Digital-Evolutions

Tessellations with Maya

In the TOP View . . . Make a cylinder with 6 sides. *This is to be used as a reference object.

Create Primatives > Polygon > Cylinder ◻

It should look like this.

Push it back in the Translate Y: –1 units.

Change the Pivot Point to the lower left side. Press {Insert} in the keyboard to toggle ON the Pivot Point movement. Use Snap to curve {c} to align it with the corner. While holding the {c} key, move the cursor over the curve you want to snap it to, hold down the middle-mouse button, and move it to where you want it on the curve. In this case, all the way over to the lower left.

Press {Insert} to toggle OFF the Pivot Point movement. Move your hex shape to Origin (0,0,0) Use Snap to Grid {x} align it with the center of the workspace. While holding the {x} key, move the cursor over the point you want to snap it to, hold down the middle-mouse button, and move it to where you want it on the grid. In this case, in the center of the grid.

Make a new layer and add this object to it. Select the Reference Cyclinder and in the Display Menu which is located at the bottom of your Channel Box, press the icon with the white sheet and blue sphere. This will create a new layer and add the selected objects. Toggle reference setting to on, a ‘R’ will appear, click twice.

Label the layer Hex. Double-click on the layer name and Edit Layer menu will appear. Change the name to “HEX_Reference”

Also turn-on wire-frame on shading. The edges should turn grey. In the workspace menu Shading > check the box next to Wireframe on Shaded

OR you can toggle on Wireframe on Shaded here:

Create a curve from the Origin (0. 0. 0) to the right, one unit long to the right. Create > Curve Tools > EP Curve Tool *Reset tool first. This is also the length of the HEX_Reference base. I used Snap to Grid {x} to make sure it was exactly 1 unit long. Hold down {x} while you click on each location on the grid.

Now hide the HEX_Reference Layer – Toggle the Visibility. Click the first check box for the Hex Layer.

*** Before you Duplicate, reset settings.

Using Duplicate Special, create an Instance of this curve Reflecting it over the Y-axis or vertical axis. Select the curve Edit > Duplicate Special and change the Scale x to –1.

Make a new layer for each curve. Change color of each layer. Make the first curve layer a dark color (Dark Blue) Select the object you want added to the group and press the button with the white sheet and Sphere, “Create a new layer and assign selected objects”

Your layers should look like this.

Your curves should look like this.

We are making pair of curves that reflect over the Y-Axis just like in math.

Test to see if it worked. Switch to vertex mode, and move a vertex. The curve should be reflected over the Y-axis basically mirror itself. If you select any vertex the mirrored corresponding vertex will also become selected. If not, you might not have selected Instance when you duplicated the curve.

*Undo the moved vertex.

Select only the left curve (light blue) and Reflect it over the X-axis this time. Change the Scale Z to –1.

Change the Scale Z in the Channel Box.

It will appear that nothing has changed, until you move a vertex.

Switch to vertex mode, and move a vertex again. The curve should be reflected over both the x-axis & the y-axis.

Undo the moved vertex.

Rotate the new curve –60 degrees in the y-axis. Unhide the the Hex Reference Layer again.

Change the Rotate Y in the Channel Box to –60.

It should align with the reference hex. If it doesn’t, start over.

Select both curves and group them. {CTRL} + {G} Label the group “Blue_Curves”

Now unhide the HEX_Refernce Layer.

Move the pivot point of the group “Blue_Curves” to the center of the Hex Reference using snap to curve.

Now hide the Hex Layer, we just used it to find the center of the Hex. **Moving the pivit point is really the only reason why we need the reference cylinder.

Hide the Hex again.

*** Use ‘Duplicate’ not ‘Duplicate Special’ DO NOT use Instance for this step. Using Duplicate make two more sets of the grouped curves. Select the group, “Blue_Curves”, Duplicate it, {CTRL} + {d} and rotate it -120 degrees in the y-axis. Label each of the new groups “Red_Curves” and “Green_Curves”

Make Layers for each curve and change the colors. It should look like this . .

Select all the light colored curves and press the arrow up key.

Group the colored groups. This will select the 3 groups. You are grouping the 3 curve groups.

Then label it “Tessellation_1”.

Test to see if ONLY 1 pairs moves together.

Test all Curve pairs to see if they are mirrored.

SAVE NOW WITH NEW NAME – Single .

Show the HEX REF layer

Middle-Mouse Drag the HEX object and drop it on Tessellation_1 Group.

Using Duplicate Special, make two more Instances of Tessellation_1, rotating them 120 degrees in the y-axis. This will be a set of three hexes. *Make sure you turn on Instance. Select the Tessellation_1 group, change the following settings, and Duplicate Special.

It should look like this.

Hide the HEX REF Layer.

It should look like this.

TESTING: Switch to Vetex Mode, move one vertex and the corisponding vertices should follow. *You should not be able to see curves beneath the moved curves.

Undo the moved vertex.

Centering the pivot point on each tessellation

Show the HEX REF Layer.

Select the Tessellation_1 group

Press the {Insert} key. Hold down the {V} key and wiggle the cursor over the center of the associated HEX REF. This will snap the move tool to the center of the HEX REF. Press the {Insert} key again to deactivate.

Repeat centering pivot for the Tessellation_2 group

Repeat centering pivot for the Tessellation_3 group

The main Tessellation is now done.

SAVE NOW WITH THE NAME “Tessellation_Group_Of_3”

In the Outliner, select while holding down {Shift}: Tessellation_1, Tessellation_2, & Tessellation_3

Duplicate Special

Turn on Instance
Change X Translation to 8.0
Number of Copies to 2

It should look like this.

Change Rotate Y to 120

Change Rotate Y to 240

Change Rotate Y to 360

Change Rotate Y to -120

Change Rotate Y to 0

Change Rotate Y to 120

TEST TO SEE IF IT WORKS: Move one vertex and 14 other vertices should move as well . . .

Select one curve.

Press the {Arrow Up} twice.

It should look like this.

With this group selected, create another instance of just the group. See settings.

A new instance should be created like this.

TEST TO SEE IF IT WORKS: Move one vertex and 16 other vertices should move as well . . .

Undo and SAVE NOW WITH THE NAME “Tessellation_3_Groups_Of_3_Single”

Again Select one curve.

Press the {Arrow Up} twice.

It should look like this.

With it still selected, create a Planar Surface. Surfaces > Planar

Repeat for the 2 other corresponding hexes. Right-Click on all 3 surfaces and assign a new material. This will be Color1.

It should look like this or a different color.

Repeat for the 2 other corresponding hexes. Right-Click on all 3 surfaces and assign a new material. This will be color 2 & 3. It should look something like this - different colors.