TIMOTHY MICHAEL

FARRUGIA ALGORITHMIC SKETCHBOOK ARCHITECTURE DESIGN

STUDIO AIR THE UNIVERSITY OF MELBOURNE

TIMOTHY MICHAEL FARRUGIA STUDENT NUMBER | 585 370 ARCHITECTURE DESIGN STUDIO: AIR ALGORITHMIC JOURNAL HASLETT + PHIL

T R I A N G U L AT I O N ALGORITHMS

Within this exercise, it became apparent just how quickly, and easy, geometry can be realised with the aid of computation. The ‘Populate 3D’ tool was used in this instance - which created a random set of points within a rectangular prism. Then the ‘Voronoi 3D’ tool was included into the algorithm, which divided the geometry into a number of smaller, triangulated pieces. From this and after baking, these pieces could be deleted, which left the original geometry disfigured.

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To the right, a similar process was used, however, the ‘Brep Edges’ tool was used to find the edges of the Voronoi geometries, which were then transformed into pipe surfaces.

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U N D E R S TA N D I N G CURVES

U N D E R S TA N D I N G INTERSECTIONS

Many interesting and useful tools were found within the Grasshopper ‘curves’ toolbar. From the online videos it was shown that end points could be determined at the extremities of Rhinoceros drawn polylines, and these points that were created could be used to draw a line between each. The offset tool, which can be so frequently used within Rhino for parametric design, bears the ability to offset multiple curves at the one instance, whereas in Rhino, the tool could only be used for one curve at a time. It’s important to also make note of the ‘Evaluate Curve’ tool, which, by adding a slider bar, allows one to find a specific point along that curve. From this, an object, or plane can be placed in a specific and precise location about the curve. Grasshopper’s curve toolbox was found to be most appropriate when it came to producing form from a series of intersecting curves and arcs. From the Curve’s division drop-down menu, a list of tools become accessible for dividing a curve into sections. From dividing multiple curves, with an equal amount of divisions, one can then place another curve or arc between the two to create this form.

The Intersection tab of Grasshopper was another area thoroughly explored this week. The process demonstrated in the online video was to specifically place a line on the intersection of two curves. A group of Rhinoceros curves were to be selected and ‘set’ into Grasshopper. From here, one command allowed all intersections to be shown. Then planes were to be created at each intersections’ tangent to define the perpendicular connection of each line. This was taken further (as shown opposite) with cylinders replacing the lines, which were then baked into Rhinoceros. The intersection tool may become useful when it comes to realising the fabrication of a model, as the intersecting curves may represent real surfaces which may need to be fixed at that intersecting point.

Dividing curves into evenly spaced arcs

Joining respective points with arcs in the Z axis

Again, interpolating the arcs to create evenly spcaed points

Adding a polyline which intersects with each point in its list

Locating the intersections of multiple curves

Locating the intersections of multiple curves

Placing cylinders at each intersections

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I N T R O D U C I N G PA R A M E T E R S PA C E , D ATA T Y P E S A N D F U N C T I O N S Field Fundamentals & Expressions For this exercise, I wanted to explore the point charge’s parameters in three dimensions, in order to produce some sort of geometric form off a two dimensional surface. Firstly, this was achieved by dividing the Rhinoceros surface into a series of points about the u and v axes, which became the center points for a series of circular planes. These circular planes were then extruded by the default factor in the z direction. This lead to the result of all circles extruding at a uniform height. So, at this point, a number of point charges were incorporated, fields merged and evaluated with the surface’s original points, to produce a form with more variation in height. Due to the point charges locations about the surface, and the circular panels, certain forms began to occur. To achieve differing forms, and to create iterations, the ‘charge’ of each point was numerically altered, and left either ‘positive’ or changed to ‘negative’. This Grasshopper algorithm was quite fragile, as in small manipulations to inputs lead to big changes to the outcome, having said this algorithm was in a way, hard to control. Due to this, a similar definition was created, however this time, instead of relying on the point charges to define form, the focus shifted to a mathematical evaluation. In this definition, two point charges were used as components for the expression (x), and two sliders were used to deal with the factors of y and z. The function in this case was (x*y) + z, and with this function, a form

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began to emerge. The lengthened extrusions, in this case, were growing in the z axis towards the point charge. But what is interesting about this definition is that the form was more controllable, as in slight manipulations to the algorithm lead to slight manipulations to the outcome. It was also found that when relying on the point charges alone, the form began to spike dramatically, however with the expression within the algorithm, the form produced a harmoneous wavey and curved form.

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Rhinoceros surface ‘set’ into Grasshopper Dividing the surface into a series of base points and setting the locations of point charges Adding circular planes as the components which were to be extruded into a particular form Including the extrude tool into the algorithm lead to a uniform extrusion of the circular planes about the surface, however more variation was wanted The point charges were then evaluated with the base points (circular planes), which were then given certain values to their charge input by a positive of negative factor - note the harsh spikes about the form Another definition hoping to achieve the same outcome used two point charges, instead of the previous five This specific algorithm relied heavily on the input of a mathematical expression, which used the point charges as the main factor - and using others as numerical values The algorithm could easily be manipulated to creat certain iterations

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Week Four: Algorithmic Exercise This week’s algorithmic exercise was to producing some sort of form about the LAGI competition site. To begin with, the focus was on the material field of sectioning, as this field was thoroughly explored within journal parts B1 and B2. There was also some study producing other forms using the point charge within the algorithm. Office dA’s definition for the ceiling structure of their Banq Restaurant was used initially as a starting point. This required a surface that had been manipulated in Rhinoceros with the rebuilding and movement to its control points. This curved surface would determing the form of the sectioned elements. Using a directional line as a reference for the sectioning planes, the first form emerged, which consisted of a number of uniform in length, wavey section panels. At this point the Grasshopper definition was altered with, in order to create multiple iterations. Incorporating an ‘Image Sampler’ in the form of a Nolli Diagram lead to an interesting impression to the heights of the panels. Adjusting the expression from positive to negative also created another iteration, which trimmed the panels about the z axis, where the panels were equal or less than 0. Also, flattening the points of the surface lead - which produced somewhat an error - actually allowed for slightly interesting forms to emerge. The focus then shifted to creating some form with the use of Grasshopper’s point charges, which were thoroughly explored within this week’s online videos. Again, using knowl-

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edge gained within ‘Field Fundamentals and Expressions’, a number of rectangles upon a surface were extruded to in the direction of the z axis to the point charges. Due to the large scale of the site, the charges of the points had to be quite a large numerical factor to produce some variation, which again, was hard to manually control. Therefore an expression was used to produce a more desired form.

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Using a Rhinoceros surface as means to determine the form produced by a number of panels to be sectioned A line was used as a refernce for the sectioning panels The section panels were then projected onto the surface The section lines were then extruded to creat sectioning panels off the surface Altering the algorithm, specifically the vector components, changed the direction of the section panels A Nolli Diagram was used within an image sampler component, to determine the shape of the section panels, about the z axis, in accordance with the surface The result of the image sampler and surface Making the expression positive allowed the panels to extrude from the z direction ‘Flattening’ points lead to small outcomes such as this Starting with Rhinoceros surfaces for another way to produce form Circular panels added to the surfaces’ divided points Using the extrude component to extrude the circles in the direction of multiple point charges - issues with control Using an expression to ease control of the extruded heights The result produces a more wavy form

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D E M O N S T R AT I N G C O N T R O L L E R S , SAMPLERS AND FIELDS

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Evaluating Fields This particular exercise focused upon Grasshopper’s field components as tools to produce geometry. There was a particular interest in this case, to experiment with what occurs to the geometry created about a Rhinoceros surface. From experimenting, it was found that specific geometries can emerge quite quickly, and given the multiple inputs and components to the algorithm, can also produce multiple iterations. First, a series of point charges were needed, which in this case were placed about a Rhinoceros surface. These points where then surrounded with circules, that were divided into equal arcs - this dividing points upon the curves would be the basis of the geometry created, reacting to the centered point charge. After incorporating a ‘field line’, curves started to emerge from the circles, moving away from their charge - which was expected. This first iteration, the curves within the center of the surface were diverted to one direction, as opposed to the end point curves, which spiraled in all directions. This occured due to the points about the surface were not flattened. Having said, this adjustment to the definition lead to further experimentations. Grafting specific inputs and outputs lead to the emergence of sketchy-like patterns, which resembed a weaving aesthetic - which, personally seemed a very interesting outcome. This was continued by adjusting numerical values to the inputs (through sliders), which dramatically altered the outcome of the geometry. The spin charge was then experimented

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with. These iterations that were sculpted with the use of the spin charge demonstrates the possibilities of generative design. At this point, there was no end in sight, as in, the final outcome of the experimentation was unclear as Grasshopper offers so many variations with this field charge componets. The spin charge essentially spun the filed lines in a clockwise direction, about the center of the point charge. This produced bizzare twister-like geometries.

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Using a Rhinoceros surface as means to see what occurs to fields in close proximity to one another, and in three dimensions - instead of a regular polyline Dividing the surface into points The points were then used to determine the location of the point charges Basing circular curves around the charges, and dividing them into equal parts After incorporating the field line component into the deinition, these curves appeared, which demonstrated each field’s charges. Grafting the surface points lead to geometries that followed the form of the original surface This was then experimented with further... And further... And further. Each iteration shows Grasshopper’s ability to produce a different variation from the one before This example shows the outcome of flattening the points - the field charge extends in all directions The spin charge component was added to the algorithm, which spun the filed lines in a clockwise manner Further manipulations to the definition produced multiple iterations

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Graphing Section Panels As for this exercise, the primary component that was of particular interest, was the Graph Mapper. The online video demonstrated this component as a continuation from the previous ‘Evaluating Fields’. This basically transformed the field lines into three dimensional curves, and with my experimentation, the curves were already three dimensional. However, this previous exercise did experiment with the Graph Mapper, but was producing ridiculous amounts of curves, which cause the computer to lag slightly. Having said, another approach was taken to experiment with the Graph Mapper component. The Graph Mapper uses it’s component to shape a particular object - such as the two dimensional curves into three dimensions. But through exploration it was found that the Graph Mapper could determine the height or various extrusions. Using three curves, and dividing them into equal parts, the Graph Mapper component

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Graph Controllers for each rectangle - on a particular point - to extrude to a certain height. The varying levels were dependent upon the shape of the graph itself. Having said, the ‘graph type’ in the component’s settings was experimented with in order to achieve different iterations.

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Rhinoceros curves ‘set’ into Grasshopper Curves divided into equal parts Rectangular planes were created at each point Using the extrusion component within the algorithm, each rectangle’s height was increased. At this stage the Graph Mapper component was incorporated as a tool to achieve varying extrusion heights. This specifc graph type was a Bezier graph. Adjusting the points on the graph altered each solid’s height Interestingly, the shape of the graph, as in the curves, is what ‘trims’ the height of the extrusion. This instance, the graphy type Linear was used For the last iteration, the graph type of Perlin was used as it offered great variation to the heights

Grasshopper’s Graph Mapper could also be used as a component to create patterns and cells. In this instance, the experimentation derived straight from the demonstation video, however the different graph types were also explored with. This definition consisted of the Voronoi component, which produced the cells within a circle component. The Graph Mapper’s curve was to be manipulated in order to produce interesting patters.

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Iteration one, using the Graph Mapper componenet to control the distance between each circle Relying on the slider component connected to the number of voronoi divisions - this number had to be negative Essentially, the Graph Mapper component is very flexible, and can be used to produce varying outcomes. In this case, the outcome is a pattern

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Image Sampling (Nolli Diagrams) Grasshopper’s ‘Image Sampler’ tool was thoroughly explored in last week’s task of B. 2, as the case study our group chose - Office dA’s Banq restaurant - had a definition that included a Nolli Diagram, so we had the chance to experiment with the Grasshopper component already. For more of this experimentation with Image Sampling, please refer to B. 2 in the Journal. For the purpose of this exercise however, it was intended that a Nolli Diagram could be incorporated in a definition to determine the extrusions of particular objects. Using a black and white image of a hand (an x-ray image), I wanted to achieve a geometry similar to when one leaves an impression of their hand in the needles of a pin-art toy. First of all, as per usual, a Rhinoceros surface was set into Grasshopper, which then was divided into a number of points, and had circular panels placed at each of these points. This was then connected to the Image Sampler com-

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ponent through the Surface Divide’s uv output. By doing so, the Nolli Diagram of the hand reflected its image in the geometry. After extruding the circles, it was found that the hand image was only delimiting the number of circles being extrude - perhaps this was because the image wasn’t a true black & white diagram? In anycase, this algorith was incorrect, when trying to achieve the intended task. Having said, it was found that using the Image Sampler as the factor of extrusion height would be the answer.

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Setting Rhinoceros surface into Grasshopper Dividing surface and adding circular panels to points Adding the image sampler as uv output Extruding the circles - issue with impression Using the Image Sampler as the extremities of extrusion height Result

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Week Five: Algorithmic Exercise For week five, it was determined that the experimentation within the journal entry of B.3 (Case Study 2.0) would contibute to this weekâ€™s algorithmic exercise. Screen grabs of the Rhino viewport were taken during this process and logged. For more information regarding the process, please refer to the journal entry B.3. In addition to this, and further explanation of the Grasshopper definition, please see overleaf.

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As usual, the first input to the algorithmic definition setting a Rhinoceros surface into Grasshopper The surface was then divided into a number of points about the u and v axes. These points would become the points at which the timber blocks extrude from. Immediately after dividing the surface, the Cull Pattern component was placed within the definition, culling every second point. This was important as due to the timber blocks upon one row, intersect with that on another - 1 st row points 1, 3, 5 and 2 nd row points 2, 4, 6 A polygon component was then used as the basis of the timber blocks, these polygons were connected to each point that wasnâ€™t culled. Extruding the polygons about the z axis. However, these extrusions had to be rotated in order to imitate the Sequential Wall. These extrusions represent the timber blocks. As for the rotation of the timber blocks, they had to be individually rotated according to that of a Sin wave. To do this, the original points were deconstructed into x and y components, which were to be used within a mathematical evaluation. In addition to this, the evaluation needed a function, and of course to achieve a Sin pattern about the wall, a Sin fuction was needed. The rotation of the extrusions were then bound between 0 and 90 degrees This rotation can be seen when examining the wall from the elevation Final result. See journal for more.

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