como modelar con shape modeling

8/18/2019 como modelar con shape modeling

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Modeling Tutorial

Autodesk Shape ModelingPlug-in for Rhino


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FOREWORD

Dear User,

This tutorial is a guide to using Autodesk ® Shape Modeling for Rhinoceros ®.

By the example of a beach buggy, the tutorial demonstrates a possible design process

from sketches to the actual 3D model. The Autodesk®

plug-ins allow you to embark uponadvanced surface modeling, aimed at creating top-quality surfaces with very simple sur-face descriptions.

You should already have gained some basic experience with Rhino ® and should have com-pleted the required installations of the Autodesk tools. These are available for download at:

http://www.autodesk.com/store/shape-modeling-plug-in-for-rhino

In this tutorial, we will use the plug-ins Autodesk ® Shape Modeling and Autodesk ® ShapeAnalysis. The required image data and Rhino les with the design data are supplied by usin addition. The Rhino data refer to the individual operations described in this tutorial.The corresponding les are indicated at the bottom right of the relevant tutorial pages.

The supplied data are not only meant as a means of assistance, but you will actually needthem to be able to begin with the tutorial. The image data provide sketches of the beachbuggy (previously created by us) in different views, based upon which the model will bedesigned. Generation of the image data was done outside of Rhino and will therefore notbe explained in this tutorial.

Provided that the above mentioned prerequisites are fullled, you can now begin withthe tutorial.

We hope you will enjoy working through it!


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The tutorial pages are subdivided into three columns. On the very left, you will nd theicon of the command you will be using in the described operation and the correspon-ding command name that you can enter directly in the command window. The middlesection shows screenshots illustrating the current task. On the right-hand side, you willnd explanations for the operations shown in the screenshots.

This tutorial is in English language and all commands and terms therefore refer to theEnglish version. A German version of this tutorial, providing the corresponding Germancommands and terms, is also available.

Overview and description of the symbols used in this tutorial:

_Command

On the left-hand side, thecommands you will be usingare displayed hierarchicallyby means of their icons,and the corresponding com-

mand name is given.

RMBRight mouse button

LMBLeft mouse button

Several clicks (point by point)Drag & drop with LMB

Translate

Click with RMB to open apull-down menu

In grey boxes you will nd additional information.

Copy Mirror

Click

Rotate about a point

These symbols mean thatyou have to press the Tab,Shift or Alt key or to keepthem pressed.

TIP

LEGEND


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CONTENTS

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Introduction ...........................................................................5Toolbars .........................................................................................6Settings ........................................................................................10Aligning the blueprints ..................................................................13

First surface ..........................................................................19Surface from curves .......................................................................21Surface analysis ............................................................................32Surface comparison .......................................................................37

Design of the other basic surfaces ..........................................39Surface creation .............................................................................40Surface transitions .........................................................................54

Surface cutting ......................................................................67

Surface modeling ..................................................................68

Global analysis ......................................................................84


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INTRODUCTION 1Until recently, high-quality class-A surfaces could be created only with costly specializedsoftware systems. With Autodesk ® Shape Modeling, Autodesk ® is bringing this technolo-gy into the Rhinoceros ® world. Due to the dialog- and handle-based functionalities, theuser can reach a new level of efficiency. A wide range of commands allows the surfacesto be analyzed and modied already during their creation.

Numerous functions of the Autodesk ® Shape Modeling plug-in include integrated analysistools, giving the user maximum control over the geometry under creation or modicationat any time. In addition to these integrated analyses, an arbitrary number of additionalanalyses from the ’Shape Analysis’ toolbar can be dened. These respond with full as-sociativity to any modication of the geometry, even before the command is actuallyterminated. The user can thus reach the desired shape with high-quality surfaces of loworder in a very short time.

In the following sections, we would rst like to introduce you to the toolbars of the Au-todesk plug-ins and then proceed to make some preparatory settings in Rhino ® and alignthe previously prepared sketches.

Toolbars

Settings

Aligning the blueprints


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TOOLBARS

Autodesk Shape Modeling

The ‘Autodesk Shape Modeling’ toolbar provides you with numerous functions for geometry creation

and modication. The below gure gives an overview of the toolbar that will be displayed as part of yourusual Rhino user interface, after you have installed this plug-in:

CONTROL POINT MODELING Modify single control points or control point rows/connectinglines of a curve or surface, optionally on reference geometry.

SMOOTHING Smooth a surface according to selected criteria.

ALIGN TO SYMMETRY PLANE Align objects with a selected symmetry plane.

CREATE SYMMETRY Create symmetry of the geometry.

PROJECTION Project points, curves, and surfaces onto target geometry with deviation control.

SUBMESH CREATION Separate individual polygon surfaces from a mesh.

SURFACE ON MESH Create a surface on top of a selected mesh.

SURFACE FROM POINTS Create a surface based on 4 selected points, optionally on referencegeometry.

SURFACE FROM CURVES Create a surface based on 2-4 edge curves, optionally with the inte-rior of the surface lying on reference geometry.

MULTI BLEND Create several single surfaces (with tangent or curvature continuous transitions)from a set of connected curves and/or surface edges.

SURFACES FROM CURVE NET Create several surfaces (with continuous transitions) from a netof curves.

SURFACE BLEND Create a blend surface between reference surfaces with a dened degree ofcontinuity (up to G 3).

FILLET SURFACE Create a llet surface between reference surfaces with a dened radius.

FLANGE Create a (planar) ange surface from a selected curve or surface edge in an arbitrarydirection.


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TOOLBARS

SURFACE MATCHING Match a surface to a reference surface or a reference curve (with continu-ity up to G 3 for surfaces).

SURFACE ALIGN Match a surface to up to 4 reference curves or surfaces at once.

SURFACE SPLIT Split a surface into 2 new surfaces using a trim curve or a reference surface.

SURFACE APPROXIMATION Re-approximate an existing reference surface by a new simple (single-span) surface.

EDGE APPROXIMATION Re-approximate and thereby simplify complex edges of trimmedsurfaces.

CURVE APPROXIMATION Re-approximate an existing reference curve or polygon by a newsimple curve.

SKETCH DYNAMIC CURVE Sketch curves dynamically, optionally on reference geometry.

SKETCH CURVE POINT BY POINT Sketch curves point by point.

CURVE BLEND Create a blend curve between reference curves or edges with a dened degreeof continuity (up to G 3).

CURVE MATCHING Match a curve to a reference curve or edge with a degree of continuity upto G3.

SHAPE OPTIONS Options for displaying the newly created or modied geometry in the Auto-desk modeling functions.


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TOOLBARS

Autodesk Shape Analysis

The Autodesk® Shape Analysis plug-in is an add-on to Rhino. It provides you with a variety of powerful

diagnostic tools aimed at making your everyday work more efficient:

ANALYSIS MANAGEMENT Open the dialog window that gives you access to all existing analy-sis instances.

SHOW/HIDE ANALYSIS Activate or inactivate the display of all dened analysis instances in thegraphics.

CURVE MATCHING ANALYSIS Measure the deviation in position, tangents, curvature, andcurvature ow between two selected curves.

SURFACE MATCHING ANALYSIS Measure the deviation in position, tangent planes, curvature,and curvature ow between two surfaces along their (common) surface edges.

GLOBAL MATCHING ANALYSIS Verify the quality of surface transitions for all surfaces of amodel (or for a selected subset).

DYNAMIC SECTIONS Cut a planar section through the selected surface by means of a dynami-cally controlled intersection plane; can be combined with clipping planes.

SECTIONS Create a dened number of planar sections using the selected plane.

DISTANCE ANALYSIS Determine the minimum distance between any two objects.

DEVIATION Determine the deviation between two selected geometry objects and display the

result graphically.

CURVATURE Analyze the curvature properties of surfaces and curves.

SHADED DEVIATION ANALYSIS Measure the deviation between two selected geometry objectsand visualize the result by a shaded display.

SHADED CURVATURE Visualize the curvature properties of the selected surface objects by ashaded display.


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TOOLBARS

LIGHT LINES Tool to visually analyze the quality of surface objects.

DRAFT ANGLE ANALYSIS Display the visible or demoldable areas of selected surface objects.

SCALE VIEW/RESET SCALE VIEW Scale the current viewport to maximize the active visiblearea and to get a detailed view by non-proportional scaling.


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SETTINGS

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Whether the Autodeskonline help should be dis-played in English or Germanlanguage can be selected inthe ‘Rhino Options‘ under‘Autodesk Shape Modeling‘.

To access the online help for the individual Autodesk commands, go to the Autodesk ‘Shape Modeling‘

menu and select the option ‘Online Help‘.

After you have started a command, youcan press the ‘F1’ key to get quick helpfor this command. Please note that com-mands going immediately into selectionmode when they are activated require anadditional click in the corresponding dialogwindow, before the link to the quick helpcan be correctly executed.


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SETTINGS

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1When starting Rhino, you are prompted to select the size and unit to be used for the current document.

For this tutorial, please select ‘small objects’ and ‘mm’. To make it easier to recognize the objects, wehave set the background to White. In the workspace, the Autodesk toolbars are always visible in theforeground. If you wish, you can change their position by simple drag & drop.

In order that the data we will create can be structured sys-tematically, we will rst prepare the layer structure. Createa layer named ‘Blueprint’ for the sketches, and the fol-lowing sub-layers: ‘Zero‘, ‘Blue_sideview‘, ‘Blue_topview‘,‘Blue_rearview‘, and ‘Blue_frontview‘. Set the layer ‘Zero’to red and lock it. This layer will serve as orientation duringthe next operations and must therefore not be moved.

In addition, create the layers ‘Auxiliary’ and ‘Middle’ andset these to green. These layers will be used sporadicallyto copy or create objects that are needed only temporarily.Since they may later be deleted, their color should differfrom that of the relevant objects. As a rst step towardsthe design of the beach buggy, the vehicle has to be sub-divided into its component parts. To this end, create thelayer ‘Autodesk’ with the sub-layers ‘Side‘, ’Rear‘, ‘Front‘,‘Floor‘, and ’Cover‘.

TIP It is part of our work method to always keep the dialog windows ‘Planes’ and ‘Properties’ openat the right edge of the screen. This enables quick access to the objects and an overview of their statusat any time.

_Properties

_Layer


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SETTINGS

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1To facilitate the orientation, dene the ori-

gin by using the ‘Point’ command.

Type the gure 0 into the Rhino commandprompt.

By doing so, you dene a point at the ori-gin of the coordinate system. This pointwill later serve as reference for the buggy’sfront axle.

To move this point to the layer ‘Zero’, markthe point and change its layer in the ‘Prop-erties’ window.

Open the pull-down list for the object type‘Layer’ and select the layer ‘Zero’.

_Properties

Rhinodatei:8.2 Hanomag.3dmRhino le: 1.1_settings.3dm


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ALIGNING THE BLUEPRINTS

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We will base the design of the beach buggy on so-called blueprints in the form of bitmaps. These sketch-

es, created according to the principle of normal projection in the three principal directions, display whitelines on blue background. These colors offer the best contrast. Black curves, for example, can be betterdistinguished on this background.

Select the layer ‘Blue_sideview’ as activelayer. Then execute the ‘PictureFrame’ com-mand in the viewport ‘Right’. This will opena dialog prompting you to select a le tobe opened. Select the bitmap named ‘side-view.png’.

Rhino subsequently prompts you to denea start point for positioning the picture.This point should be the previously denedorigin. Conrm this by entering the gure 0.

In the next step, Rhino prompts you to de-ne the length of the picture frame. Enter972 mm and conrm by pressing the Returnkey.

_PictureFrame


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A rectangle representing the dimensions of

the selected picture is now displayed in theviewport. Press the Shift key to align it or-thogonally. Once you have positioned therectangle on the red x-axis of the coordi-nate system, conrm with the LMB.

The blueprint ‘sideview.png’ has now beeninserted.

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TIP You may nd the Tab key useful within the commands ‘Translate’, ‘Copy’, ‘Rotate’ etc. If you

press the Tab key while you move the cursor in one direction or snap to a point, this will activate the‘Direction Lock’ mode. This means that the current direction is maintained and you only have to denethe length – either numerically via ‘Object Snap’ or simply with the LMB. By pressing the Tab key oncewhile keeping the Shift key pressed you can insert the picture with orthogonal alignment. To inactivatethe ‘Direction Lock’ mode, simply press the Tab key again.

In the viewport ‘Perspective’ you can see the bitmap in its orthogonal position.



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_Move

To exactly align the blueprint, change to

the right viewport and zoom in the buggy’sfront wheel. Activate the ‘Move’ commandand select the bitmap surface. Conrm bypressing the Return key.

Rhino then prompts you to select the startpoint. Click on the center of the crosshairsto select it. Then dene the new positionby entering the gure 0 into the commandprompt and conrming the entry.

The axle of the beach buggy optically nowcoincides with the red origin and will serveas reference for positioning the other bit-maps.

Repeat the bitmap positioning procedurewith the ‘PictureFrame’ command for theblueprint ‘topview.png‘ using ‘Blue_top-view‘ as active layer. For this operation, ac-tivate in addition the check box ‘End’ under‘Object Snap’.

The viewport suited best for this operationis ‘Perspective‘, which you should rst ad-

just to a view angle as shown in the gureon the left. As start point for the pictureframe, snap the ‘End’ point at the front(right) of the blueprint (1.). For the secondvalue (length), snap at the rear ‘End’ (2.).

_PictureFrame2.

1.



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TIP If need be, you can suppress the active ‘Object Snap’ settings by keeping the Alt key pressedduring the operation.

_Move

_Move

In the next step, move the blueprint ‘side-view.png’ to the end points of the blueprint‘topview.png’. To do so, snap the ‘End’ pointat the corner of the ‘sideview.png’ bitmap(corresponding to the ‘Mid’ point of the ‘top-view.png’ surface) to the ‘End’ of the ‘top-view.png’ bitmap.

The red origin is now located at the height ofthe axle and in the buggy’s symmetry plane.

Stay in the viewport ‘Perspective’ and posi-

tion the middle of the buggy on the originby moving the blueprint ‘topview.png‘.

The right settings under ‘Object Snap’ areimportant for this operation. Activate thecheck boxes ‘Mid’ and ‘End‘. Using the‘Move’ command, then translate the blue-print ‘topview.png’ from the ‘Mid’ to the‘End’ position, as shown in the gure.



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_PictureFrame

To position the next bitmap ‘frontview.png’, change to the layer ‘Blue_

frontview’. As start point, snap to the corner of the previously alignedsketches in the viewport ‘Perspective’, as shown in the gure.

In an intermediate operation, redene the viewport ‘Back’ as ‘Front’ usingthe RMB.

To snap the endpoint, activate ‘Project’ and ‘Planar’ in the second stepand snap to the right ‘End’ point in the viewport ‘Front‘ (lower left in themiddle gure).

For the blueprint ‘rearview.png’ repeat theabove described procedure at the opposi-te edge of the layer. Position the rst ‘End’point in the viewport ‘Perspective‘ and thenchange to the viewport ‘Front’ to positionthe second ‘End’ point. You should inacti-vate ‘Project’ and ‘Planar’ before you do soand change to the layer ‘Blue_rearview’ forthis bitmap, to maintain a proper data struc-ture within the document.



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TIP At rst sight, the blueprints ‘frontview.png’ and ‘rearview.png’ do not correspond to the namesof the corresponding viewports. With the normal projections we performed to create the sketches,however, the sketch of the buggy’s front is at the rear and vice versa. At second sight, you will quicklyrealize that this makes your work more comfortable. Take a look, for example, at the viewport ‘Front‘:Switch off the layer ‘Blue_rearview’ and you can then work on the sketch ‘frontview.png‘.

If the bitmaps were not switched, you would be operating behind the blueprint in this case or you

would have to change to the viewport ‘Back’. To work on the blueprint with the rear view and alignobjects to it, switch off the layer ‘Blue_frontview‘ and work in the viewport ‘Back‘ in front of the blue-print. We will repeatedly point this out to you in the course of the tutorial.

For the subsequent operations, it is helpful to make the inserted blueprints transparent. To do so, select

one bitmap at a time and go to the ‘Material’ tab under ‘Properties’. Under ‘Basic Settings’ change the‘Transparency’ value to 60 percent, as shown in the below gure. The easiest way to do this is to placethe mouse cursor on the slider and scroll the mouse wheel to adjust the value.



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In this chapter, we will be using the Autodesk ® tools for the rst time. We will start with the alignedblueprints and adjust some more settings so as to facilitate our work.

FIRST SURFACE 2_Options

To improve visibility, go to the ‘Rhino Op-tions’, select the menu item ‘Grid’ and in-

activate the display of grid lines and axes.Conrm this change by clicking on ‘Ok’.

To avoid any unintentional changes duringthe subsequent operations, lock the layerscontaining the blueprints. In the following,you will be working on the layers for thedesign of surfaces, starting on the sub-layer‘Side’.

TIP The display of grid lines and axes can be activated and inactivated directly by pressing the functionkey F7 in the active viewport.


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FIRST SURFACE

_SplitViewportVertical

For a better overview, add another viewport to the layout. To do so, select the viewport ‘Front’ and exe-

cute the command ‘SplitViewportVertical’.

Dene one of the two resulting front views as ‘Back’.

Rhino le: 2.1_preparations.3dm


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SURFACE FROM CURVESThe following operations are performed in

the viewport ‘Right’. Activate the Autodeskfunction ‘Sketch Curve Point by Point’ byclicking with the RMB on the commandicon and dene single points on the uppercontour of the buggy by means of LMBclicks.

In the sketching mode using the LMB, de-ne the points through which the desiredcurve is to be approximated. We recom-mend that you use a maximum degree of4. To this end, set the ‘Max. Degree’ in thedialog to this value. Once you have clickedon all points to be used, press the Returnkey or the RMB to nish the curve. Aftercompletion of a curve, the sketching moderemains active. You could thus create an-other new curve now by pressing the LMBagain.

TIP By means of the ‘Autodesk Shape Options’ you can dene how you want geometry elements tobe displayed while you create or modify them with the Autodesk ® Shape Modeling commands. Fur-thermore, you can dene the selection status of these elements. If the option ‘Select Results‘ is active,the geometry just created or modied will remain selected after you have terminated the function with‘Ok’.

_ADSketch

_ADShapeOptions


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1

SURFACE FROM CURVESThe Autodesk command ‘Curvature Analy-

sis’ provides you with a tool to quickly andintuitively visualize the curvature propertiesof curves and surfaces.

The system prompts you to select the objects to be included in the curvature analy-sis. You can select an arbitrary number ofcurve and surface objects. Terminate theselection by pressing the Return key. If thecurve was preselected through the ‘SelectResults’ option, it is already included in theselection set and you can start directly withthe analysis.

This parameter allows you to dene thenumber of points (per isocurve of a surfaceor per curve) for which curvature values areto be computed and displayed.

Changing the scaling factor will inuencethe height of the resulting curvature graph.

A click on the ‘Adjust Scale’ button will optimize the scaling factor to enhance visibility of the graph. Thescaling factor for the curvature graph is often quite high for at objects like our curve here. The smallerthe curvature, the higher the scaling factor.

_ADCurvatureAnalysis


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SURFACE FROM CURVES

The below gure shows the effect of the control point modication on the curvature graph.

In parallel with the analysis, activate the

function ‘Control Point Modeling’. This toolallows you to quickly and easily modify sin-gle control points or control point rows ofsurfaces and curves.

_ADModeling

In the dialog window that will be opened,the selection button marked in blueprompts you to select the objects to bemodied.

Under ‘Mode’ you can change the desiredmodeling mode for the current controlpoint modication. Since we only want tomove single control points, we stay withthe option ‘Single’ here.

The selected curve is displayed in dark blueand the control points as light grey spheres.If you move the cursor near the controlpoints that can be modied, they turnyellow, indicating their selection. You canmove the points by drag & drop and willimmediately see the resulting changes inthe graph. The currently selected controlpoint is displayed in red.

TIP A smooth curvature ow is an indicator of a well-designed curve.


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SURFACE FROM CURVES

The modeling steps you performed in the‘Control Point Modeling’ command can beundone and redone one by one by meansof the arrow buttons. Once you have ter-minated the command by clicking on ‘Ok’,a single Rhino ‘Undo’ will undo all modi-cations made in the ‘Control Point Model-ing’ function.

In single-span curves and surfaces, the

number of control points equals the degree+ 1.

The aim of the control point modeling is to achieve a smooth curvature ow, as displayed in the below

gure._ADCurvatureAnalysis

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_ADModeling

To move the curve with all its control pointsto the outer contour of the sketch in thetop view, set the ‘Mode’ to ‘All’.

In addition, restrict the moving directionby locking the Y- and Z-directions, so thatthe selected points can be moved only inX-direction. To do so, activate the checkboxes ‘Y’ and ‘Z’. These control point coor-dinates will then remain unchanged duringthe modeling.


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SURFACE FROM CURVESTo adjust the curve to the contour, change

the ‘Mode’ back to ‘Single’ and move thepoints individually in X-direction.

As soon as the curve coincides with thecontour and the curvature ow is smooth,terminate the dialog by clicking on ‘Ok‘.

Since the curvature analysis is associative,changes in the curve lead to an immediate,automatic recalculation of the curvaturedata. The display of the curvature proper-ties is thus always up-to-date, and you cansee at once how the modications youmake affect the curvature of the modelcomponents. Even after you have conrmedand quit the dialog of the analysis by click-ing on ‘Ok’, all modications you make tothe object will continue to be analyzed inthe background.

TIP Double-clicking on the handle ‘Curvature_1’ will reopen the dialog of the analysis, allowing youto modify its settings. In addition, the handle can be freely moved by drag & drop.


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SURFACE FROM CURVES

_ADAnalysisManager

The ‘Analysis Management’ tool gives youdirect access to all commands of the Au-

todesk®

Shape Analysis plug-in. Via thecorresponding dialog, you can create newanalyses and modify, rename, activate/ inactivate, and delete existing analysis in-stances. In addition, you can control thevisibility of the handles.

The ‘Analysis Management’ tool can beactivated via the Autodesk toolbar or by aclick with the RMB on a handle and subse-quent selection in the context menu.

TIP A click with the RMB on the ‘Curvature Analysis’ command in the Autodesk toolbar can be used toactivate or inactivate the display of all analyses of this type. This quick command is available for almostall Autodesk analysis tools._ADCurvature

Analysis

Rhino le: 2.2_rst_curve.3dm


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SURFACE FROM CURVES

_ADModeling

_ADSketch

To move the created curve to the positionwhere the buggy has its maximum opticalwidth, change to the viewport ‘Top’.

Activate the Autodesk function ‘ControlPoint Modeling’ and lock the X- and Z-di-rections this time.

Select the mode ‘All’ to reposition the wholecurve.

As an additional aid for this operation, ac-tivate the option ‘Quadrant’ under ‘ObjectSnap’ and move the curve to the outermostposition of the previously used contour.

Change to the viewport ‘Front’ and blank

the layer ‘Blue_frontview’ to improve visi-bility.

Sketch the relatively straight part of thebuggy’s right lateral contour on the bit-map ‘rearview.png’. To do so, activate theAutodesk function ‘Sketch Curve Point byPoint’ with the RMB. Alternatively, you canuse the LMB here to activate the Autodeskfunction ‘Sketch Dynamic Curve’ and drawthe curve while keeping the LMB pressed.

TIP To make sure the subsequent design of surfaces based on this curve does not become unneces-sarily complex, the sketching operation should generate as few control points as possible. To this end,enter the value 3 as ‘Max. Degree’ in the Autodesk dialog ‘Sketch Curve Point by Point’.

TIP When you use the Autodesk functions, the ‘Object Snap’ should generally be inactive, unlessstated differently in this tutorial. Otherwise, your operations in 2-D can easily lead to unintentional

snapping, and the curve or surface thus created will then not be as you wanted it.


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SURFACE FROM CURVES

_ADModeling

Change again to the viewport ‘Front’,

blank the layer ‘Blue_rearview’ and displaythe layer ‘Blue_frontview’. Sketch the innercontour of the buggy as shown in the g-ure.

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_ADSketch

If you activate the mode ‘Extrapolate’, youcan move the outer control point to extendor shorten the curve without adding anyadditional control points or control pointrows.

The geometry of the rest of the curve willremain unchanged during this operation.The control points will be redistributed pro-portionally, keeping the curve in its originalposition.

Use the ‘Control Point Modeling’ com-mand to move the individual points such

that the curve coincides with the contourin the blueprint.

If the option ‘Mouse Move Scale’ is active,the control points will not be moved 1:1with your mouse movements. Instead, themodication is scaled down according toa user-dened factor, so that very smallchanges are also possible. The range ofvalid values for this factor is from 1 (corre-sponding to the option being inactive) to

50 (extremely small control point modica-tions).

TIP The degree of the selected object can also be modied directly in the graphics. To do so, movethe mouse cursor onto the selected curve or an edge of the selected surface and press a number keybetween 1 and 9 on your keyboard. The selected object will directly adopt the degree thus specied.


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SURFACE FROM CURVES1

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TIP Instead of copying objects via the command ‘InPlace’, you can also use the keyboard shortcutsCtrl+C followed by Ctrl+V.

_Copy

_SetPt

To design the buggy’s lateral surface you

need yet another curve, which we willplace at the bottom. Select the upper curveand copy it ‘InPlace’.

Select the command ‘Set Points’ and ac-tivate the check box ‘Set Z’ in the dialogthat will be opened. Conrm by clicking on‘Ok’. In the command prompt, you will beprompted to indicate the desired position.Select this position in the side view. Movethe cursor to the height of the buggy’slower edge. The system then projects thecurve points onto this plane.

_Rotate

Select the command ‘Rotate’ in the side view and rotate the previously copied curve such that it coincideswith the lower contour of the buggy.


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_Move

Change viewports again, and in the view-

port ‘Front’ align the curve with the hori-zontal curve using the ‘Move’ command.

Then change to the viewport ‘Perspective’and move the curve at the front to a posi-

tion next to the horizontal curves. Use the‘Control Point Modeling’ command for thisoperation and activate ‘All’, ‘Y’, and ‘Z’, sothat the points can be moved only in X-direction.

_ADModeling

Rhino le: 2.3_four_curves.3dm


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_ADModeling

_ADSurfaceFromCurves

Activate the ‘Control Point Modeling’ com-mand to extend the created surface alongthe side of the buggy.

If you activate the mode ‘Extrapolate’, thesurface will be extrapolated at the end youpick. When using this mode, the shape

of the selected geometry will remain un-changed, it will merely be extended orshortened. Since the moving directionof the control points is predened in thismode, any other activated ‘Constraints’will be ignored.

Extend the surface to match the buggy’sside by moving the control points in the di-rection of the arrows over the front, rear,and top view blueprints.

You have now dened and positioned all

curves required to create the rst surface,so that you may proceed to generate thesurface with the command ‘Surface fromCurves’.

Start by selecting the four edge curves ofthe surface. If the curves do not intersect,you can use the option ‘Curve IntersectionTolerance’ to compute intersection pointsof the curves. If you select at least threecurves to create a surface with this func-tion, these have to intersect within the tol-erance dened in this option. Increase thevalue to 10 and conrm your entry by click-ing on ’Ok’.


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SURFACE ANALYSIS

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You can use the analysis tool ‘Light Lines’ to visually inspect the quality of the generated surface. Similar

to traditional lighting methods, the different light intensities of the individual surface points here dependon the corresponding surface (or mesh) normal direction and the direction of the incident light. Thedifference is that surface material denitions are ignored here and only the resulting light intensities aredisplayed. This results in lines of surface points with identical or similar light intensities.

The result and the smoothness of the boundaries between colors in addition depend on the settings con-trolling the resolution of the polygon meshes. You can change these in the ‘Rhino Options’ under ‘Mesh’.

To enable a uniform/smooth display at a later time point, select ‘Custom’ and set the ‘Maximum angle’and ‘Maximum edge length’ to 3 and all other options to 0.

The different parameters that can be set in this context are explained in more detail in the Autodesk ® Realtime Renderer tutorial.

_Options


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SURFACE ANALYSIS1

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Start by blanking the layer ‘Blueprint’ andactivate the ‘Light Lines’ command. Theanalysis automatically includes all currentlyvisible surfaces and meshes of your model.

The direction vector of the incident lightcan be changed dynamically. To do so,place the cursor on the manipulator (‘LightSource’) and move it to the desired posi-tion and direction while keeping the LMBpressed.

The check box ‘Enable’ allows you to tog-gle the display of the ‘Light Lines’ analysis

on a temporary basis. In the input eld ‘Cy-cles’ you can dene the number of light orcolor cycles to be displayed.

The position of the ‘Light Source’ can alsobe dened directly by entering its coordi-nates at the bottom of the dialog.

Via the ‘Color Options’ you can inuencethe visualization of the analysis. You canchoose between the modes ‘Light’, ‘Col-ored’, and ‘Black&White’.

If you activate the check box ‘Transparent’,the result of the analysis is displayed in atransparent manner on top of the regularRhino object color, which remains visible atthe same time.

_ADLightLines


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SURFACE ANALYSIS1

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The analysis tool ‘Shaded Curvature Anal-

ysis’ provides you with a tool that enablesquick and intuitive visualization of the cur-vature properties of surfaces.

The parameter ‘Mode’ allows you to selectthe type of curvature data to be analyzed.Set this parameter to ‘Gaussian’ and verifythe curvature of the created surface, whichwill be displayed in false color. By meansof two numeric values you can control theassignment of colors in the shaded displayto the computed curvature values.

The ‘Mesh Quality’ slider under ‘Mesh Op-tions’ allows you to increase or reduce themesh quality, enabling more detailed anal-yses.

Other types of analyses such as the cur-

vature of the ‘Minimal Radius’ or the cur-vature in ‘Y direction’ can be selected in thepull-down menu ‘Type’ of this dialog.

_ADShadedCurvatureAnalysis


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SURFACE ANALYSIS1

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Under ‘Options’ you can activate the visu-alization of the radius values computed inthe sections.

You can choose between isocurves withconstant U-parameter and/or isocurveswith constant V-parameter or activate bothdirections.

If you click on the button ‘Adjust Scale’, thesystem will determine a new scaling factorthat depends on the maximum curvaturevalue or curvature radius computed. Thisvalue will be displayed in the ‘Scaling Fac-tor’ eld and will be immediately applied,resulting in an instant update of the graph-ics display.

The gure shows a curvature course thatis not yet optimal in vertical direction. Ac-tivate the ‘Control Point Modeling’ com-mand to optimize it.

Curvature analyses by means of graphs are

not unknown to Rhino users. The Autodesktool ‘Curvature Analysis’ enhances the dis-play options and in addition visualizes thecourse of the radius.



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SURFACE ANALYSIS1

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In the ‘Control Point Modeling’ dialog, ac-

tivate ‘Single’ and ‘Tangent’ and move thecontrol points so as to improve the cur-vature course. Modeling the inner controlpoint rows will yield the most effective re-sults in this case.

By activating the ‘Blend’ option, you canallow the modications you make to theposition of a control point or control pointrow to be applied also to the adjacent con-trol points/control point rows according tothe selected blend law.

Try to achieve a harmonious and uniformdistribution of the control points.

_ADModeling



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Activate the Rhino command ‘NetworkSrf’

(Surface from Curve Network) and use theexisting curves to create a surface that canthen be used for comparison.

In the ‘Surface from Curve Network’ dialogset the ‘Edge curves’ tolerance to 0.001.

To enable a proper comparison, extrapolatethe surface. Specify an extension factor of30 mm for the lower edge curve and of300 mm for the lateral edge curves.

_NetworkSrf

_ExtendSrf


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SURFACE COMPARISON1

_PointsOn

TIP The command ‘PointsOn’ allowsyou to display the control points of thesurface. Visually, the surface is of goodquality, however, because of the largenumber of control points it cannot befurther modeled.

TIP The side-by-side comparison clearlyshows the reduced number of controlpoints of the Autodesk surface, whichprovides the basis for class-A modeling.

Rhino le: 2.4_comparison.3dm

Create a layer ‘Side_curves’ as a sub-layer of ‘Side’ and set this sub-layer for auxiliary elements to green.Then move the curves to this sub-layer.

Since the other surfaces of the buggy will also be created from curves, you can add already now therequired sub-layers for the rear, front, cover, and oor.

The Rhino surface we created for comparison can subsequently be moved to the corresponding auxiliarylayer or deleted.


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In this chapter, we will add the missing surfaces to complete the basic structure of our beach buggymodel. Both Autodesk ® and Rhino ® tools will be used for this in a complementary manner.

Surface creation

Surface transitions

DESIGN OF THE OTHER BASICSURFACES 3


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1

2Since the curve is not yet symmetric, usethe Autodesk ‘Symmetry’ command nowto create symmetry. Click on the icon withthe RMB to open the dialog of the ‘Sym-metry’ command. Select the rear curve andactivate ‘X’ as constant of the ‘SymmetryPlane’.

The option ‘Average around Plane’ will re-sult in the curve to be averaged betweenthe existing control points. The option‘Master/Slave around Plane’ will use theside indicated by the yellow vector in the

graphics as reference and will adapt theother side accordingly to create symmetry.

Assuming that none of both sides of thecurve coincides much better with the rearcontour than the other side, use the option‘Average around Plane’, which will modifyall control points to create symmetry, whilekeeping the modications to a minimum.Click on ‘Apply’ to conrm your settings.

The control points will then be arrangedsymmetrically with the x = 0 plane. To ter-minate the function, click on ‘Ok’.

Activate the layer ‘Blueprint’, the sub-layer

‘Rear’, and inactivate the sub-layer ‘Side’.Then go to the viewport ‘Top’ to start de-signing the rear of the vehicle.

Use the Autodesk curve sketcher (mode‘Dynamic’ or ‘Point by Point’) to draw acurve with Degree = 3 on top of the rearcontour. Here again, the dened curve canbe longer than the contour in the sketch.The aim of this operation is to create a sym-metric curve that can subsequently be usedto dene the rear surface.

If necessary, modify the curve with the‘Control Point Modeling’ command, so thatit matches the rear contour in the blueprintas accurately as possible.

_ADSymmetry

SURFACE CREATION

_ADModeling

_ADSketch


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_Move

_Rotate

_Copy

Hide the curve control points again by pres-sing the Escape key, change to the view-port ‘Right’, and activate the command‘Rotate’. Snap the center of rotation to thecurve endpoint and rotate the curve untilthe angle matches the one in the blueprint.

Deactivate the layer ‘Blue_frontview’ andactivate ‘Blue_rearview’. Move the curve tothe upper edge of the buggy in the view-port ‘Back’. This change will make it obvi-ous that the curve is still planar. To adjustit to the upper contour of the buggy, pressF10 to display the curve control points, se-

lect the two outer control points and movethem symmetrically a little bit in upward di-rection while keeping the Shift key pressed,thereby creating the desired symmetric arc.

Verify the created curve using the Auto-

desk ‘Curvature Analysis’ command.

Click on the button ‘Adjust Scale’ to adjustthe display of the curvature graph. If youwish to adjust the scaling according to yourindividual requirements, change the scalingfactor manually.

The analyses are numbered chronologically.You can dene an individual name for theanalysis instance, under which the ‘AnalysisManagement’ will know the current anal-ysis tool. This name is also displayed in asynchronized manner in the handle of theanalysis.

Change to the top view, copy the curve,and move the copy onto the rear contourof the buggy.


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_Move


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_Copy

_Rotate

_Move

_Move

_PointsOn

_Move

Copy the curve in the viewport ‘Right’ andmove the copy to the lower edge of the carbody. Use the Rhino command ‘Rotate’ to

adjust the curve to the lower contour.

Change to the side view and move the

copied curve in downward direction to theheight of the sharp bend.

Adjust the curve in the viewport ‘Back’,with the layer ‘Blue_rearview’ being visible.

Using the Autodesk command ‘Sketch CurvePoint by Point’ with a ‘Max. Degree’ of 3,sketch a curve between the upper edge ofthe buggy and the sharp bend. Again, thecurve can be longer than that in the sketch.

If need be, subsequently modify the con-trol points until the curvature graph looksregular.

During the next operations, you will needthis curve to be at the ends of the horizon-tal lines. Therefore, move the curve youhave just created onto the short curve, asshown in the gure.


_ADSketch

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_Mirror

_Mirror

Change to the viewport ‘Top’ and move

the curve from the middle to the right edgeof the buggy. At the new position, rotate itin outward direction so that it will coincidewith the (shorter) curve in the blueprint,and then mirror it about the middle.

Change viewports again and create thenext curve at the bottom rear of the buggyin the side view.

Again use the command ‘Sketch CurvePoint by Point’ with a ‘Max. Degree’ of 3and evaluate the curvature graph using the‘Curvature Analysis’. Then move the curveroughly to the height where the middlecurves intersect.

As described above, move this curve as well to the outer edge, rotate it, and mirror it about the middle.

_Rotate

_Rotate

_Move

_Move

_Move

_ADCurvature Analysis

_ADSketch

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TIP We mostly use the command ‘Mirror’ about the middle, since the middle corresponds to the zeroplane of the coordinate system. To save a few clicks, enter the gure 0 with the ‘Mirror’ command,keep the Shift key pressed, and click anywhere near the mirror plane to conrm.

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Having installed the Autodesk plug-ins, you

have at your disposal a new display option:‘Autodesk Shape Display‘. Its predenedsettings provide a high-contrast and uni-form display for the work on your model.

Activate the Autodesk command ‘Surfacefrom Curves’ and select the upper fourcurves to begin with. Like you did for theside surface of the buggy, create a surfacealso between these four curves.

In the ‘Autodesk Shape Options’ dialog youcan inuence the display of the geome-try elements created or modied with theAutodesk® Shape Modeling commands.These display options override the activeRhino display options for the current dis-play mode (Grid, Shaded, Autodesk Real-time Renderer etc.), however, they will notbecome effective until you have completedthe selection.


_ADShapeOptions

Rhino le: 3.1_rear_curves.3dm

SURFACE CREATION


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Repeat the surface creation procedure

using the lower four curves. You have nowcreated two surfaces that are not connect-ed.

Move the curves to the sub-layer ‘Rear_curves’and subsequently blank them.

The ‘Surface Matching’ command can beused to connect the two surfaces with adened degree of continuity at the transi-tion (e.g. position continuity).

As soon as you activate the command, theselection becomes active. Only natural, un-trimmed surfaces can be selected as sur-faces to be matched. Select the lower edgeof the upper surface. The selection will thenautomatically try to nd the best referenceand select it. If no reference can be identi-ed automatically, you will be prompted toselect one manually. Should you have unin-tentionally selected a wrong surface edge,you can re-initiate the selection at any timeby clicking on the button ‘Matching Edge’.


_ADSurfaceMatching

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Rhino le: 3.2_rear_surfaces.3dm

SURFACE CREATION

Set the desired degree of continuity to ‘Position (G 0)’. Given the very small distance between the twosurfaces, we can leave the other settings unchanged.

The option ‘Minimize Changes’ tries to keep control point changes in the surface to be matched to aminimum.

The option ‘Keep Opposite Edge’ allows you to restrict changes in the control point rows at the oppositeedge of the surface to be matched, so as to preserve the quality of an existing transition at that edge.

The ‘Analysis’ section of the Surface Matching dialog offers two integrated analyses. With ‘Matching’you can visualize in the graphics the transition quality achieved with the current settings. The displayedvalues will normally refer to the selected degree of ‘Continuity’.

If the option ‘Deviation’ is active, the deviation of the matched surface from the input surface will be dis-played. The dialog that will be opened if you click on ‘Options’ allows you to dene different parametersfor this analysis, such as the number of points, the number of graphs, and the scaling. Click on ‘Apply’;the deviation in position should now be 0.

Eventually conrm your input by clicking on ‘Ok’.


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_PointsOn

_Move

_Copy

_Move

_Rotate

To create the front surface, change to

the viewport ‘Top’, activate the sub-layer‘Front’ and inactivate the layer ‘Rear’.

Using once again the ‘Sketch Curve’ com-mand, draw a curve of degree 3 and, ifneed be, adjust its shape with the ‘ControlPoint Modeling’ command. Then createsymmetry, like you did at the rear.

Change to the side view and move the curvein Y-direction to the desired contour posi-

tion. Rotate it until it is at the right angle.Proceed by creating an orthogonal curvecorresponding to the front contour ofthe buggy. Use the middle contour in thesketch as orientation, as shown in the g-ure. Sketch the curve with the AutodeskSketcher, making sure the control pointsare uniformly distributed. To achieve this,dene the curve by picking three pointsand set the ‘Max. Degree’ to 2.

In the ‘Front’ viewport, move the curveonto the upper contour and adjust the con-trol points symmetrically so as to create aslight arc. The layer ‘Blue_rearview’ shouldbe active and the layer ‘Blue_frontview’ in-active during this operation.

Now invert the visibility of the layers byinactivating ‘Blue_rearview’ and activating‘Blue_frontview’. Copy the curve you justcreated and position it at the height of thebuggy’s lower edge.

_ADSketch

SURFACE CREATION

_ADSketch

_ADSymmetry

_ADModeling


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Rhino le: 3.3_front.3dm

_Mirror

_DupEdge

_Sweep2

Use the ‘Duplicate Edge’ command to ex-tract the outer edge from this auxiliary sur-face and subsequently discard the auxiliarysurface.

Using the ‘Autodesk Curvature Analysis’command you can compare the cross sec-tion curve with the extracted curve.

The newly created curve is dened by onlythree control points. This is benecial forcreating high-quality surfaces. Mirror thecurve about the middle to get the fourthcurve that is required to create the buggy’sfront surface.

Use the ‘Surface from Curves’ command toeventually create the front surface. The gen-erated auxiliary curves can then be trans-ferred to the sublayer ‘Front_curves’.

An alternative that you can use in the sur-

face design process is the ‘Sweep2’ (sweepsurface using two rails) command. The hor-izontal curves serve as rails and the ortho-gonal curve is used as cross section curve.

Make sure the sweep surface is not createdwith a simplied cross section curve. There-fore, activate the option ‘Do not simplify’ inthe dialog.



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_Mirror

_Mirror

_CopyToLayer

_CopyToLayer

To create the cover surface, copy the up-

per curves from the layers ‘Rear_curves’,‘Front_curves’, and ‘Side_curves’ to thelayer ‘Cover’. In addition, select the latteras active layer.

Mirror the side curve about the middle. Younow have four curves that you can use tocreate the cover surface.

Create once more a surface from four curveswith the ‘Surface from Curves’ command.The resulting surface represents the coversurface.

Transfer the auxiliary curves to the layer‘Cover_curves’.

Repeat this procedure for the oor surface.To do so, change to the sub-layer ‘Floor’,inactivate the layer ‘Cover’, and copy thelower curves from the layers ‘Rear_curves’,‘Front_curves’, and ‘Side_curves’ to thelayer ‘Floor’. Again, the side curve has tobe mirrored about the middle to obtain thefourth curve for surface creation.

Create another surface with the command‘Surface From Curves’. The resulting sur-face represents the oor surface. Again,transfer the auxiliary curves to the corre-sponding sub-layer, once you have createdthe surface.



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A look at the layer structure shows that we

have created an additional sub-layer withthe suffix ‘_curves’ for each componentpart of the buggy.

For a better data structure, the curves re-quired to design the surfaces of the bug-gy chassis are led in corresponding sub-layers.

In addition, create a new layer with thename ‘Chassis’. Then copy all created sur-faces to this layer. Activate the layer ‘Chas-sis’ and blank all other layers.

In the following, we will thus only workwith the surface copies, avoiding the risk ofmodifying the generated original surfaces.

The gure to the left shows the active layer‘Chassis’.

Mirror the side surface about the middleto complete the basic constituents of thechassis.

This gives you a rst three-dimensional im-pression of the buggy.

_CopyToLayer

_Mirror

Rhino le: 3.4_corpus.3dm

SURFACE CREATION


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_Mirror

_SrfPt

Mirror the remaining half about the middleand use the ‘Shaded Curvature Analysis’to verify whether there are any symmetry

errors. A smooth color ow in the analysisshows that the transition area includes noirritations.

You could also use the ‘Autodesk Light Lines’for this verication.

To make sure the surfaces have been creat-

ed symmetrically and no mistakes havecrept in, create a surface in the middle tosplit the data set at the zero plane. Use theAutodesk ‘Split’ command for this. The ad-vantage of this approach is that the edgecurve will be reapproximated, resulting ina new, untrimmed surface. The use of un-trimmed surfaces can help avoid the prob-lems that are frequently encountered withtrimmed surfaces.

Activating the command will open the cor-responding dialog. Select the intersectingelement as ‘Limitation’, that is, the surface

just created at the zero plane. Then selectthe surface to be trimmed, for example, thecover surface. Clicking on ‘Apply’ will ac-tivate the preview, including indication ofany deviation of the new edge curve. Thesurface descriptions here are so simple thata ‘Max. Degree’ of 3 is sufficient. Set the‘Max. Split Curve Deviation’ value to 0.001

to assure a minimum deviation within thedened tolerance. Terminate the dialog byclicking on ‘Ok’. Repeat this operation withall other surfaces crossing the middle.

Discard one half of the buggy and the in-tersection plane as well.

_ADSurfaceSplit


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Activate the display of all previously de-

ned analyses by pressing the RMB and se-lecting the corresponding command. Notethat analyses on inactivated planes will notbe visible.

You can click on the handles with the RMBto delete the corresponding analyses ordouble-click on a handle to see the param-eters of this analysis. Delete all existinganalyses except those of the cover and sidesurfaces. All existing analyses can then beinactivated with the LMB.

You can subsequently delete the mirroredsurfaces again. They were created only toverify symmetry.

We will now start designing the fender.Blank all objects and continue to work onthe layer ‘Chassis’.

Activate the Autodesk Curve Sketcher andset the ‘Max. Degree’ to 5.

In the top view, move the curve created lastto the front of the buggy. Then dene therear curve of the fender.

First sketch the two curves in the side view.Then change to the front view and movethe curves to the right positions: the shortercurve to the inside and the longer curve tothe outside of the fender.

In a further step, sketch the curve that re-presents the top of the fender.

_ADAnalysisManagement

SURFACE CREATION

_Move

_Move

_ADSketch

_ADSketch

_ADSketch


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_ADModeling

The surface will again be created from fourcurves using the Autodesk tool ‘SurfaceFrom Curves’. The result is an arch-like,vaulted surface.

Use the ‘Control Point Modeling’ functionto model the fender according to the blue-print, until you are happy with the result.Make sure the lower edge of the fenderis roughly at the same height as the loweredge of the side surface.

Once you have completed the design ofthe fender, you can transfer the curves tothe ‘Auxiliary’ layer.

Change to the viewport ‘Front’ and adjust

the height of the front and rear curves ofthe fender. Use the viewport ‘Perspective’as reference.

TIP Once again, you do not have to adhere exactly to the lines in the blueprint. They simply serve as

an orientation for the further design process. Your free modeling of the surfaces and your own speci-cations determine the nal shape and its effects.

Rhino le: 3.5_fender.3dm


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SURFACE TRANSITIONS

Use the Autodesk command ‘Fillet Surface’to create a llet at the rear. According tothe command prompt, rst select one sur-face and then, having conrmed this selec-tion, the second surface for llet creation.

Proceed by modeling the side and coversurfaces with the ‘Control Point Modeling’command.

For the side surface, select the option ‘Tan-gent’ and move individual points in such away that the upper part becomes narrowertowards the front.

If this approach does not yield the desiredresult, you can try the following alternativeway: Reduce the height of the side surfaceusing the mode ‘Extrapolate’ and subse-quently pull the points at the rear back tothe top with the option ‘Tangent’.

Due to the different options and parametersettings available, different approaches can

be used to reach the same goal.

In the following steps, we will continue by creating surface transitions. Continue working on the ‘Chassis’

layer and start preparing the surfaces that will serve as input for the design of a blend surface. To thisend, display again the previously blanked surfaces of the layer ‘Chassis’.

Set the ‘Radius’ of the llet surface to 3.0.A click on ‘Apply’ will activate the previewof the llet surface at the rear. Try changingthe settings of the ‘Options’ as shown inthe gure to the left and click on ‘Apply’to see the effects each time in the preview.We will eventually use ‘Arc Bezier (G1)’ andactivate ‘Fit Join Tolerance’. Conrm thesesettings by clicking on ‘Ok’ and terminatethe dialog.

You can now see a llet that captures thelight where the two input surfaces form anangle.

_ADFilletSurface

_ADModeling


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When moving the points of the cover sur-

face, again activate the option ‘Tangent’and the mode ‘Single’ in the Autodesk ‘Mod-eling’ command. The cover surface has tobe narrowed at the front as well. The trimedge in the zero plane and the second con-trol point row from the middle must not bemodied. Using the above mentioned set-tings, model the surface such that a wedge-shaped gap is created between the side andcover surfaces. The aim of this modelingprocess is to modify the surfaces such thatthere is enough room for the blend sur-face to be created, while preserving at thesame time the shape characteristics of thesurfaces. To model the cover surface, youmay nd the blueprint ‘topview’ helpful.It includes a sketched curve to which thenew surface edge can be adjusted. At therear, it is essential that the cover and sidesurfaces intersect the rear surfaces. This canbe achieved by extrapolating the rear andcover surfaces using the ‘Extrapolate’ modeof the ‘Control Point Modeling’ command.

Since modeling of the control point rows may have led tosymmetry errors, please correct these using the Autodeskcommand ‘Align to Symmetry Plane’. Having activated the

dialog, select the cover surface and activate ‘Tangency/ Curvature’. Make sure ‘x’ is selected as ‘Symmetry Plane’.Conrm your selection with the RMB. If ‘Display MirroredImage’ is active, you will now be able to see the theo-retically mirrored cover surface in the preview. Given thatthere will be only minimal deviations, if any at all, in thegeometry, a modication will hardly be noticeable. Con-rm by clicking on ‘Ok’ and terminate the dialog. The sur-face has now been adjusted with a tangential transition tothe plane at x = 0.

TIP To optimally support the modeling process in the next steps, always display the Rhino control pointsof the opposite surface (as in the above gure) during your modeling operations with the ‘Control PointModeling’ tool. Take into account their position and distribution and adjust the control point rows youmodel accordingly. A high degree of similarity in their position and distribution and in the length andborder of the surfaces will lead to smoother and more homogeneous results in the following steps.

_ADModeling

_ADSymmetry

Rhino le: 3.6_model.3dm

SURFACE TRANSITIONS


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_Curve

Continue on the layer ‘Chassis’ to create in

the next steps the blend between the coversurface and the fender.

To create this blend surface, you need tocut out part of the existing surfaces. To thisend, dene a wide arc around the fender inthe viewport ‘Top’.

Extrude the arc in linear direction using the

Autodesk ‘Flange’ command.

The active dialog prompts you to select asurface edge or a curve. Select the arc justcreated.

Since our curve was projected onto thezero plane, select ‘Both Sides’ to extrudethe curve in both directions.

To avoid creating two surfaces extrudedeach in two directions, activate ‘Single Sur-face’ and specify a length of ‘200’, therebymaking sure the surfaces will completelyintersect each other.

_ADFlange

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_Split

Slightly curve the lower part of the auxiliary

surface in outward direction. Use the Au-todesk ‘Control Point Modeling’ commandwith the options ‘Normal’, ‘Single’, and‘Blend Law’, pick the lower outer controlpoint and slightly pull it towards the back.You can leave the ‘Degrees’ in V-directionat 1 or increase the value to 2.

Due to the active ‘Blend Law’, controlpoints that have not been selected explicit-ly will be affected by the modeling as well.The rear part of the surface will sweep backa little. The options ‘Linear’, ‘Strong’ and‘Weak’ allow you to control the strengthof the modeling effect on the other controlpoints.

Using the Autodesk ‘Split’ command, splitthe side surface with the auxiliary surface.Keep the rear part of the split surface, whiledeleting its front part.

Split the cover surface at the auxiliary sur-face with the common Rhino method,using the Rhino ‘Split’ command, becauseAutodesk split operations can generateonly natural surface borders (four-sidedsurfaces).

The cut-off surface parts and the auxiliarysurface can subsequently be deleted.

_ADModeling

_ADSurfaceSplit

Rhino le: 3.7_split.3dm

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_ADEdgeApproximation

Activate the ‘Edge Approximation’ com-mand. The dialog prompts you to select anedge. Select the edge of the cover surfaceand conrm by clicking on ‘Apply’.

A new curve is displayed in blue, includingits maximum deviation from the originalcurve.

TIP Trimmed edge curves include surface data that is not necessary and furthermore may cause prob-lems during further surface creation. This is why we will perform an approximation for the edge curves.As a general rule, the quality of natural edges is better than that of trimmed edges – which is why wewill not yet create the blend surfaces between the rear and side surfaces at this stage.

In the dialog, increase the ‘Max. Degree’from 5 to 6, set the ‘Max. Local Spans’ to1, the ‘Max. Deviation’ to 0.001, and con-rm by clicking on ‘Apply’. The preliminaryresult will again be displayed as a preview.By selecting different ‘Discretization’ op-tions you can try out different reapproxi-mation methods. You should eventuallyuse the method yielding the most uniformcontrol point distribution and the smallestdeviation.

The visibility and parameters of the inte-grated deviation analysis can be controlledunder ‘Deviation – Options’.

In our example, we decide to use a ‘Scaling

Factor’ of 10 and the ‘Discretization’ opti-on ‘Curvature’.

Click on ‘Ok’ to terminate the dialog andnally reapproximate the edge curve of thetrimmed surface.

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_ADSurfaceBlend

Activate the ‘Surface Blend’ command to

create a blend surface. The dialog that willbe opened prompts you to select the rstsurface edge. Select the edge of the coversurface and conrm with RMB. Then clickon the adjacent edge of the side surfaceand conrm again.

You can move the arrow-shaped handleson the surface edges to limit the blend sur-face. Since the side surface is considerablylonger than the blend surface to be cre-ated, select the handles on the side of therear surface and reduce the extent of theblend surface.

Move the handles at the rear of the buggybeyond the position where the rear surfaceintersects the adjacent surfaces. This is tomake sure the blend surface is long enoughto be split with the rear surface.

In addition to the quality of the surfacetransition, you can dene the desired de-

gree of continuity at the edges of the blendsurface. The corresponding options areavailable in the ‘Advanced’ section of the‘Blend’ dialog or can alternatively be ac-cessed via the context menu of the handlesin the graphics.

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1Before proceeding, we will modify a few

more parameters in the dialog.The main requirement to be met by theblend surface is a curvature continuoustransition (‘G2’).

The ‘Shape’ factors determine the controlpoint distribution and thus the shape of theblend surface.

The option ‘Degree/Spans’ controls thenumber of control point rows. Set theseparameters to ‘5’ and ‘1’.

In the lower part of the dialog, you can acti-vate an analysis. Activate the option ‘Match-ing’ and click on the ‘Options’ button.

This will open further dialog windows, al-lowing you to verify the continuity condi-tions at the surface transitions. Our mini-mum requirement on the desired transitionis tangent continuity. To verify this, activate‘Tangency’ and ‘Show Max.’. The maximum

deviation is displayed in the graphics. Thisvalue results from the strong narrowing ofthe blend surface. Since the blend surfacewas created nearly up to the position wherethe surfaces almost intersect, it must befurther adapted.

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Blend surfaces are normally created with the minimum or-

der and number of segments required by the input geome-try and the desired degree of continuity. If the two inputedges have different numbers of segments, this may resultin unwanted small segments. You can avoid this effect byactivating the option ‘Merge Segments’. In our situation,however, this option is not necessary, as the input edgesare not segmented.

The options under ‘Order/Segments’ allow you to denethe order and number of segments of the surface to becreated in the direction of the edges. In our example, theminimum order used to create the input surfaces causes anexcessive curvature of the blend surface. To mitigate thiseffect, we are setting the ‘Degree‘ to 5 here.

The button ‘Advanced’ offers some more parameters youcan dene for the surface transitions. The settings for the‘Start’ and ‘End’ will be described in detail on the followingpages.

The ‘Shape Factor’ sliders provide additional variation pos-sibilities for the effects of the shape factors by allowing thestart and end of the same side to be set to different values.

As soon as you apply your changes of the different set-tings, the display of the previously activated ‘MatchingAnalysis’ is updated and gives you feedback on the effectof your modications on the transition quality.

Activate the Autodesk ‘Shape Display’ to evaluate the Au-todesk ‘Shaded Curvature Analysis. The sliders dene therange of curvature values, with lower values being dis-played in blue and higher values in red. As you move thesliders, you will see that the transitions between the blendsurface and the side and cover surfaces are smooth. Thereare no sharp boundaries visible between the different col-or shades, nor any color irritations at the transitions. Thisindicates a good distribution of the surface tension.

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SURFACE TRANSITIONS

To create the next transition, the blackfender has to be modied. To this end,dene the fender on the auxiliary plane asprojection base by clicking on ‘Select’ in

the Autodesk ‘Shape Options’ and select-ing the fender surface. If ‘Display’ is active,this surface will be displayed in blue.

Activate the Autodesk ‘Modeling’ com-mand and select the black fender surfacefor modeling.Set the ‘Degree’ in U-direction to 7 or 8and activate ‘Use Projection Base’. Via theoption ‘Use Projection Base’ you activatethe green reference surface selected in theprevious step via the ‘Shape Options’ asprojection base.The aim of this modeling operation is tomodify the fender surface such that it isnarrowed almost along half its length and

adopts a slight S-shape to match the adja-cent cover, blend, and side surfaces. There-fore, model the edge curve into a slight S-shape on the fender, as this will facilitatecomputation of the intended blend surfacetowards the chassis. Modify the controlpoints accordingly.To enable this extreme modication of thegeometry, the substantial increase in thenumber of control point rows was neces-sary.

For the next operation, copy the fender

to the auxiliary layer. You will then have agreen fender surface and a black one lyingon top of one another (in Rhino shaded dis-play mode).


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TIP During free modeling processes, the shape of the geometry is up to the user. The curve shapeand the surface tension are determined primarily by the user and by any specications that need to betaken into account.

Rhino le: 3.9_fender_modeled.3dm

SURFACE TRANSITIONS

The aim of this curve modeling process is tocreate on the fender a curve with a smoothshape that can subsequently be used asinput edge for the creation of a blend sur-face.

Please note that an increased number ofcontrol point rows is required at the posi-tion where the S changes its direction.

Looking towards the rear of the buggy, thelower part of this curve should be locatedto the left of the adjacent edge of the side

surface.

In the top view, the curve is almost parallelto the edge of the chassis. Once you are sat-ised with the shape of the curve, conrmwith ‘Ok’. The fender on the auxiliary layercan now be blanked.

At rst, move the inner edge of the fender

surface approximately to the middle of theoriginal surface, using the mode ‘Extrapo-late’.

Then reduce the number of control pointrows in this direction to three (correspond-ing to a degree of two).

Subsequently set the ‘Mode’ to ‘Single’and activate the option ‘Tangent’.


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SURFACE TRANSITIONSActivate the Autodesk command ‘Surface

Blend’ to create the next blend surface.

Select the opposite edges to be connectedin the right order.

The automatically computed blend sur-face still requires some modeling. Use thearrow-shaped handles in the graphics toachieve a more uniform distribution of con-trol point rows.

Once you have conrmed your selection,set the desired continuity for both sides to‘Curvature (G2)’. The option ‘Degree/Spans’should be inactive, but you should activatethe ‘Fit Join Tolerance’ option.Click on ‘Apply’ to activate the preview ofthe blend surface.


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SURFACE TRANSITIONSBy keeping the left mouse button pressed

on an arrowhead, you can change the dis-tance of the control point rows from theinput edge.

A RMB click on the start point of a handlewill open a context menu where you candene additional parameters.

For example, upon selection of the option‘Angle’, a handle in the graphics allows youto modify the angle between the blend sur-face and the edge of the input surface.

In parallel with the modeling, you can ac-tivate the display of ‘Light Lines’, allowingyou to keep control of the surface transitionquality during the modeling operation. Feelfree to use other analysis tools in addition.


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SURFACE TRANSITIONSTo further optimize the connected surfaces,

activate the ‘Control Point Modeling’ com-mand in addition. You can model the fend-er surface and adapt the blend surface tothese modications in parallel. Even thoughthis approach is rather uncommon in theRhino world, we recommend making useof it by all means!

The Autodesk ‘Shape Options’ allow you tocontrol the display options for the surfaceyou are currently working on.

For example, you may want to hide thecontrol points when you verify the surfaceshape by means of light lines, or you canchoose whether or not you want to be ableto see the control points through the sur-face.

To further optimize the surface shape, youhave to insert an additional ’Shape’ handle.This handle must be translated to an appro-

priate position and adjusted there.

To this end, select the option ‘Shape – AddShape’ in the context menu. Place the startpoint of the new handle at a position whereyou want more control of the surface shape.Smooth out unwanted waves and steadythe course of the isocurves.

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Use the Autodesk analysis tool ‘Light Lines’to check surface shapes and transitions.

To allow the surfaces to be split with theirrespective adjacent surfaces in the nextstep, we have to make sure that all surfacesintersect each other. If your model does notyet meet this requirement, use the ‘ControlPoint Modeling’ command with ‘Extrapo-

late’ to extend the rear and oor surfaces.Make sure not to extrapolate the surfacesbeyond the zero plane. Once all surfacesintersect, you can start with the splittingoperation.

Start by splitting the rear surface and thenthe side surface with the adjacent surfaces.Finally, split the blend surface and the coversurface with the rear surface. The oor sur-face and the front will not be split.The red lines in the above gure show thecutting curves.

Delete the surface parts cut off during thesplitting operation. As a result, you nowhave half the buggy as a surface cluster.

Rhino le: 4.1_half.3dm

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Use the ‘Control Point Modeling’ command to move the points of the upper row until the shape of theupper edge corresponds to the shape of the wheel case. The ‘Degree’ in the corresponding direction is 3.The aim of this modeling operation is to prepare a surface edge as input for the next blend.

For the next steps, create a new layer ‘Wheelcase_front’ and select it as active layer. Create a plane (approxi-mately at the height of the front wheel) in the side view and rotate this plane by about 40°.

Looking at the front sketch of the buggyin the viewport ‘Front’, move the planeroughly onto the line that marks the wheelcase in the sketch and tilt it such that it lieson the contour.


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_Hide

To improve visibility, blank as much geom-

etry as possible. Copy the fender and itsblend surface as auxiliary surfaces to thesub-layer ‘Wheelcase_front_auxiliary’ andinactivate the layer ‘Chassis’.

The copies of the fender and blend surfacescan be deleted again after the next opera-tion. The next steps will be carried out onthe active layer ‘Wheelcase_front’.

_ShrinkTrimmedSrf

_CopyToLayer

Like for the modeling of the fender surface,again create a copy of the fender, copyingit this time to the layer ‘Wheelcase_front’.

Since we split the surfaces with the oorsurface in the previous step, you shouldnow shrink the trimmed fender surfaceson the wheel case layer, so as to obtain asurface description that is as simple as pos-

sible.

Then activate the Autodesk ‘Shape Op-tions’ and dene the fender surface on theauxiliary layer as projection base.


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1In the following step, we will use the Auto-

desk ‘Control Point Modeling’ command toreduce the number of control point rows inU-direction to 3. The ‘Projection Base’ op-tion is active during this operation.

The aim is to create a surface roughly cor-responding to a rectangular strip on thefender. To this end, the control points haveto be modeled accordingly with activated‘Tangent’ and ‘Single’.

In addition, we will try to reach a harmo-nious control point distribution. If you clickon the ‘Smooth’ button in the ‘ControlPoint Modeling’ dialog, the distribution ofcontrol points will be harmonized automa-tically. Subsequent additional modicationof the overall shape is also possible. Youraim should be a straight, uniform surfacestrip.

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The ‘Deviation Analysis’ command allows

you to determine the distance betweentwo objects. The dialog that will be openedprompts you to select the object to be ana-lyzed. Click on the surface you have justcreated. Furthermore, this command requiresa reference surface. Click on the fender toselect it as reference. Make sure you selectthe upper fender surface and not the adja-cent blend surface.

Once you have selected the two objects,the corresponding deviation graphs are dis-played in green. Via the settings in the di-alog, you can inuence the display of thegraphs.

Model the new surface with the ‘ControlPoint Modeling’ command to further cleanup the surface structure. Reduce the ‘De-grees’ in cross direction to 3. Activate ‘UseProjection Base’ to project the surface youwant to model onto the target surface. Donot use too many control point rows, only

a sufficient number to enable straightfor-ward and optimal surface manipulationwith the options ‘Row’ and ‘Normal’ in orderto minimize its deviation from the targetsurface. The graphs of the ‘Deviation Anal-ysis’ will be helpful in this operation. Acti-vating ‘Mouse Move Scale’ and setting it toa value larger than 1 allows you to makevery ne modications.If need be, you can model individual pointswith the options ‘Single’ and ‘Blend Law’to achieve a uniform distribution.

To improve visibility, set the parameter ‘No. of Graphs’ to 6. You will see the number of longitudinal lineson the object change simultaneously. For the parameter ‘No. of Points’ the same holds true as for the‘Curvature Analysis’: the higher the number of points, the more detailed the graph. Set the scaling factorto 13 and activate the check boxes ‘Show Min.’ and ‘Show Max.’. The deviation values between thetwo surfaces are then indicated in the form of labels in the active viewport. This analysis will likewise bestored in the ‘Analysis Management’ and will be updated in the background during future modicationsof the geometry, even after the dialog has been closed.

Activate the ‘U/V’ view in the Autodesk ‘Shape Options’. This will provide better orientation during thenext steps.


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Now model the new surface with the ‘Con-trol Point Modeling’ command.The aim of this operation is to create a sur-face that closely resembles the geometry ofthe fender, but is located at a distance from

the original surface of about 10 mm at thefront and about 15 mm at the rear – simi-lar to an offset surface, though not with aconstant distance at all positions.To this end, activate the constraints ‘All’and ‘Normal’ to rst move the completesurface away from its initial position. Con-tinue to pull until the distance has reached10 mm. If you click on ‘Reset Scale’ in the‘Deviation Analysis‘ dialog, the shaded de-viation analysis is updated. The result is a

surface that is almost parallel to the fender.Activate the options ‘Row’, ‘Normal’, and‘Blend’ to move the control point rows inthe lower rear part of the surface until themaximum distance has reached about 15 mm.You are on the right way, if the result is anarc with a uniform swing from the front tothe rear and a homogeneously increasingdistance from the fender. In addition, the‘Shaded Deviation Analysis’ must displaya regular ow of the corresponding colorvalues.

For the next step, activate the analysis tool

that allows you to visualize the deviation bymeans of false color representation.

The dialog prompts you to select rst thesurface to be analyzed and then the refer-ence surface, which in our case is the fendersurface on the auxiliary level. Once theanalysis has been computed, the surface isdisplayed in a color spectrum ranging fromred via yellow and green to dark blue. Inthe dialog, you can see the deviation valuescorresponding to each color. If ‘Show Min.’and ‘Show Max.’ are active, the positionsof the minimum and maximum deviationsare indicated on the surface.

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Once you have achieved a satisfactory re-sult, you can verify it by using the appro-priate settings. Set the maximum deviationvalue to 15 and t

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