Aalborg University – Architektur og Design - Exercise by Dario Parigi

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FREEFORM GRID

What you will learn

1. How to handle grasshopper “trees

data structure”

2. To parametrically define a freeform

grid of points

List of relevant components used

Merge

Interpolate Curve

Divide

LineSDL

Cross product

Flip matrix

Move

Aalborg University – Architektur og Design - Exercise by Dario Parigi

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This exercise will get you through the procedures to create a grid that adapt curved surfaces, with the

application of vector operations and the careful handling of tree data structure.

1- Create four separate points in Rhino canvas in the xy plane

2- Now open the grasshopper canvas and reference the four points into four separate points

grasshopper components (params>geometry) by right clicking on the component, select set

one point, and then selecting the point in the rhino interface

3- Now collect the four points into a single list with a merge component (Sets>tree) connecting

each one into a different input. Inputs will be created automatically the more you add points.

4- Create a curve through the points (curve>spline>interpolate)

5- Create points along the curve (curve>division>divide curve) and set in the input N the number

of divisions (>10) with a slider of type “integer” (right click for options).

6- Use a panel component (params>input) and a param viewer (params>util) to visualize how

the data is organized. Points are organized in a single list, or branch which path is {0;0}

7- To find the perpendicular vector to the curve at each point, use a cross product component

(vector>vector), and visualize the result with vector display (vector>vector).

’

Aalborg University – Architektur og Design - Exercise by Dario Parigi

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8- Create vertical lines from the points with a component lineSDL (curve>primitive), using the

points in the input S as (the starting point of the lines), a unitz for the direction vector

(vector>vector) and a slider for the L length.

9- Create points on the lines with a divide component, similarly as what you made previously in

step 5

10- Our goal is to create a grid of curves across the points in two directions. Before doing so we

need to learn how data is organized by grasshopper. Preview off the LineSDL and the divide

component (right click on the components to find this option) and examine how the points are

organized with a both a Panel and a Param Viewer component (Params>Util). The Param

viewer pane tells us that the points are organized in 6 branches, each branch is characterized

by a numeric path on the left column (example:{0;0;0}) and contains a list of 4 points (N=4).

(If you double click on the panel a graphic rendition of the data structure is also provided).

The component point list (vector>point) plot the point indexes in the viewport.

If we use an interpolate curve component a different curve will be created for each branch,

spanning the point list that the branch contains.

Aalborg University – Architektur og Design - Exercise by Dario Parigi

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11- With the component flip matrix (sets>tree) it is possible to "flip" the tree data structure. The

data structure changes from ‘X’ points in ‘Y’ branches to ‘Y’ points in ‘X’ branches). Please

note that the points’ location and the points’ number remains unchanged. It is only the data

structure that changes. If we use now an interpolate curve, the curves will be created in the

other direction.

Branch 2 Branch 1

Point 1

Point 2

Branch 4 Branch 3

Branch 6 Branch 5

Point 3

Point 4

Aalborg University – Architektur og Design - Exercise by Dario Parigi

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12- You can remove the unnecessary components to have a cleaner canvas as below, and visualize

the grid of curves.

13- Now we want to create a three-dimensional geometry out of this grid. We start by taking the

points contained in the flip component and we move them perpendicularly to the surface with

the perpendicular vectors that we created in step 7 with the cross product. So we´ll use a

Branch 2

Branch 1

Branch 4

Branch 3

Point 2 Point 1

Point 4 Point 3

Point 6 Point 5

Aalborg University – Architektur og Design - Exercise by Dario Parigi

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move component (transform>euclidean) . Because there are 4 branches containing the

points, the vectors will be applied to the points in each of the 4 branches by the move

component.

14- Now we create curves with the displaced points and create surfaces between the original

curves and the displaced ones with the loft component (surface>freeform)

15- Let´s create the curves in the other direction after flipping the data structure of the displaced

points, and then loft with the correspondent original curves.

Aalborg University – Architektur og Design - Exercise by Dario Parigi

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The geometries in the two loft components constitute your final freeform geometry. By moving the

four original points in Rhino, the 3d grid will adapt and modify in real time.