GRASSHOPPER TUTORIAL 02 PERFORATED CURVATURE
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RIAL PERFORMANCE pon a exploration on the material properties of a perforated minate presented at the ACADIA regional conference in 2011. hole article, see the link on the DDA\scripts page: http:// ida.net/gh/
ept is to use the inherent structural properties of a material, power and accuracy of computational design tools to te a surface in a virtual space and be able to replicate it with in reality.
PERFORATED CURVATURE
l documentation provided above (fig.1) shows the structural of a 10x10 sheet of timber laminate, with varying perforations. shows an initial curvature analysis of a NURBS surface (fig.2) THIS TUTORIAL EXTENDS UPON TUTORIAL 01 BY CREATING nerates perforations a design script. (fig.3) A SIMPLEusing DEFINITION THAT ANALYSES THE CURVATURE OF mation required to inform a CNC cutting machine is then A DOUBLY CURVED SURFACE AND INDICATES HOW THIS BE FURTHER EXTENDED TO MANIPULATE MATERIAL to enable theCOULD bottom fabrication, (fig.4) which appears to QUALITIES TO ACHIEVE COMPLEX DOUBLE CURVATURE FROM he bending of the material to the desired direction.
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PERFORATIONS IN A FLAT SHEET. FURTHER INFORMATION REGARDING THE FURTHER EXTENSION OF THIS DEFINITION IS AT THEmaterial END OF information THE TUTORIAL. happened toPROVIDED the additional from above?
some of the complexity of the initial analysis has been lost. rial sets up an initial definition which creates perforation hich are informed by surface curvature to get you started.
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GH TUTORIAL - 02 PERFORATED CURVATURE DAVID LISTER, JAS JOHNSTON - 28082011
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EXERCISE CREATE A DOUBLY CURVED SURFACE IN RHINO THAT WILL BE ANALYSED BY THE GRASSHOPPER DEFINITION. REFERENCE THIS SURFACE FROM RHINO INTO GRASSHOPPER USING THE SURFACE COMPONENT. RIGHT CLICK ON THE COMPONENT AND SELECT “SET ONE SURFACE”
(PARAMS/GEOMETRY/SURFACE) TO EVALUATE CURVES ONTO THE SURFACE POINTS MUST BE DEFINED ACROSS THE SURFACE. THIS IS ACHIEVED BY DIVIDING THE SURFACE INTO U&V TOPOLOGICAL CO-ORDINATES USING THE DIVIDE SURFACE COMPONENT.
(SURFACE/UTILITY/SDIVIDE)
SURFACES ARE DEFINED BY TWO DIRECTIONS IN PARAMETRIC SPACE, REFERRED TO AS U AND V DIRECTIONS. THE DOMAIN OF EACH OF THESE DIRECTIONS ARE DIVIDED BY THIS COMPONENT, RETURNING POINTS AND U,V PARAMETERS OF THE DIVISION POINTS, AND THE VECTOR NORMALS AT THESE POINTS.
SPECIFY THE NUMBER OF DIVISIONS IN EACH OF THE U-DIRECTION AND V-DIRECTION USING NUMBER SLIDERS.
(PARAMS/SPECIAL/NUMBER SLIDER) THE NUMERIC DOMAIN (THE MINIMUM, MAXIMUM AND RANGE) OF THE SLIDER AND THE TYPE OF NUMBER ROUNDING CAN BE ALTERED BY RIGHT CLICKING ON THE SLIDER AND SELECTING EDIT. WE ARE GOING TO MAKE A PERFORATION AT EACH OF THESE DIVISION POINTS INITIALLY BY CREATING A CIRCLE USING THE DIVISION POINTS AND NORMAL VECTOR AT THAT POINT.
(CURVES/PRIMITIVES/CIRCLE CNR)
GH TUTORIAL - 02 PERFORATED CURVATURE DAVID LISTER, JAS JOHNSTON - 28082011
EXERCISE N.B. YOU CAN SEE THAT THE GH WIRES ARE NOW DOTTED AND ‘HOLLOW’. THIS INDICATES THAT THE OBJECT DATA HAS BEEN SEPARATED INTO ‘BRANCHES’. THE DATA STRUCTURE CAN BE VIEWED BY USING THE PARAM VIEWER COMPONENT.
(PARAMS/SPECIAL/PARAM VIEWER)
THE RADIUS OF THE CIRCLE CAN BE ALTERED BY ADDING A NUMBER SLIDER TO THE RADIUS INPUT. THIS RESULTS IN UNIFORM PERFORATION CURVES OVER OUR SURFACE, BUT NOTHING THAT RELATES TO SURFACE CURVATURE. WE WILL NOW ANALYSE THE SURFACE AT THE DIVISION POINTS AND USE THESE LOCAL CONDITIONS TO INFORM THE PERFORATIONS.
TO ANALYSE THE SURFACE CURVATURE AT EACH OF THE UV COORDINATES INSERT THE SURFACE CURVATURE COMPONENT.
(SURFACE/ANALYSIS/SURFACE CURVATURE) FOR FURTHER INFORMATION ON SURFACE CURVATURE SEE REFERENCE MATERIAL.
INPUT THE LOCAL GAUSSIAN CURVATURE TO INFORM THE RADII OF THE CIRCLES.
INPUT THE LOCAL MEAN CURVATURE TO INFORM THE RADII OF THE CIRCLES AND EVALUATE THE DIFFERENCE.
GH TUTORIAL - 02 PERFORATED CURVATURE DAVID LISTER, JAS JOHNSTON - 28082011
EXERCISE DEPENDING ON THE SURFACE YOU HAVE CREATED, THE SIZE OF THE GENERATED PERFORATIONS MAY BE TOO SMALL. THE SIZE OF THE RADII INPUTS CAN BE VIEWED BY USING A PANEL.
(PARAMS/SPECIAL/PANEL)
INSERT A FUNCTION COMPONENT TO RE SCALE THE NUMERICAL DATA TO THE TARGET SURFACE. FUNCTION COMPONENTS ALLOW YOU TO ENTER ALGORITHMS TO ALTER THE DATA USING DIFFERENT NUMBERS OF VARIABLE INPUTS. IN THIS CASE WE WANT TO INCREASE THE SIZE OF THE CURVATURE ANALYSIS DATA TO INCREASE THE RADII INPUT TO A PERCEPTIBLE AMOUNT.
(MATH/UTIL/F2)
RIGHT-CLICK ON THE ‘F’ INPUT OF THE COMPONENT TO INPUT A MATHEMATICAL EXPRESSION. THIS CAN BE DONE IN THE WINDOW BELOW ‘EXPRESSION EDITOR’
OR BY SELECTING ‘EXPRESSION EDITOR’ FOR A SEPARATE WINDOW WITH EXPRESSION ICONS
IN THIS CASE I HAVE ENTERED THE EXPRESSION X*(Y*1000) TO ACHIEVE AN ADEQUATE RESULT. THE EXPRESSION REQUIRED WILL DEPEND ON THE SIZE OF THE INDIVIDUAL SURFACE. EXPERIMENT WITH DIFFERENT EXPRESSIONS UNTIL AN ADEQUATE OUTCOME IS REACHED WHERE THE CIRCULAR PERFORATIONS ENLARGE AS CURVATURE INCREASES, ALTERING THE RIGIDITY OF THE MATERIAL. GH TUTORIAL - 02 PERFORATED CURVATURE DAVID LISTER, JAS JOHNSTON - 28082011
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MATERIAL PERFORMANCE Based upon a exploration on the material properties of a perforated MATERIAL PERFORMANCE MATERIAL PERFORMANCE timber presented at conference in 2011. Basedlaminate upon a exploration onthe theACADIA materialregional properties of a perforated For the whole article, see the link on the DDA\scripts page: http:// timber laminate presented at the ACADIA regional conference in 2011. BASED UPON EXPLORATION ON THE MATERIAL scripts.crida.net/gh/ For the whole article, see the link on the DDA\scripts page: http:// PROPERTIES OF A PERFROATED TIMBER LAMINATE
scripts.crida.net/gh/ THE ACADIA REGIONAL MATERIAL PERFORMANCE The PRESENTED concept is toATuse the inherent structuralCONFERENCE properties of IN a material, 2011.Based FOR upon THE WHOLE ARTICLE, SEE THE LINK ON THE a exploration on the material properties of a perforated and the powerisand accuracy of computational design tools TheDDA\SCRIPTS concept toPAGE: use the inherent structural of atomaterial, HTTP://SCRIPTS.CRIDA.NET/GH/ timber laminate presented at the ACADIAproperties regional conference 2011. manipulate a surface in a virtual space and be able to replicate it in with and theFor power and accuracy ofthe computational design tools tohttp:// the whole article, see link on the DDA\scripts page: precision in reality. THE CONCEPT IS TO THE INHERENT STRUCTURAL manipulate a surface inUSE a virtual space and be able to replicate it with scripts.crida.net/gh/
PROPERTIES OF THE MATERIAL, AND THE POWER OAND precision in reality. The ACCURACY initialThedocumentation provided above (fig.1) shows OF DESIGN TOOLS TOtheofstructural conceptCOMPUTATIONAL is to use the inherent structural properties a material, MANIPULATE A SURFACE IN A VIRTUAL SPACE AND BEtools analysis of a 10x10 sheet of timber laminate, with varying perforations. and the power and accuracy of computational design to TheABLE initialTOdocumentation provided above (fig.1) shows the structural REPLICATE ITcurvature WITH PRECISION INaREALITY. Figure 2 shows an initial analysis of NURBS surface (fig.2) manipulate a surface in a virtual space and be able to replicate it with analysis of a 10x10 sheet of timber laminate, with varying perforations. which generates precisionperforations in reality. using a design script. (fig.3) Figure showsDOCUMENTATION an initial curvaturePROVIDED analysis ofABOVE a NURBS surface (fig.2) THE 2INTIAL (FIG.1) The information required to inform a CNC cutting machine is then which generates perforations using a design script. (fig.3) SHOWS THE STRUCTURAL ANALYSIS OF A 10X10 SHEET The initial documentation provided above (fig.1) shows the structural extracted to enable the bottom fabrication, (fig.4) which appears to TIMBER LAMINATE, WITH VARYING PERFORATIONS. TheOFinformation required to inform a CNClaminate, cutting machine isperforations. then analysis of a 10x10 sheet of timber with varying restrict the to bending ofthe thebottom material to the desired direction. FIGURE 2enable SHOWS AN INITIAL CURVATURE ANALYSIS extracted fabrication, (fig.4) which appears to
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Figure 2 shows an initial curvature analysis of a NURBS surface (fig.2)
OF Athe NURBS SURFACE (FIG.2) WHICH restrict bending of the material to theaGENERATES desired direction. which generates perforations using design script. (fig.3) But PERFORATIONS what happened to the additional information USING A DESIGNmaterial SCRIPT (FIG.3). THE from above? The information required to inform a CNC cutting machine is then INFORMATION REQUIRED TOofINFORM A CNC CUTTING ItBut seems some of tothe complexity thematerial initial analysis has been lost.to enable bottom fabrication, (fig.4) whichfrom appears whatextracted happened toEXTRACTED thethe additional information above? MACHINE IS THE TO ENABLE THE BOTTOM This tutorial sets up an initial definition which creates perforation restrict bending of the material the desired direction. It seems somethe of (FIG.4) the complexity of the to initial has been lost. FABRICATION, WHICH APPEARS TO analysis RESTRICT THE curves which are informed by surface curvature to get you started. This tutorial sets up an initial definition which creates perforation BENDING OF THE MATERIAL TO THE DESIRED DIRECTION.
But what thesurface additional materialtoinformation from above? curves which arehappened informedtoby curvature get you started. It seems some of the complexity of the initial analysis has been lost. This tutorial sets up an initial definition which creates perforation curves which are informed by surface curvature to get you started.
TUTORIAL - CURVATURE PERFORATION DAVID LISTER - 05072011 TUTORIAL - CURVATURE PERFORATION DAVID LISTER - 05072011
TUTORIAL--02 CURVATURE PERFORATION GH TUTORIAL PERFORATED CURVATURE LISTER DAVIDDAVID LISTER, JAS- 05072011 JOHNSTON - 28082011
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REFERENCE MATERIAL
Curvature As the name suggests, curvature is the amount of curve in a surface, or how much an object’s geometry deviates from being flat. Curvature is measured locally but often represented via a colour gradient (see icon, right) to show the differentiation of values across a surface. Concave and convex curvature values are often represented as positive and negative values.
principal and surface curvature icons within Grasshopper positive Gaussian curvature, ‘bowl-like’ surface
Curvature on surfaces Surfaces are defined by two directions in parametric space, often referred to as U and V directions. It is the combination of curvature in each of these directions at a point which defines the surface curvature. There are two forms of curvature you will come across in NURBS modelling and in these tutorials; mean curvature and Gaussian curvature. As the name suggests, mean curvature is the mean value of the two directional curvatures; one half the sum of the principal curvatures at a point. Surfaces with zero mean curvature across them are minimal surfaces. Gaussian curvature is the product of the two values. Therefore developable surfaces, otherwise called ruled surfaces,curve only in one isoparametric direction and have a Gaussian curvature of zero across their entirety.
negative Gaussian curvature, ‘saddle-like’ surface developable surface, zero Gaussian curvature
Further explanations of curvature: http://en.wikipedia.org/wiki/Principal_curvature Mean Curvature http://en.wikipedia.org/wiki/Mean_curvature Gaussian Curvature http://en.wikipedia.org/wiki/Gaussian_curvature GH TUTORIAL - 02 PERFORATED CURVATURE DAVID LISTER, JAS JOHNSTON - 28082011
*Gaussian curvature examples from Essential Mathematics for Computational Design