/davidejones/alternativa3d_tools/issues/1

# Snap Cursor to Active
original_type = bpy.context.area.type
bpy.context.area.type = "VIEW_3D"
bpy.ops.view3d.snap_cursor_to_active()
bpy.context.area.type = original_type

# Save the current location of our object origin
saved_location = bpy.context.scene.cursor_location.copy() # returns a copy of the vector

# Snap origin to geometry center median
bpy.ops.object.origin_set(type='ORIGIN_GEOMETRY', center='MEDIAN')

# Snap Cursor to Active Again
original_type = bpy.context.area.type
bpy.context.area.type = "VIEW_3D"
bpy.ops.view3d.snap_cursor_to_active()
bpy.context.area.type = original_type

# Get Current Origin
center_location = bpy.context.scene.cursor_location.copy()

# Put Cursor Back At Original Location of Object Origin
bpy.context.scene.cursor_location = saved_location

# Set the origin on the current object to the 3dcursor location
bpy.ops.object.origin_set(type='ORIGIN_CURSOR')

# Add and place our Lattice
bpy.ops.object.add(type='LATTICE', view_align=False, enter_editmode=False, location=center_location, rotation=rotXYZ)

# Get Our Lattice
lattice = bpy.context.active_object
lattice_name = lattice.name

# Scale Lattice to Dimension of Object
lattice.scale = dimensionXYZ

# Return our object as active
bpy.context.scene.objects.active = bpy.data.objects[object_name]

# Apply Lattice Modifier
bpy.ops.object.modifier_add(type='LATTICE')
bpy.data.objects[object_name].modifiers["Lattice"].object = bpy.data.objects[lattice_name]



NOTE: For object that is "Flat", one of the Lattice axis becoming ZERO and you probably need to turn the Scale back to 1 and making one of Lattice UVW axis to value of 1. You don't want zero value in Lattice object scale, otherwise, you will not be able to Translate perpendicularly in that axis.

With that script above, hopefully, you can now use Lattice Modifier more often for your modeling needs with no sweat.

Lattice is now easy.
HOOK IT (CTRL+H):
Ever "Points" of Lattice can actually be hooked (go to Edit Mode, select Point and CTRL+H), just like mesh "Vertices" can be hooked. This will give the ability for animator to animate Lattice Points in Object Mode.

BLENDER SUSHI SCRIPT: Hook every Lattice Points (All or Outside Only)


import bpy

object = bpy.context.active_object
object_name = object.name
points = bpy.context.active_object.data.points

# Deselect and select all points (that are visible)
bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.lattice.select_all(action = 'SELECT')

# Need to do this refresh to get rid of Inside points if needed
if (bpy.context.object.data.use_outside):
bpy.context.object.data.use_outside = False
bpy.context.object.data.use_outside = True

# Get List of Points
selected_points = []
selected_points = [points[i] for i in range(len(points)) if points[i].select == True]

# Create Hook for every specified Points
for point in selected_points:
#bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.lattice.select_all(action = 'DESELECT')
point.select = True
#bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.object.hook_add_newob()

# Switch ack to Object mode and deselect all
bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.ops.object.select_all(action='DESELECT')









BLENDER SUSHI SCRIPT: Hook every Mesh Vertices (BONUS)


import bpy

object = bpy.context.active_object
object_name = object.name
vertices = bpy.context.active_object.data.vertices

for i in range(len (vertices)):

bpy.ops.object.mode_set(mode = 'OBJECT')
bpy.context.scene.objects.active = bpy.data.objects[object_name]

# Deselect everything
bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.mesh.select_all(action = 'DESELECT')

bpy.ops.object.mode_set(mode = 'OBJECT')

# Select one vertex iteratively
vertices[i].select = True
bpy.ops.object.mode_set(mode = 'EDIT')
bpy.ops.object.hook_add_newob()
vertices[i].select = False

# bpy.ops.object.mode_set(mode = 'EDIT')
#bpy.ops.transform.translate(value=(-0.145401, 0.411997, 0.196826), constraint_axis=(False, False, False), constraint_orientation='GLOBAL', mirror=False, proportional='DISABLED', proportional_edit_falloff='SMOOTH', proportional_size=1, snap=False, snap_target='CLOSEST', snap_point=(0, 0, 0), snap_align=False, snap_normal=(0, 0, 0), texture_space=False, release_confirm=False)


# Deselect everything
#bpy.ops.object.mode_set(mode = 'EDIT')
#bpy.ops.mesh.select_all(action = 'DESELECT')






Are you hooked by Lattice yet?


EVEN AWESOMER: SOFT IT
Apply Soft Body into Lattice and apply Force to it. Such as Turbulance maybe?

Instance procedural jiggle distortion Lattice thing:
Suzanne inside Distortion Lattice
EVEN MORE AWESOME: BULLET IT (?) OR PARTICLE IT?
In theory, one can probably create some kind of setup that is using Blender Bullet Physics hooked into Lattice that deform the object.

I might be wrong. But deep thinking in term of Points component and having Points ability to deform thing may result in something interesting.

Maybe it's not really a job for Lattice, more like a hacky stuff. Anyways, I leave that for one day, just a note to self.

UPDATE 20130505:
See also:
http://blenderartists.org/forum/showthread.php?290925-Easy-Lattice-editing-addon-you-are-going-to-like-the-way-you-lattice

MKRdezign

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