Algorithmic Sketchbook

MANIPULATING PLANE POSITIONS WITH CURVED LINE AS ITS REFERENCE

CREATING SPIRALS WITH THE USE OF THE PIPE FUNCTION

USING THE PIPE FUCNTION ON CLOSED POLYGONS

USING WEAVERBIRD PLUG-IN TO CREATE SIDES ON MESHES

KANGAROO PLUG-IN TO CREATE PLATES ON SURFACE OF SPHERE

CREATING CONES BY CULLING CURVES

CREATING ARCS ON GRIDS

CREATING DIFFERENT SIZES OF CIRCLES WITH ATTRACTOR POINTS ON GRID

CREATING CONES ON SQUARE GRID AND MANIPULATING CONE SIZE WITH GRAPH MAPPER

MANIPULATING SHAPE OF VORONOI FRAME

CREATING EXTTRUDED PANELS WITH LUNCHBOX PLUG-IN ON CURVED LINES

CREATING FRAMES ON POLYLINES WITH WEAVERBIRD PLUG-IN

SMALL EXPERIMENTS WITH THE CONE COMPONENT

LOFTING AND EXTRUDING THE SURFACE WITH VECTORS

NOTES AND GRASSHOPPER WORK

USING DATA INFORMATION ON GRASSHOPPER

Flatten Tree:

You flatten a tree to reconstruct the data in the tree structure. This is done by deleting the branch and putting that data under the root of the data tree.

Graft Tree:

This is used to reconstruct the data of a tree structure too. But it is done by addiing a branch to each data item. It is different to flattening but it can be used in combination with it too. To graft a tree, firstly, delete the original branch. The data items at the root will then be on a new branch.

LONGEST LIST SHORTEST LIST AND CROSS REFERENCE TO CONNECT POINTS

Longest list definition

Longest list connects points to lines until all points are connected

Shortest list definition

Shortest list connects points to lines until one curve’s points run out

Cross reference definition

Cross reference makes all possible connections between points

END POINTS

The ‘end point component’ defines the ends of a curve with points.

The end point can be useful when you want to connect the ends of two curves together.

The definition below shows how you can extract end points out of cuves and connect them together via the ‘line’ components.

This is what the component looks like

EVALUATE CURVE

The ‘evaluate curve’ component can be used to define a particular location of a curve.

There two methods to do this and they both give the same result

Method 1: The first method involves right clicking on the ‘curve’ component then selecting ‘reparamatise’/ If you do this the slider should be set to be from 0-1 as the the units of the curve is reparamatised to have values from 0-1. Therefore, after it is reparamatised 0.5 means the mid way point of the curve, 0 is the start,a nd 1 is the end point. Method 2: This method is to not reparamatise it. If you don’t reparamatise it the slider value is dependent on the actual numerical unit of the length of the curve. So if the slider unit is set at 0.5 in this case the point would be 0l.5 units upwards from the start of the curve.

This is what the point of the

This is what the component looks like

curve looks like

LOFTING

To loft curves you just need to reference the curves from Rhino onto Grasshopper. Referencing multiple curves can be done in two ways:

- The first way is shown through the Grasshopper definition at the top from the left page. You right click and select ‘refernce multiple curves’ to compile all the curves onto one component. This method is the most convenient.

- The way is to reference each curve from Rhino individually to each curve component on Grasshopper. You have to hold onto the ‘shift’ button on the keyboard to allow multiple inputs on the ‘loft’ component. Overall, this way to do it is more time consuming but it is useful if you want to manipulate each lofted area from a particular curve uniquely.

To alter the form of the loft press ‘F10’ on the keyboard to have the points of the curve displayed on the screen. Click on the points and move it around to change the loft form.

So far the loft only exists on Grasshopper even though it is displayed on the Rhino screen. This is why you cannot select the loft on Rhino with your mouse. To have the loft on Rhino select the entire definition, right click, the choose ‘bake’. After it is baked the loft is not physically present in Rhino.

1. Create curves on Rhino and reference them on Grasshopper

2. Loft curves with ‘loft’ component on grasshopper

3. (Optional) Press ‘F10’ to display points on the curve.

4. (Optional) To change the form of the curve, move the points.

5. Bake the Grasshopper definition to have it on Rhino.

EXTRUDE

The extrusion example on the right utilises an ‘offset’ component to have many sets of curves offsetted at once when there was only a singular set of curves to begin with.

The ‘extrusion’ component requires a ‘vector’ component to be present in order for it to extrude towards a particular directionl.

There are 3 different types of vectors:

Unit Z - Directs the extrusion along the z axis

Unit Y - Directs the extrusion along the y axis

Unit X - Directs the extrusion along the x axis

USING THE ‘EXTRUDE’ COMPONENT ON MULTIPLE CURVES

PFRAME, POLYGON AND SERIES

Pframe:

The ‘pframe’ component creates perpendicular frames on a curve.

Polygon:

The polygon component allows users to create polygons of a shape. The component inlcudes the manipulation of the polygon’s base plane, radius, number of sides and the curviness of its corners.

Series

The ‘series’ component evenly spaces certain elements.

Example of using the the combination of the 3 to create panels based on the shape of a curve: Create perpendicular frames on a curve >> Create polygons of a certain shape aligned perpendicularly by relying on the ‘Pframe’ component’ >> Evenly space the polygons with a ‘Series’ component

MANIPULATING PLANE POSITION WITH ‘SERIES’

MANIPULATING PLANE POSITION WITH ‘SERIES’

MANIPULATING PLANE POSITION WITH ‘SERIES’

CREATING PATTERNS ON SPHERES

IMAGE SAMPLING

Notes for using circles based on image data to create a picture with circles of the same picture:

- The ‘Sdivide’ component create a grid of points on a surface. These points form the location of where the circles will be located at. Must remmeber to right click on the ‘S’ input of the component and select ‘reparamatise’. This is so that the points resign within the space form 0-1. The reason for this is because the ‘image sampler’ is det on default to take the values 0-1 on the x and y axis. Therefore, for the ‘Sdivide’ and ‘image sampler’ to work together the ‘Sdivide must be reparamatised.

- For the ‘image sampler’ it on default uses the values 0-1 to quantify its image data. In which, black has a value of 1, white a value of 0 and grey a value between 0-1. The bigger the value the bigger the size of the circle.

- There is an ‘expression’ component before the circles. This expression component says: (x*y)+0.1. The 0.1 defines the minimum size for the circle so there are circles everywhere on the surface. White has a value of 0 but with this expression you’ll see a circle deifned to a size of 0.1 units and not 0 which means no circle at all. But you can change that number to any number, the value 0.1 is only used as an example in this case.

THE TOP ARE THE NOTES FOR DEFINITONFOR USING ONE IMAGE’S DATA. THE BOTTOM ARE THE NOTES FOR LAYERING IMAGE DATA TOGETHER.

MAKING A GRID SHELL WITH UNSUAL GEOMETRIES AND USING THE ‘PIPE’ COMPONENT

USING ‘CULLING’ FUNCTION ON ‘VORONOI’

USING ‘BOX MORPH’ ON SOLIDS

CREATING COLOURED SHAPES ON GRIDS

CREATING PATTERNED PLANES AROUND CIRCLE

NOTES

Kangaroo cn be used to self organise structures by manipulating its forces of attraction and repulsion. The following are examples of what kangaroo can do:

Springs (run on sets of 2 particles):

Force particles - if the forces between two particles are repulsive at short distances but attractive at long distances the particles will settle at the distance where the force is zero - this is used to cause a set of particles to self organise.

Equalisation (run on sets of 2 particles):

Measure the lengths of a set of lines, find the average, then treat those lines as springs with this average as their rest length.

Planarisation:

Get the shorest vector between the diagonals of a quadrilateral, and use it to pull the top two vertices down, and the bottom two up. This causes it to become planar.

Bending (runs on a set of three particles):

If you apply a force from the central vertex towards the average of its two neighbours, there is half the oppsite force to the neighbours. this creates bending.

Circularisation:

To see if a shape is a perfect sphere of circle first place O randomly inside the shape in kangaroo. Then equalise the radial lines and planarise it. O is then siutated in the middle of the shape and A, B, C and are on the edge of the shape. If OA, OB, OC and OD have equal lengths then A, B, C and D lie on a common sphere. If ABCD is planar it can also mean that they lie on a common circle.

In this case the shape on the left is a perfect circle but the shape on right is not. This is because OA, OB, OC and PD are only of equal lengths on the left.

CP Meshes:

If the sum of the lengths of the opposite edges of a quad made of two triangles are equal then the triangles have tangent incircles.

In meshes if all adjacent triangles have equal opposite edge lengths for tangent incircles then this is called ‘circle packing’ or ‘CP’ meshes.

Having tangent circles within the individual triangles mean that the geometry can form a very structurally stable construction with torsion free beam layouts.

If the oppsite lengths of a the triangles are the same you can make tangent insircles within them. Such form is very structurally stable.

CREATING DRAPES WITH KANGAROO PLUG-IN

MANIPULATING PLANE POSITIONS WITH A CURVED LINE AS ITS REFERENCE

CREATING SPIRALS WITH THE USE OF THE ‘PIPE’ COMPONENT

USING THE PREVIOUS ‘PIPE’ FUNCTION ON CLOSED POLYGON SHAPES

USING ‘WEAVERBIRD’ PLUG-IN TO CREATE SIDES ON MESHES

USING ‘KANGAROO’ PLUGIN TO CREATE PLATES ON SURFACE OF SPHERE FACING DIFFERENT DIRECTIONS

CREATING DIFFERENT SIZES OF CIRCLES WITH ATTRACTOR POINTS ON GRID

CREATING CONES ON SQUARE GRID AND MANIPULATING CONE SIZE WITH ‘GRAPH MAPPER’

CREATING EXTRUDED PANELS WITH ‘LUNCHBOX’ PLUG-IN ON CURVED LINES (NOTE: IT DOES NOT PRODUCE OFFSETTED PANELS EFFECT WITH STRAIGHT LINES)

CREATING FRAMES ON POLYLINES WITH ‘WEAVERBIRD’ PLUG-IN

EXPERIMENTING WITH THE ‘CONE’ COMPONENT: I TRIED TO USE IMAGE SAMPLING WITH THIS DEFINTION TO CHANGE THE LOCATION OF THE POINTS ON THE INTERPOLATED CURVES BUT IT YEILED NO VISIBLE RESULTS

EXPERIMENTING WITH THE ‘CONE’ COMPONENT: THE CIRCLES PRODUCED A VERY INTERESTING MESH EFFECT. THE PICTURE ON THE LEFT IS THE WHOLE DEFINTION BAKED AND THE IMAGE ON THE RIGHT HAS ONLY THE CIRCLES BAKED

EXPERIMENTING WITH THE ‘CONE’ COMPONENT: THIS CREATE A WEIRD LOFT ON THE BASE OF THE CONES, POSSIBLY DERIVED FROM THE POINTS GENERATED BY ‘POP 2D’

EXPERIMENTING WITH THE ‘CONE’ COMPONENT: I USED THE ‘PIPE COMPONENT HERE. THE IMAGE ON THE LEFT HAS ONLY THE ‘PIPE’ BAKED AND THE IMAGE ON THE RIGHT HAS THE WHOLE DEFINITION BAKED

EXPERIMENTING WITH THE ‘CONE’ COMPONEN: THE INTERPOLATED CURVES ARE LIFTED UP WITH A ‘UNIT Z’ VECTOR. WHEN I TRIED TO LOFT THE LEFTED AREAS NOTHING HAPPENED AND IT MIGHT BE BECAUSE IT’S COMPOSED OF ONLY ONE CURVE AND THE CURVE IS TOO COMPICATED TO LOFT WITH

EXPERIMENTING WITH THE ‘CONE’ COMPONENT: I ADDED ‘VORONOI’ TO THE ‘INTERPOLATED CURVE AND IT GAVE A VERTICAL FRAME THAT GOES THROUGH THE CONES

FAILED DEFINTION OF USING IMAGE SAMPLING TO CREATE CURVED FRAMES

IT'S THE 'DECONSTRUCT MESH' THAT BECAME A RED BOX FIRST SO IT MEANS THAT THE DEFINITION STARTED TO BECOME INVALID FROM THERE.

THE FOLLOWING ARE THE REASON FOR WHY I THINK THE DEFINITION FAILED: -THE START OF THE DEFINTION WASN'T A MESH SO I WASN'T ABLE TO USE 'DECONSTRUCT MESH' -THE 'IMAGE SAMPLING' DIDN'T PRODUCE DATA THAT IS SUITABLE FOR THE 'DECONSTRUCT MESH' TO CREATE POINTS WITH -THE 'IMAGE SAMPLING' WAS NOT ABLE TO CONVERT THE 'SURFAE DIVIDED POINTS' IN A SIMPLE WAY

I TRIED TO CONNECT THE 'IMAGE SAMPLING' WITH THE INTEROPLATED CURVES THIS TIME AND THE RED ON THE 'DECONSTRUCT MESH' DISSAPEARED. BUT THE OTHER COMPONENTS ARE STILL IN ORANGE AND IT SAYS THAT THEY CANNOT READ THE DATA INPUT. I TRIED FLATTENING, SIMPLIFYING, REPARAMATISING AND GRAFTING TO REARRANGE THE DATA ON THE 'INTERPOLATED CURVE' BUT IT STILL DIDN'T WORK.

CREATING FRAMES BASED ON 'IMAGE DATA

NOTE: I ONLY BAKED THE END OF THE DEFINITION FOR THE FRAME STRUCTURE

HANDWRITTEN NOTES

BASICS

MORE ON HOW TO CREATE THE STRUCTURE OF A GRIDSHELL

NOTES ON CREATING LINES, LOFTING

BI-ARCS AND THE SHORTCUT TO NAMING TEXT PANELS

BASICS ON BREP EDGES, LOFTING AND TRIANGULATION ALGORITHMS

IMAGE SAMPLING

BASIC DEFINITION FOR USING IMAGE SAMPLING ON A SURFACE

VECTORS

VISUALISING FIELDS WITH A ‘TENSOR DISPLAY’

USING AND MANIPULATING DATA IN GRASSHOPPER

USING EXPRESSIONS AND THE MATH MENU

COMPONENTS THAT ARE USEFUL IN COMBINATION WITH EXPRESSIONS

HOW DIFFERENT COMPONENTS CREATES

DIFFERENT TYPES OF SPIRALS

MAKING PHYSICAL MODELS