A I R : ALGORITHMIC SKETCH

2015 SEMESTER 1 STUDIO AIRSTUDIO 9 |TUTOR : ALESSANDRO LIUTI

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W E E K O N E

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

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 ge-ometries of the resulted parametric vase. Face boundary is used to cap the base of the vase.

STRATEGY 1

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

STRATEGY 2

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A polygon in which its radius could be altered serves as the base of the vase. With transformations such as mov-ing 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 off-set outwards to create thickness of the vase. The base is patched with planar surface command. With the con-cept of boolean, the top is capped with solid difference command between the inner and outer lofted surfaces.

STRATEGY 3

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A polygon as a base is created with variable inputs of segments, radius and fillet. A planar surface is then cre-ated 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 loft-ed. Lastly, pipe command is carried out for the top poly-gon; outlining a curved and smooth cap for the top of the vase.

STRATEGY 4

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Similar strategy with polygon as the base form, unit z com-mand 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 pla-nar 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.

STRATEGY 5


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W E E K T W O

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W E E K T W O | DEVELOPMENT OF AN INSTALLATION/PAVILION (FREEFORM SURFACE) FOR MERRI CREEK

With two base curves, catenary is used to form the sec-tion 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.

SECTION PROFILE

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W E E K T W O | DEVELOPMENT OF AN INSTALLATION/PAVILION (FREEFORM SURFACE) FOR MERRI CREEK

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

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. Consider-ation of a possible issue of surface frame that intersects is important here.

WEAVERBIRD TOOL ALGORITHM.

WEAVERBIRD TOOL

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WEAVERBIRD TOOL ALGORITHM.

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 perpen-dicular from the base form, having driftwood effect.

DRIFTWOOD ALGORITHM.

DRIFTWOOD

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

INTERPOLATE CURVE

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

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INTERPOLATED CURVE .

TRANSLATED CURVE TO POLYILINES.

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W E E K T W O | DATA TREE MANAGEMENT

From Grasshoper Primer, data tree is a hierarchical struc-ture 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 in-put A has 11 points whereas the closed curve has 10.

Longest list would result in all points to be definitely con-nected to the points on other line, despite there is no equal points on both curves. This algorithm keeps con-necting 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 connec-tions between points.(EG. 1-1,1-2,1-3...1-10,1-11; 2-1,2-2...2-10,2-11)

DATA TREE 1

LONGEST LIST. SHORTEST LIST.

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SHORTEST LIST. CROSS REFERENCE .

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LONGEST LIST.TWO CURVES.

W E E K T W O | DATA TREE MANAGEMENT

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

DATA TREE 2

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LONGEST LIST. SHORTEST LIST. CROSS REFERENCE.

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W E E K T H R E E

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

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

SURFACE GRID

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A square grid is generated and culled with a cull pattern decided by toggles again. However, this time, an explo-ration 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.

GRID DATA

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

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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.

RADIAL GRID DATA 1

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

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

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.

RADIAL GRID DATA 2

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A cross-referenced lines are connected via a surface and square grid. Like previous experimentation, the sur-face (a geometry formed in Rhino) is surface divided. Points on square grid is culled with a cull pattern gener-ated by toggles and flattened to ensure that points are a continuous connection.

SURFACE GRID

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

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

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With a square grid, points are now translated into an im-age. 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 trans-lates the value of radius in each circles.

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

The multiple option allows the circles to be connected into more circles to generate a much more detailed pat-tern. 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 “dis-appear”.

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

IMAGE SAMPLING

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

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

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With a surface that is divided and flatten into continous connection of points, a cull pattern is inserted to gener-ated a culled list of points. This points are than connect-ed 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.

VORONOI - UNIFORM

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

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

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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.

VORONOI - IRREGULAR

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

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

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W E E K F O U R

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

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.

EXPRESSION 1

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

From several trials on creating expressions, I realised it is important to input an expression that Grasshopper un-derstands, (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 primi-tive from functions.

EXPRESSION 2

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

Rather similar formula for the algorithm, an if function is in-put 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 inter-esting surfaces and spatial organisation of points.

‘IF’ CONDITION

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

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 multiplica-tions (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.

EXPRESSION 1

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

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.

EXPRESSION 2

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

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

‘IF’ CONDITION

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

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W E E K F I V E

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

Extrapolating the structural behavior and overall princi-ples 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 pat-tern 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.

SPIDER WEB - XY

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

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

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.

SPIDER WEB -YZ

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

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N O N - T E A C H I N G W E E K

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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, ex-ploding 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

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N T W | FABRICATION

MAKING TABS

Making tabs to an already unrolled surface allow the joining of surfaces for model mak-ing 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

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N T W | FABRICATION

WAFFLE GRID TYPE 2 FOR SOLID GEOMETRIES

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

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N T W | FABRICATION

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F I N A L D E S I G N P R O P O S A L

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SURFACE PATCH MESH SURFACE

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.

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MESH SURFACE TRIANGULATE MESH FORM FINDING

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FORM FINDING

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.

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SPHERE PACKING

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A I R : ALGORITHMIC SKETCH