A I R : ALGORITHMIC SKETCH

2015 SEMESTER 1 STUDIO AIR STUDIO 9 |TUTOR : ALESSANDRO LIUTI

W E E K 0 1 05 W E E K 0 2 17 W E E K 0 3 29 W E E K 0 4 47 W E E K 0 5 61 N T W 67 F I N A L 75

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WEEK ONE

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W E E K O N E | FIVE STRATEGIES TO CREATE A PARAMETRIC VASE

STRATEGY 1

Using a circle as a base form and a rail curve, railsweep command is used to form the structure. A sectional curve generated by 6 vertices hence play the role to then create 5 different geometries of the resulted parametric vase. Face boundary is used to cap the base of the vase.

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W E E K O N E | FIVE STRATEGIES TO CREATE A PARAMETRIC VASE

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STRATEGY 2

This strategy implements the concept of boolean. A surface is resulted from solid difference between two geometries - sphere and extruded polygon. A variety of structures are formed with the adjustment of radius and base plane of the shapes. The bottom is capped with planar surface command.

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W E E K O N E | FIVE STRATEGIES TO CREATE A PARAMETRIC VASE

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STRATEGY 3

A polygon in which its radius could be altered serves as the base of the vase. With transformations such as moving its z-axis and scaling its radius, two other polygons are created. These three polygons are translated as curves and then lofted. The resulted surface is thus offset outwards to create thickness of the vase. The base is patched with planar surface command. With the concept of boolean, the top is capped with solid difference command between the inner and outer lofted surfaces.

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W E E K O N E | FIVE STRATEGIES TO CREATE A PARAMETRIC VASE

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STRATEGY 4

A polygon as a base is created with variable inputs of segments, radius and fillet. A planar surface is then created as the bottom of the vase. Two variable polygons are formed; lofted together with the first polygon base.

Rotation angles are implemented before surface is lofted. Lastly, pipe command is carried out for the top polygon; outlining a curved and smooth cap for the top of the vase.

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W E E K O N E | FIVE STRATEGIES TO CREATE A PARAMETRIC VASE

STRATEGY 5

Similar strategy with polygon as the base form, unit z command is used instead for direct moving of polygon along the z-axis. Transformation such as rotation and scaling is applied once again, with base being capped with planar surface and main structure being formed via lofting command. An addition of extrusion command is utilised to explore the effect on its top area of surface.

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WEEK TWO

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W E E K T W O | DEVELOPMENT OF AN INSTALLATION/PAVILION (FREEFORM SURFAC

SECTION PROFILE

With two base curves, catenary is used to form the section profiles. The loft is the challenge in this algorithm as it tends to have entangled flipping. Profiles are again examined carefully with checking the points on curves.

Reason for entangled flipping is due to a chaos in orders of points. This is when a lists operations comes in handy to investigate where are the points that need to be split.

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CE) FOR MERRI CREEK

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W E E K T W O | MATERIAL TECHNIQUE ON FREEFORM SURFACE

WEAVERBIRD TOOL

A plug-in for grasshopper, this tool is used to create a mesh from the outcome from section profiling. Edges and thickness of the frame could be varied. Consideration of a possible issue of surface frame that intersects is important here.

WEAVERBIRD TOOL ALGORITHM.

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DRIFTWOOD

This method is based on extruding offsetting curves. The intersections between brep obtained from offsetting curves and that from previous lofted section profile is then used to split surfaces with the exploded extruded curves. This result in layers of surfaces that stands perpendicular from the base form, having driftwood effect.

DRIFTWOOD ALGORITHM.

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W E E K T W O | VIDEO TUTORIAL - CURVE MENU

INTERPOLATE CURVE

This is actually another method of forming a freeform surface. Polyline command is used to flatten and panel the surface in order to be buildable.

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INTERPOLATED CURVE .

TRANSLATED CURVE TO POLYILINES.

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W E E K T W O | DATA TREE MANAGEMENT

DATA TREE 1

From Grasshoper Primer, data tree is a hierarchical structure for storing data in nested list. Data tress are created when a component is structured to take in data set and output multiple sets of data.

From the sample I examine, the open curve listed as input A has 11 points whereas the closed curve has 10.

Longest list would result in all points to be definitely connected to the points on other line, despite there is no equal points on both curves. This algorithm keeps connecting inputs until all streams run dry.

(EG.1-1,2-2, 3-3...10-10, 11-10) Shortest list is a connection of inputs one-on-one until one of the streams run dry.

(EG. 1-1, 2-2, 3-3...10-10, 11-N/A) Cross reference hence is a result of something interesting and complex. This algorithm makes all possible connections between points.

(EG. 1-1,1-2,1-3...1-10,1-11; 2-1,2-2...2-10,2-11)

LONGEST LIST.

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SHORTEST LIST.

CROSS REFERENCE .

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W E E K T W O | DATA TREE MANAGEMENT

DATA TREE 2

Applying the same concept, this is to further explore what patterns could be obtain from the lists via two rather more complex curves.

TWO CURVES.

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LONGEST LIST.

SHORTEST LIST.

CROSS REFERENCE.

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WEEK THREE

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W E E K T H R E E | CULL/LIST ITEM FROM A GRID/CONNECT POINTS

SURFACE GRID

“Divide surface” into grid points is useful in order to formulate a pattern on it. With that, “cull pattern” generates a formula of points with a culling pattern that could be decided by toggles. Using cross referencing between initial points from surface and that from culled list, a symmetric and interesting pattern is formed.

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W E E K T H R E E | CULL/LIST ITEM FROM A GRID/CONNECT POINTS

GRID DATA

A square grid is generated and culled with a cull pattern decided by toggles again. However, this time, an exploration on culled list of points on grid is cross referenced with a geometry created in Rhino. Again, the geometry is to be surface divided in order to generate points on surface.

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W E E K T H R E E | LIST ITEM FROM A GRID/CONNECT POINTS

RADIAL GRID DATA 1

For this, a radial grid is generated. By cross referencing with its points itself, a pattern is formed.

This is important in order to understand the differences between this radial grid data with the next radial grid data that is flattened.

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W E E K T H R E E | LIST ITEM FROM A GRID/CONNECT POINTS/FLATTEN TREE

RADIAL GRID DATA 2

Exactly the same algorithm as Radial Grid Data 1, a much more complex pattern is formed when the points on grid is flattened.

This flattened grid data illlustrate that the points on grid are now a continous connection.

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W E E K T H R E E | CULL/LIST ITEM FROM A GRID/CONNECT POINTS/FLATTEN TREE

SURFACE GRID

A cross-referenced lines are connected via a surface and square grid. Like previous experimentation, the surface (a geometry formed in Rhino) is surface divided.

Points on square grid is culled with a cull pattern generated by toggles and flattened to ensure that points are a continuous connection.

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W E E K T H R E E | IMAGE SAMPLING TO MODULATE CIRCLES/CURVES ON A GRID

IMAGE SAMPLING

With a square grid, points are now translated into an image. With this, image recognise the points by its value of grayscale.

With an algorithm of circle connected from the grid points, the value of grayscale from the image then translates the value of radius in each circles.

(EG. 1 is white & 0 is black, range in between would be the gradient of gray/black).

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The multiple option allows the circles to be connected into more circles to generate a much more detailed pattern. Again, applying the cull list, this time, a “larger than x-value” input is connected to generate a cull pattern.

This means circles that has radius larger than x would “disappear”.

This method is useful as it could associate image with points, for instance, taking a response to translate into data,

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W E E K T H R E E | VIDEO TUTORIAL - PATTERNING LIST

VORONOI - UNIFORM With a surface that is divided and flatten into continous connection of points, a cull pattern is inserted to generated a culled list of points. This points are than connected to form voronois. In order to randomly allocate points that scatters around the surface, jitter is used. This list of random connection of points are than unioned to form a voronoi-patterned surface.

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W E E K T H R E E | VORONOI/CULL/LIST ITEM

VORONOI - IRREGULAR A square surface generated in grasshopper using x-axis and y-axis points, pop2D is used to generate a random allocation of points on surface. This is then again culled in order to create more arbitrary location of points. This list of points are then voronoi-ed.

The voronoi is offseted to create thicker lines of voronois.

With a slight extrusion from this voronoi, they are then capped and resulted in this honeycomb-like pattern.

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WEEK FOUR

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W E E K F O U R | DEVELOP SURFACE FROM MATHEMATICAL FUNCTION

EXPRESSION 1

It is important to realise that functions could produce primitives.

With an idea of creating a pattern similar to Nautilus shell, the functions that create spiral effects are hence explored. This is done by lofting two primitives that have a certain z-axis distance with another primitive from an expression that acts as a base point of attraction.

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W E E K F O U R | DEVELOP SURFACE FROM MATHEMATICAL FUNCTION

EXPRESSION 2

From several trials on creating expressions, I realised it is important to input an expression that Grasshopper understands, (i.e. accuracy of symbols is crucial to avoid syntax errors).

Again, this algorithm sketch illustrate the definition of series of points that could be used to generate a primitive from functions.

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W E E K F O U R | DEVELOP SURFACE FROM MATHEMATICAL FUNCTION

‘IF’ CONDITION

Rather similar formula for the algorithm, an if function is input to generate a pattern list of points to create a curve.

This function of ‘if’ clause could be used to cull a list of pattern that then could be further developed into interesting surfaces and spatial organisation of points.

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(IF)

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W E E K F O U R | GENERATE PATTERN FROM MATHEMATICAL FUNCTION

EXPRESSION 1

A play of transformations such as scaling, rotation and mirror are done to a series of points that are generated again, from mathematical functions.

It is important to note that in order to perform multiplications (or any other kinds of mathematical operators) , the definition of graft tree is ought to be input. The results of transformation are then flattened to create a continuous series of points. These points are then set in lists to create a final pattern from intersecting lines via the points.

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W E E K F O U R | GENERATE PATTERN FROM MATHEMATICAL FUNCTION

EXPRESSION 2

With similar algorithmic commands used for EXPRESSION 1, the function input is altered.

Voronoi is then added to the curves to generate a rather random sequence of circles from few points through a cull pattern.

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W E E K F O U R | GENERATE PATTERN FROM MATHEMATICAL FUNCTION

‘IF’ CONDITION

Charged points are added, creating a magnetic field which would further affect the points from the mathematical expression.

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(IF)

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WEEK FIVE

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W E E K F I V E | GRAPH CONTROLLER - XY PLANE

SPIDER WEB - XY Extrapolating the structural behavior and overall principles of spider webs, a pattern is created on the x-y plane with Graph Controllers. It is then relaxed with Kangaroo, a plug-in for physics simulation. It is important to note that as a graph mapper is inserted as an input to manipulate the radius distances between circles, alteration to the domain is done at graph mapper, not the initial domain input. Points should also be flatten in order to create a continuous connection for further Voronoi components.

The exploration of further complicated spider web pattern is restrained. This is because errors would occur when these segments are translated into springs. However, through this task, it is realised that Kangaroo could relax a pattern through unary force and spring.

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W E E K F I V E | GRAPH CONTROLLER - YZ PLANE

SPIDER WEB -YZ Similar strategy as the previous sketch, this time, a spider web pattern is created on the YZ plane. This is done by rotating the plane. The same Z-unit vector is input as the unary force to retain its form of stretching downwards due to gravity.

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NON-TEACHING WEEK

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N T W | FABRICATION

UNROLL BREP

Unrolling polysurface for fabrication is useful in having an outcome of flat surface on xy-plane.

As seen in this example, there are overlapping surfaces after using this definition. Hence, exploding them to individual surface (bottom right) is the optimum way to be printed and cut for model making consideration.

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N T W | FABRICATION

MAKING TABS

Making tabs to an already unrolled surface allow the joining of surfaces for model making easier. Red curves hence represent folded edges where lasercut/card cutter would only cut with less force. Black curves hence would be fully cut through.

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N T W | FABRICATION

WAFFLE GRID TYPE 2 FOR SOLID GEOMETRIES

Waffle Grid is useful to be explored for fabrication related to structure and geometries that emphasise on contour design.

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FINAL DESIGN PROPOSAL

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FORM FINDING From the final form boundary through merging all functional zones, surface patch is done before meshing the surface. The mesh is then refined with triangular mesh for even distributed mesh pattern.

The mesh is inflated with several constrain points and curves with the aid of Kangaroo physics simulation and Smartform. This is the process when only 3-dimension form emerged. Structural feasibility and its functional purpose are considered in this form finding process.

SURFACE PATCH

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ME

ESH SURFACE

TRIANGULATE MESH

FORM FINDING

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SPHERE PACKING Spheres are packed in a delaunay format to minimize gaps among the spheres. Kangaroo physics simulation is used to pack the spheres together. Sphere packing would prevent overlapping of spheres that are formed from the mesh previously. *note: there are errors in the definition below because the mesh is supposed to connect to the mesh formed in Smartform previously.

FORM FINDING

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SPHERE PACKING

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