3point Perspective Drawing Worksheet

3point Perspective Drawing Worksheet

May 2000AutoCAD 2000 in 3D - A Monkish Shot TowerUNIVERSITY OF NEW SOUTH WALESFACULTY OF THE BUILT ENVIRONMENTTUTORIAL INTRODUCTIONS TO CADAutoCAD 2000 in 3D - A Monkish Shot TowerJim PlumeThis tutorial introduces the conceptstechniques used to build 3D models inAutoCAD 2000.

As a vehicle for learning these techniques, we develop a modelof a whimsical structure that I have called the Monkish Shot Tower after a groupof imaginary Monks who have refined the technology of manufacturing lead shotfor firearms, and the like.

The tower is designed around the perfect number 7,features an external spiral stair, an elaborate canopy on top, and a hole downthe centre.

The final structure is illustrated in Figure 1 below.This tutorial will introduce the following concepts and techniques: simple solid modelling with solid primitives & CSG operations (the tower); construction of complex solid objects (stair and landing); user coordinate systems and positioning of objects (external stairs); advanced use of the CSG operations (tapering the stairs); simple surface modelling (the roof canopy and handrails); surface modelling versus solid modelling (the handrails); meshed surfaces (the landing sails for shading).Figure 1Four Perspective Views of the Monkish Shot TowerAs you are probably aware, thetraditional technology formanufacturing lead shot involvesdropping blobs of lead fromsignificant heights such that, as thelead cools during its descent, itforms perfect spherical balls .2Updated:

May 2000AutoCAD 2000 in 3D - A Monkish Shot TowerGETTING STARTEDAs with every drawing that you produce with AutoCAD you should begin byestablishing your drawing area by setting the Drawing LimitsUnits and usingZoom All to expand out to a full view of your drawing area.

Do that now, settingthe limits to For this model, we will make use of several different layers for handling differentparts of the model.

Begin by calling up the Layer Control dialogue box (seebutton at left) and create two new layers called Construction and Tower,setting each to a different colour (I used green and white layer will be used for construction lines that do not form part of thefinal drawing.

The Tower layer will contain the central tower.The last thing to do before beginning the tower is to create a single referencepoint for this model

we will do this by placing a

entity on theConstruction layer at the centre of the drawing area (which will become thecentre of the base of the Shot Tower).

We will be using

a few times inthis drawing as reference markers, so we need to set a Point Style that will beeasily visible (the normal way AutoCAD marks a point is with a single dot

wewill use an X-shaped cross instead).

To do all that, proceed as follows Begin by setting the current the list of layers(illustrated at left) and click on Construction

then proceed as follows Format Point StyleSelect from the pull-down menus

in the resultingdialogue box select the X-shaped cross and then click [Draw.Point]Issue the

command (illustrated) and click a positionat about the centre of the drawing area To cancel the command.CONSTRUCTING THE CENTRAL TOWERIn keeping with the principle that everything in this Shot Tower is designedaround the perfect number 7, we will construct a 7-sided polygonal tower, 19.6metres high (7 levels at 2700), with an outside diameter of 7 metres, andtapering inwards at a gradient of 1:70 (which converts to an angle of 1.3vertical).

Proceed as follows:current layerTower[Draw.Polygon]Select from the Draw ToolbarNumber of sides

then use the |NODe| object snap modeto fix the centre at the point entity just created.Specify an inscribed polygon.of the polygon.[Modify.Offset]Issue the Offset command (as illustrated).Offset distance

select the polygon just drawn and thenpoint to the inside to show the side to offset

press complete the command.We now have to extrude these two polygons in the Z-direction to the heightrequired, specifying the 1 in 7 taper as we do so.

We will then subtract the innerLayer Control buttonHintTo create a new layer in thisdialogue box, simply click the Newbutton and type a name for thelayer in the list.

To set the colour,click on the colour box adjacent tothe corresponding layer.Pull-down layer list Draw point tool Polygon toolOffset tool3Updated:

May 2000AutoCAD 2000 in 3D - A Monkish Shot Towerone away from the outer one to create a polygonal shell with an empty interior.Once we have done that, we will position a box to serve as the doorway atground level and subtract that away from the shell to create the opening.

Thatwill complete the basic tower!

To do all that, proceed as follows ToolbarsOpen the Toolbars dialogue box, scroll down the list to find toolbar, and then click on the check-box next toit.

Position it anywhere convenient on the screen, taking amoment to examine each tool, and noting the briefdescription of each on the status line as you move themouse across them..[Solids.Extrude]Pick the Extrude command (as illustrated)

dont forget towatch the prompts on the command line so that youunderstand the process!

select both polygons and thenpress

to complete the selection.of each extrusion.Taper angleTo see the effect of this in 3D, select D Views

Isometric from thepull-down menus

this will create a parallel projection (not a perspective) ofthe 3D object looking from the +X / -Y quadrant.

You can then use the normalZoom commands to alter the screen display to suit you own purposes,while maintaining that parallel projection.

Experiment with this until you have a3D view of the whole tower near the centre of your drawing area.The CSG tools are located on the Solids Editing Toolbar (illustrated).

You cankeep this on the screen or you may feel it is easier to execute these commandsthrough the pull-down menus Modify

SolidsEditing SubtractIssue the Subtract command

note that this commandallows you to select two sets of objects:

the second set arethen subtracted from the first

we will have only oneobject in each set in our case

select the outer shapeand press

(the primary object), and then select theinner object and press

again (the object to be subtractedfrom the primary one)

dont forget to watch theprompts to understand how this workshide Issue the Hide command

this draws the current viewwith all hidden lines removed or truncated as necessary notice that your tower is now one single solid object whichis hollow down the centreThe next step is to punch a doorway through the base of the tower.

zooming in to the base of the tower with a view similar to that shown in Figure 2,over the page (: use the new real-time pan and zoom tools in the standardtoolbar).

To make this process simpler, we will position the UCS (seeexplanation at left) as illustrated (Figure 2), with the origin at the outside cornerof the tower and the X-axis in line with its base.

To do that, follow these steps:ucs Issue the

command to alter the position of the currentnotice the command prompt, showing options forsaving and restoring UCS settingsSelect the notice the variety of ways thatyou can define the UCS

we will use many of these in thecourse of this tutorial Solids Toolbar with the Extrudecommand highlighted ..Solid ModellingWith solid modelling we sculptureobjects by assembling theprimitives shown on this toolbarusing the three CSG operations ofUnion, Difference (subtract) andInteresection.

As you will discoverin this tutorial, there is almostnothing that cannot be formedusing these tools.Solids Editing ToolbarThese new tools are great formoving around your drawing hold down the left button whiledragging the mouse up and down.User Coordinate System (UCS)This is a 3D cartesian coordinatesystem that operates independentlyof AutoCADs fixed WorldCoordinate System (WCS).

It canbe positioned and orientatedanywhere in space (at any angle).All 2D drawing is always done inthe UCS X-Y plane:

normally, theUCS is coincident with the WCS!This means that you can use all the2D drawing commands that you areused to, only place them anywherein space by first positioning theUCS.

This would allow you, forexample, to draw a cross-hatchpattern on a sloping roof plane!4Updated:

May 2000AutoCAD 2000 in 3D - A Monkish Shot TowerSelect the

option keyword

this is the mostversatile option, allowing us to define the new UCSprecisely

watching the prompts, proceed as follows |ENDpoint|Use the object snap to put the origin at .|ENDpoint|Use object snap again to identify a point on the X-axis at.|ENDpoint|And again, to nominate a point on the positive Y portion of at Notice that the UCS Icon hasnow dropped the W (nolonger World Coordinates) andhas been positioned at the neworigin, oriented to suit the newSee note at left to movethe icon back to the lower leftcorner of the screen.

We nowuse the

primitive toconstruct the doorway

careful that you use the cornerbox rather than the centrebox[Solids.Box]Select from the


AutoCAD will prompt forthe corner position of the box |ENDpoint|Use the object snap mode to place the corner of the box at in Figure 2.Specify the opposite corner of the box as a relative 3Dcoordinate

alternatively, this could have been done byentering the length, width and height of the box separately.[Modify.Move]Issue the normal Move command

select the box justcreated and press

set the Base Point at the |MIDpoint|position marked

(on the box just created) and theSecond Point at the |MIDpoint| of line

- 2[Modify
3point perspective drawing worksheet
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entire drawing from a 3D perspective. ... <0,0,0>: 3point Specify new origin point <0,0,0>: 'zoom {zoom into the “A” end of the cross section} (southalabama.edu)
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Figure 1 Four Perspective Views of the Monkish Shot Tower C5 ... this drawing as reference markers, ... 3 ↵ Select the 3point option keyword — this is the most (southalabama.edu)
.Move]Re-issue the Move command

select the same objectand press

and pick any point as the Base Point@0,-100 Specify the Second Point of the displacement to move thebox so that it is centred on the thickness of the wall.Modify

SolidsEditing SubtractIssue the Solids Subtract command

pick the tower firstand then press , then pick the box and press you should now have a door opening in the base of theNotice that we deliberately made the box wider than the walls thickness (500instead of 300) so that when it was positioned, it protruded from both sides ofthe wall

this is especially necessary in this case since the tower is taperedand the wall leans in slightly.

Generally, however, when performing thistype of operation, it is prudent to always oversize the subtracted objectto ensure that no thin slivers of material are left behind!

If you try to betoo precise, you can encounter precision errors.Re-oriented UCS icon NOTE:

if the UCS icon has beenplaced at the origin (point Figure 2), then type the commanducsicon

and then type

forNo Origin ..

that will force the iconback to the lower left corner of thescreen#$Figure 2

Constructing the Door Opening atthe base of the TowerMove toolBox tool in the Solids Toolbar.5Updated:

May 2000AutoCAD 2000 in 3D - A Monkish Shot TowerCONSTRUCTING THE EXTERNAL WINDING STAIRThe decision to taper the tower inwards was deliberate because it leads to someinteresting complications in this otherwise simple model.

The first of thosecomplications occurs with the stairs since they too have to taper inwards as theyclimb the tower.

We get over this complication very simply.

We begin bybuilding the stairs straight up with no taper, each flight hugging the face of animaginary extrusion (downwards) of the 7-sided polygon that forms the insideedge of the (tapered) top of the tower:

this means that at the base of the towerthe stairs actually lie partially inside the tower.

Once the stairs are complete, wewill create another tapered tower in the middle of the stairs and subtract thataway from them to create the internal taper

the stairs will then very neatlyfollow the face of the real tower.

We then do the same with the outside taper:we build the flights very wide to begin with, and then at the end of the processwe construct a large tapered tower with very thick walls which we can alsosubtract away from the stairs, thus creating the outer taper.

This process isillustrated in Figure 12.

Producing the taper is easy:

the harder part isconstructing the stairs to begin with First, we need a few construction lines

make the Construction layer the current layer reset the

back to World (issue the UCS command and then press accept the default World), and Zoom out to a view that allows you to see the top of the Tower.We begin by tracing the inner edge of the top of the tower

to do that, weswitch on running object snap Tools DraftingDrafting Settings Dialogue box with the ObjectSnap tab (as illustrated)

I suggest that you select eachof the ones shown in the illustration at left

note the briefexplanation of how to use these if you have not done sobefore[Draw.Polyline]Issue the Polyline command

pick each of the 7 verticesaround the inside edge of the top of the tower Close the polyline.[Modify.Move]Use a Window selection rectangle to select the polyline justdrawn (you work out why!) and then press

set theBase Point anywhere you wish (well away from everythingto avoid the running object snap) @0,0,-19600 Second point of the displacement vector.Re-position your view to the bottom of the Tower, then, with ORTHO modeturned on (click the ORTHO button on the status line), construct two parallellines of roughly the same length (as illustrated in Figure 3) projecting out fromadjacent corners of the polygon just constructed.Now choose D Views lan View

orld UCSzoom inthe ends of those two lines

we will use these lines to set out the stairs inprofile as illustrated in Figure 4 (over the page).[Draw.Line]Issue the Line command

pick the start pointbottom end of the rightmost line.Height of riser (@-280,0 Length of going (Discussion Drafting Settings dialogueWith Running Object Snap turnedon, whenever you are using themouse to select a point, AutoCADwill highlight and identify thenearest snap point within the snapaperture

to use that snap pointsimply click the mouse button

ifthe snap is ambiguous, pressingthe Tab key will cycle through theavailable snaps at that point.Figure 36Updated:

May 2000AutoCAD 2000 in 3D - A Monkish Shot Towerto terminate Window selection to select both the riser and thegoing lines


to complete the selection Select the Multiple option

with using ENDpointAutoSnap, set the Base Point to the base of the riser line then place each copy at the left end of each successivegoing line to form the stair flight

stop just before youreach the second construction line by pressing [Draw.Line]Use the Line command (still with ENDpoint AutoSnap) toconstruct a line joining the bottom of the nosing to the topriser with the bottom of the nosing to the lowest riser.[Modify.Offset]Offset the line just constructed down by 140 to form thesoffit of the stair flight [Draw.Line]With ORTHO on, draw a short line from the ENDpoint ofthe bottom end of the lowest riser back in the Y-direction [Modify.Erase]Erase the right-most original construction line and the linethat was offset to produce the soffit line

you should endup with something that looks like Figure 5 ..Using Figures 5 & 4 as a guides (before and after!), use the Fillet command(with radius 0) to clean up the stair profile by joining up each of the corners.Next, we use the polyline edit command to convert the stair profile into a singlepolyline entity as follows Modify PolylineIssue the Polyline Edit command

select ANY ONE of thelines that make up the stair profile

AutoCAD will notethat it is not a polyline, but will offer to convert it into one(see say yes Select the Join option

then use Window selection to pickall the lines that make up the stair profile (it doesnt matterthat one has been selected twice!)


to completethe selection

AutoCAD will then join all those lines toform one polyline Press

to terminate the command.Now turn off the Tower layer, then create a new layer called Stair (makingit a distinctive colour) and set it as the Current Layer before proceeding.Next, use the Solid Extrude command to extrude the polyline to a height of 2500to form the width of these stairs and then set up a 3D view a little like the oneshown in Figure 6 (:

the SE Isometric view and then Zoom Window gaveme a good view).

The next step is to rotate the stair into an upright position Modify 3D Operation Rotate 3DIssue the command

select the stair and press to complete the selection Select the X-axis option (to rotate the stair around thataxis)

use |ENDpoint| to set the axis through the point shown in Figure 6 Rotation angle follows the at leftFigure 4Figure 5Pedit tool (in the Modify II toolbar)Figure 6Right Hand RuleIf you hold your right hand with yourthumb pointing in the positivedirection along the axis of rotation,then your fingers point in thedirection of positive rotation7Updated:

May 2000AutoCAD 2000 in 3D - A Monkish Shot Tower[Modify.Move]Using |ENDpoint|, move the stair using the centre ofrotation point as the Base Pointconstruction polygon as shown in Figure 7 as the Secondof displacement.The next step is to copy and then rotate this flight to create the second flight ofstairs.

We then need to form the landing between them, then we can duplicatethe stair all the way up the tower, and finally union all the parts together to forma single spiral stair.

Sound easy?Begin by selecting a NE Isometric view & zoom in the view shown in Figure 8.[Modify.Copy]Select the stair flight and press

pick the Base PointSecond Point of displacement

as shown in Figure 8,using the |ENDpoint| object snap mode.[Modify.We deliberately use 2D rotate because we only want torotate horizontally

again, pick the stair flight that we wishto rotate and press

following Figure 8 closely, set thecentre of rotation (called the Basepoint) to point

When prompted for the rotation angle, choose theReference option because we want to point to the angleof rotation (rather than calculate it, especially as it is arather odd number)

still using |ENDpoint|, pick points

as the reference angle

for the new angle, wewant to use the X & Y value (only) of the point marked taking its Z-value from point

to do that, proceed asfollows .xy This is called a Point Filter (AutoCAD will only take the XYvalue of the next point and then prompt you for the Z-value) pick the point marked

finally pick the point markedstill using |ENDpoint|).Now is a good time to learn another way of setting up a 3D view

we want toposition ourselves to look down at the gap where we need to construct thelanding.

SelectD Views ewpoint Presets

you should get theadjacent dialogue box on the screen.

The left diagram shows the plan viewingangle (with the small line pointing towards the centre showing the line of sight inplan

this is set to NE at the moment) and the right diagram shows the altitude(again, with a small line to show the current line of sight in can re-position the line of sight on either diagram simply byclicking with the mouse.

Experiment until you get a view similar to that shown inFigure 9 (over the page), remembering that this is still just a parallel projectionA Couple of Helpful Hints Now that the model is beginning to get a little complicated, you need to bewarned that Object Snapping in 3D is a little error-prone at times (althoughthe current version is
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