studio air algorithmic sketchbook part a + b

M I T C H E L L S U . 6 6 0 1 9 2A B P L 3 0 0 4 8 . S T U D I OA I R . 2 0 1 5 / 1

C O N T E N T S

P A R T AW E E K O N E ……… 0 1 - V A S E O N E - V A S E T W O - V A S E T H R E E - V A S E F O U R - V A S E F I V E

W E E K T W O ……… 1 3 - T A S K A - T A S K B

W E E K T H R E E ……… 2 1 - P A T T E R N O N E - P A T T E R N T W O - P A T T E R N T H R E E - P A T T E R N F O U R

P A R T BW E E K F O U R ……… 3 1 W E E K F I V E ……… 4 1 W E E K S I X ……… 4 7

P A R T AW E E K O N E

“ PROVIDE 5 DIFFERENT STRATEGIES / SET 5 DIFFERENT PROBLEMS / CREATE 5 DIFFERENT GRASSHOPPER FILES FOR CREATING A PARAMETRIC VASE. “

0 1 . S T U D I O A I R . P A R T A

S T U D I O A I R . W E E K O N E . 0 2

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The first vase uses an array of four rectangles that have been spaced out on the Z-plane, rotated then lofted.

For the sake of simplicity, the rectangle definition was shaped to be a square and a translation vector was applied to three of the rectangles to create the vertical spacing. The middle two rectangles then have a rotat ion definition applied to them to create the twisting motion.

It was challenging to create an ideal rotation movement due to two factors - the point of the rotation had to be set and leaving it in default would have caused the rotation to occur instead at the corner of the rectangle. Secondly, the angle of rotation was not set in degrees. Rather the data had to be entered in radians, requiring the formula,

Radians = ⦰ × ∏/180

In doing so, it was also discovered that the degree of rotation should remain ideally between 0 to 2 Radians to prevent any undesirable iterations.

N O T E S

1. Angle of rotation to be set in radians and ideally remain between the values of 0 to 2.

2. Grasshopper appears to be order specific when connecting each rectangles’ algorithm into the loft definition.

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The second vase uses a cylinder’s curved face as a mesh surface to populate with a random set of points that was converted into spheres at that point. Creating an aesthetically pleasing solution in this case was difficult.

Choosing the right sized cylinder to best showcase the outcomes possible in the algorithm was difficult as too small of a set radius would result in a crowded and awkward looking vase.

After creating the cylinder extrusion, the curved face of it was converted into a BREP surface and then a mesh. This allowed the Population Geometry definition to created a population of random points on it.

Initially, the spheres were generated on the points with only a slider to adjust the radii of each sphere in masse, but the appearance of the vase afterwards

proved to be unwieldy and bulky. A solution to this was to apply a ratio for both the number of points populated onto the mesh as well as the radius of the sphere with a division definition.

N O T E S

1. Angle of rotation to be set in radians and ideally remain between the values of 0 to 2.

2. Grasshopper appears to be order specific when connecting each rectangles’ algorithm into the loft definition.

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The third vase uses a similar cylinder extrusion base but plays with linear arrays in order to loft the cylinder. In theory this could be used to create a less uniform and organic shape in the final outcome show later.

After lofting, the curved surface was converted into a BREP surface then a regular surface with the surface being divided into a grid. Then the surface box definition was used to create a more solid form akin to a tube.

Using a pre made geometry created in Rhino, a tile was made to be replicated in the grid. By using the morph definition together with the the cylinder that has now been turned into a tube, the final results in the pre made geometry being fit into the shape of the grid created earlier and within the bounds of the Surface Box definition.

N O T E S

1. Linear array then lofting can serve as a good alternative to extrusion or sweep rails in some instances

2. Grouping is not necessary but is more of a nice to have in the final baked outcome.

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The fourth vase exploration uses circles spaced out in the Z-Plane and lofted, resulting with some odd curvilinear forms with the adjustment of variables to each circle.

The key to this outcome was to use the Circle Three Points definition initially. Although tedious to implement on such a scale, this allows full control of not only the radii of the circles, but also their position on the X, Y and Z plane. Scaling was applied to further distort their shape.

The circles were then moved into position using the Move definition and translated across the Z-Plane and lofted. As with previous approaches, it was noticed that Grasshopper seems to be very specific in the order in which curves are placed into the Loft definition.

The first few steps of this approach were quite tedious to execute five times but were necessary in creating enough variable parameters to produce the irregular shapes as shown above. A possible solution to this would be to create circles that can be adjusted simultaneously using an equation like with the second vase and then combining with a rotation/translation definition.

N O T E S

1. Alternate and less tedious means of generating circles most likely possible using 3D rotate with regular circle definition.

2. Grasshopper appears to be order specific when connecting each circles’ algorithm into the loft definition.


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The fifth and final vase that was explored makes use of random populations once more as well as the OcTree definition. The resulting appearance of the vases are ones that look like pixelated abstractions of a cylinder.

Initially a cylinder is created in a manner much like in the second vase’s algorithm. Then using a random population with a high point count, the OcTree definition is applied.

The OcTree definition works in a manner similar to fractals with a cube being constantly divided to a particular degree set in the parameters.

In experimenting with the parameters of the Populate Geometry and OcTree definitions, it was learnt that there needs to be a balance in values. A high point count in the Populate Geometry definition will result in more possible

points for the OcTree definition to generate upon. On the other hand, it is ideal to use a small value (Below 5) for the OcTree’s group parameters as any higher values will result in what essentially will look like a cube.

N O T E S

1. Populate Geometry number count value should be ideally of a high value.

2. OcTree group parameter value should remain as low as possible.

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P A R T AW E E K T W O

“ WITHIN A SPACE OF 20X20M DEVELOP AN INSTALLATION / PAVILION (FREEFORM SURFACE) ON THE SITE OF MERRI CREEK DEPENDING ON ATTRACTORS. “


S T U D I O A I R . W E E K T W O . 1 4


The initial task for Week Two required making a pavilion on the site of Merri Creek. The aim of it was to see how obtaining data from the site could be used and integrated to achieve a tangible form for a design.

Initially, a contour from the topography of Merri Creek was selected, parametricized and evaluated with the curves drawn as the basis of the pavilion’s form. By parametricizing the curves distance between 0 and 1, it makes it easier to deal with the range of points possible on the curves later on.

Afterwards, to achieve a form for the pavilion, a catenary curve was applied to every point in pairs. It is important to note that plane of the catenary must be set to be in the direction of the Z-Plane.

To create a more tangible form, two methods were used to create a structure out of the catenary curves - creating a piped structure from a mesh, and using a geometry as a tile pattern to be filled over a lofted surface.

The piped structure creates a net structure with a more solid form based on a square grid mesh. However a

number of issues occurred while developing the structure. Firstly, the catenary curves did not appear to be particularly smooth, so the output had to use a simplify parameter but even then it a resulted in a cluttered result. In the end, the baked form was grouped to avoid any issues with translating the structure from one point to another.

The second structure used a geometry multiplied in a boundary along a lofted surface derived from the catenary curves. This result was far less fraught with complications with the only challenge being adjusting the U and V values to create an aesthetically pleasing result.


As a side task to understanding the nature of attractor points and their effect on vectors, a data tree was created and visualized using data from the curves predetermined earlier.

The predetermined curves followed the same parameters as the initial task for Week Two. A points definition was used to visualize the sequence of numbers generated by dividing the curves into 10 and 15 points respectively. In terms of really understanding the nature of data trees, it was discovered upon experimentation that using unequal points for each curve would result in a more explicit and interesting result.

By treating the points generated as a list of numbers in a sequence, the two sets were connected to list sorters that were then visualized with vector lines between pairs of points. The list sorters in themselves produce different outcomes based on various parameters.

The shortest list definition will join only enough points as there are matching number of points in each curve. The selection of unique points in this instance can be controlled by altering the definition’s parameters or by

using a cull pattern definition beforehand. The longest list can be affected the same way but will keep creating pairs of points until the list runs out. Cross referencing will result in an output showing every possible combination of points possible.

By using vector lines and grouping them, the end result shows a general approximation of the curves’ geometries with many of the paths created by the points concentrated in paths leading towards the curves’ extremities.

P A R T AW E E K T H R E E

“ DEVELOP FOUR PATTERNS USING A RANGE OF DEFINITIONS INCLUDING CULL, LIST ITEM FROM A GRID, CONNECT POINTS, MODULATE CIRCLES, VORONOI, ETC . “


S T U D I O A I R . W E E K T H R E E . 2 2


The wave pattern in the first pattern exploration is a relatively simple design that makes use of lists in tandem weaving.

To emphasize the pattern developed using lists, a linear array has been applied to the line generated initially. Using the dispatch tool, we can sort the lines into alternating batches which is essential for creating a wave between two lists.

The cull tool is then used to discard every two points as the basis for our pattern. Within this, one of the batches has their definition reversed to the other batch then inputted into a weave definition. If one were to interpolate a line between one line from each batch, a zig zag kind of pattern would be produced.

Using this outcome, NURBS is applied to the resulting weave output and the points leftover from the cull definition. To intensify the appearance of the wave pattern, a second NURBS definition with a translation to the right was applied resulting in double the parallel waves as shown on the right.

N O T E S

1. The panel table provides a more convenient alternative too boolean toggle expressions that can become tedious to add if multiple toggles need to be applied.

2. After baking the NURB and move definitions, grouping will be required to maintain a cohesive pattern. Otherwise a group definitions can be applied to the grasshopper algorithm.

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The second pattern uses a grid of points and treats them almost like a matrices grid. The end result is a pattern that tessellates to some extent which can be attributed to the Cull Pattern tool used later in the algorithm.

The square grid is initially used as a basis for the pattern as well as a region boundary. The points are then extracted and their order flipped to change the orientation of the future pattern. By using the flatten tree data, rather than having 10 sets of a series of 10 points, the sets are combined to create a single series of points that go from 1 to 100.

This allows us to create patterns that are diagonal in nature with the help of the Cull Pattern definition. By eliminating certain points in a pattern, a diagonal gap can be generated. These points are then interpolated using the Nearest Neighbor definition which joins up a

point’s closest adjacent points based on a set of parameters such as the number of neighbor of points that can be connected and the maximum distance they can be away.

N O T E S

1. Boolean toggles are used to generate patterns for the cull pattern definition so it can determine which points to remove in the distribution.

2. Points definition only used as a visualizer rather than anything tangible in effect.

3. Grouping not necessary but is a convenient definition before baking the Grasshopper algorithm.

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The third pattern developed using grasshopper was based off making circles positioned on a grid of varying radii dimensions. To achieve this, a square grid was used and the points extracted from it.

To determined the value of the circles’ radii, an image optimized to the requirements set out in the notes to the left was used. Grasshopper reads grey scale from a 0 to 1 value scale with 1 resulting in a larger circle from the set point. It is especially important to make sure the image’s domain is set to be the same value in the image parameters as the extents of the square grid or the resulting definition will not be able to compute properly.

The scale was then used to adjust these circles to a more aesthetic result from what was originally provided by a factor of 0.8 (80%). Before scaling it was found

that the circles were too large and overpowered the balance of white space in the tile.

N O T E S

1. The image must be optimized for Grasshopper. This includes setting the image to greyscale and applying a blurring filter. A higher contrast ratio in the image will result in more obvious results. It was also noted that the domain of the image should ideally match the extents of the square grid.

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The fourth pattern exploration entailed using a voronoi definition to create a somewhat random pattern. However, an unadulterated execution of a voronoi definition will result in a visually mundane tile pattern. As a result, multiple steps were taken to further randomize the execution.

Firstly, a rectangle was produced to create a region for a random population of points to be dispersed in. For the subsequent voronoi to work, a high number of points is required to produce a visually effective outcome. However, too many points can overload a c o m p u t e r ’ s r e s o u r c e s a n d miscalculations as a result.

After executing the voronoi definition, the individual areas defined by the pattern were turned into BREP surfaces with their boundaries defined. The resulting boundaries and their vertices

were used as points to interpolate curves from NURBS. The resulting curves were then recombined with the original straight lines created from the voronoi definition earlier to produce a more irregular looking pattern.

N O T E S

1. Trimming is not necessary as a definition to the pattern but results in a much tidier computation from Grasshopper.

2. Grouping is also not necessary but highly recommended as the number of points and curves produced after baking into Rhino can result in performance issues and grouping the result makes it easier to manipulate/move.

ABC

ABC

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P A R T BW E E K F O U R

“ CREATE A SURFACE USING MATHEMATICAL PATTERNS BOTH WITH AND WITHOUT THE IF FUNCTION . “

3 1 . S T U D I O A I R . P A R T B


N O T E S

1. The initial part sets the list of points to be generated and used as an input to the function.

2. Trigonometric functions are periodic, providing a continuous pattern of lines.

3. Interpolating the points into a curve provides a continuous path on the list of points.

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S T U D I O A I R . W E E K F O U R . 3 4

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N O T E S



3. If expression changes original output orientation of selected points


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N O T E S



3. Points are put in a polar rather than linear order to create a periodic function around one point.


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N O T E S


2. If expression changes original output orientation of selected points


4. Points are put in a polar rather than linear order to create a periodic function around one point.


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P A R T BW E E K F I V E

“ EXAMINE DIFFERENT TYPES OF REAL SPIDER WEBS. EXTRAPOLATE THEIR STRUCTURAL BEHAVIOR, GENERATION LOGICS, OVERALL PRINCIPLES. . “


S T U D I O A I R . W E E K F I V E . 4 2

P A R T BW E E K S I X

“ EXPERIMENT WITH FABRICATION METHODS. “



N O T E S

1. Input brep geometry

2. Division definition for making waffle assembly

3. Output surfaces for waffle solid assembly

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N O T E S


2. Make tab on faces definition

3. Output line work settings

4. Baking operation

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N O T E S


2. Unroll brep faces definition

3. Output surfaces unrolled

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M I T C H E L L S U . 6 6 0 1 9 2A B P L 3 0 0 4 8 . S T U D I OA I R . 2 0 1 5 / 1

studio air algorithmic sketchbook part a + b

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