• wireframe modelling– uses 3D lines, arcs, circles, and other graphical objects to represent the edges and features of an object; so-called because the model looks like a sculpture made from wires. 
• surface modelling – takes 3D modelling one step further to add surfaces to the wireframe so that the model can be shaded and hidden lines removed. A surface model is like an empty shell: there's nothing to tell you how the inside behaves.
• solid modelling – a solid model is most like a real object because it represents not only the lines and surfaces, but also the volume contained within. When you create a solid modelled drawing database, in some ways it is as if the actual object were stored inside the computer. Creating a solid model is somewhat like sculpting a piece of clay. You can add and subtract material with Boolean operators and create parts by revolution and extrusion.

Three-dimensional geometric modellers extend the capabilities of two-dimensional drafting systems by providing a rich set of features to construct, transform, and project 3D geometric forms as collections of lines, surfaces, and volumes in space. In modelling systems, such geometric objects are usually constructed within a 3D Cartesian co-ordinate system, an extension to the 2D version introduced in an earlier tutorial. Point locations are described by x, y, z co-ordinate triplets.

To determine the positive rotation direction about an axis, point your right thumb in the positive direction of the axis and curl your fingers as illustrated. Your curled fingers indicate the positive rotation direction about the axis. 

AutoCAD employs the righthand 3D Cartesian co-ordinate system.

In fact, AutoCAD supports all three co-ordinate systems: 3D cartesian, cylindrical, and spherical. d Cartesian co-ordinates are specified as x, y, z triplets. Cylindrical co-ordinates are specified using the following convention: Distance<Angle, Height(z)—e.g., 5<45,4. Spherical co-ordinates are specified as Distance<Angle in xy plane<Angle from xy plane—e.g., 5<45<60. Relative 3D co-ordinates are preceded by the @ symbol—e.g., @5,4,2

In most 3D modelling systems, there is a "global" or "world" co-ordinate system, defined by origin point and x, y, and z axes. Additional local co-ordinate sysems, often referred to as reference or construction planes, can be defined by giving co-ordinates of 3 points that lie on it, or by rotating about one of the co-ordinate axes. Using these and other methods of definition, a new construction plane can be created to coincide with any surface in the model. 

In AutoCAD, the user defined reference or construction plane is called the User Co-ordinate System or UCS. 

Use the Save option to store UCS definitions, and use the Restore option to reuse them.

Each of these primitives can be created as a: 

• wire-frame object – composed of curvilinear elements, lines and curves in space, and appear as if composed of "wires".
• surface object – composed of surfaces without thickness, or 
• solid (volumetric) object – these have volume and are completely enclosed.

AutoCAD can create all three types of 3D primitives: wireframe, surface, and solid. 

Whether an object is a surface or a solid will determine what can be done with it. For example, there are powerful editing and data extraction operations applicable only to solid objects.

AutoCAD supports both translational and rotational sweeping, and sweeping along an arbitrary path. Translational sweeping is referred to as extrusion, and rotational sweeping as revolution.

• ruled – 2D profiles are connected with ruled surfaces, whereby continuity is disregarded, i.e., sharp transitions can exist between surfaces.
• lofted – continuity is maintained—the resulting surface will be smooth, without sharp edges or corners.

	A union B
	A intersect B
	A subtract B
	B subtract A

Applying Boolean operations to simple 3D geometric primitives can easily create some rather complex 3D forms. 

AutoCAD supports all three Boolean operations: union, intersection, and subtraction. 3D solid objects can also be created by slicing.

As before with 2D CAD drawing, an object must be selected before it can be deleted, replicated, or transformed. As with 2D objects, the four Euclidean transformations of translation, rotation, reflection, and scaling can be performed on 3D objects. 

In AutoCAD, the standard 2D rotate and mirror commands have 3D complements: 3D Rotate and 3D Mirror. 2D Rotate performs rotation about a point in the xy plane of the current UCS, and 3D Rotate performs rotation about an axis in 3D space. 2D Mirror performs mirroring about an axis in the xy plane, and 3D Mirror about a plane in space. 

AutoCAD provides attaching of objects through the align command. 3D objects can be aligned by a point, edge, or face. 

In AutoCAD, trim, extend, fillet, chamfer, and stretch operations have limited application to 3D objects. Surface objects cannot be trimmed, extended, filleted, or chamfered—they can be stretched, however. Solid objects can be trimmed by slicing but can't be extended or stretched; they can be filleted or chamfered. 

3D objects can be copied or arrayed anywhere in 3D space in AutoCAD. You cannot, however, offset 3D objects. As in 2D, copy creates exact duplicates of existing objects. Array replication creates circular (polar) and rectangular patterns of selected objects on a 2D plane, or cylindrical and prismatic patterns in 3D space. Offset creates at a specified distance or through a selected point a new object similar in form to the original.

To move a grip, click on one and drag it to a new position then release the mouse button. The surface object thus changes shape. 

Handles or "grips"

Layers in 3D modelling cannot be seen as analogous to transparant sheets, because the contents of layers can intertwine in 3D space. Therefore, the layers in 3D modelling can be best described as named parts of the model that contain objects with similar content.For example, the layer named 3-DOORS can contain 3D objects that represent the third floor doors. 

As in 2D drawing, 3D models can also be structured by grouping objects into hierarchies, and by using external references. For example, each floor of a building can be stored in a separate file, whereby files containing other floors are externally referenced for 3D construction and display purposes. 

In traditonal projective geometry, projections are created by establishing a picture plane somewhere in space and casting projection rays from points in space toward the picture plane. In computer graphics, projections are created by mathematics applied to xyz co-ordinate triplets. For example, plan projection is created by discarding the z co-ordinate. 

AutoCAD does not support oblique projection. Orthographic, axonometric, and perspective projection methods are fully supported. 

The creation of a perspective projection simply involves choosing the perspective option in one of the menus. However, if a specific perspective is wanted, from a particular viewpoint, the set-up requires that several parameters be provided: 

• location of the viewpoint referred to variously as the eye or camera,
• location of the target point,
• viewing angle, and
• location of the front and back clipping planes.

The view (eye) and target points define the line of sight, which, with the viewing angle, defines the cone of vision or, as it is often called, the viewing pyramid. 

AutoCAD uses a camera metaphor in setting-up a perspective projection. To change the viewing angle, adjust the zoom lens length. The camera can also be twisted and panned. 

Some modellers offer depth clipping to eliminate from the scene those objects that lie in front or in back of the viewing pyramid. This is done by specifying the distance of the front and back clipping planes from the viewpoint.. 

Most modellers can simultaneously display more than one projection. Typically, the program's window is sub-divided into four viewports, each displaying a different projection: top, front, right, and axonometric or perspective. In AutoCAD, the number, content, and configuration of viewports can easily be set-up and changed. From the View menu, choose Tiled Viewports, then Layout, to subdivide the graphics area into several viewports, and then set-up the desired projection in each viewport.

The model you've created in the exercises of earlier tutorials was displayed in wireframe mode. Wireframes show only the edges of a model, and the model appears to be transparent. You can think of the lines that make up a wireframe as "wires" that indicate the model's edges. 

Wireframes can be difficult to interpret because they are transparent; however, they are easier for the computer to display so they are AutoCAD's default method of displaying a 3D model. If the model was always displayed on the screen as a solid it would take considerable time for the computer to display changes you make in the model because of the number of calculations the computer would have to make to regenerate the figure. This would slow down the fuctioning of the program to a crawl.

What is the difference between surface modelling and solid modelling in AutoCAD? How do you select one method over the other? Consider the following points: 

• with surface modelling, only the surfaces and not the interior volumes of the object are described in the drawing database--the objects created with surface modelling are like empty shells
• a solid model is most like a real object because it represents not only the lines and surfaces, but also the volume contained within
• you cannot use Boolean operators to join surface models like you can with solid models
• surface modelling provides less information about the object
• surface modelling is more difficult to use than solid modelling
• surface modelling is better suited to such applications as 3D terrain modelling
• try not to mix solid modelling and surface modelling (and, for that matter, wireframe modelling) as you can't edit them in the same ways to create a cohesive single structure
• surface models can be converted to wireframe models using the EXPLODE command
• solid models can be converted to surface models using EXPLODE
• however, you can't easily convert wireframe to surface models or surface models to solid models

• creating the object by entering 3D points (X, Y, Z)
• setting the default construction plane (XY plane) on which you will draw the object by defining a UCS
• moving the object to its proper orientation in 3D space after you create it.

Use meshes if you don't need the level of detail about physical properties (i.e., mass, centre of gravity, etc.) that solids provide but you do need the hiding, shading, and rendering capabilities that wireframes don't provide. Meshes are useful for modelling terrain—e.g., a building site. 

A mesh can be open or closed. A mesh is open in a given direction if the start and end edges of the mesh do not touch (see figure below).

AutoCAD provides several methods for creating meshes. Some of these methods can be difficult to use if you are entering the mesh parameters manually, so AutoCAD provides the 3D command, which simplifies the process of creating the basic surface shapes.

To view the objects you are creating with the 3D command more clearly, set a viewing direction with VPOINT or DVIEW. Below are examples of surface meshes created with the 3D command. 

Try this exercise: To create a rectangular mesh: 

1. from the Draw menu, choose Surfaces > 3D Mesh

2. specify the M size, using an integer from 2 through 256

3. specify the N size, using an integer from 2 through 256

4. specify the vertex points as prompted. Specifying the last vertex point completes the mesh

Example: 

Command: 3dmesh

Mesh M size: 4

Mesh N size: 3

Vertex (0, 0): 10, 1, 3

Vertex (0, 1): 10, 5, 5

Vertex (0, 2): 10, 10, 3

Vertex (1, 0): 15, 1, 0

Vertex (1, 1): 15, 5, 0

Vertex (1, 2): 15, 10, 0

Vertex (2, 0): 20, 1, 0

Vertex (2, 1): 20, 5, -1

Vertex (2, 2): 20, 10, 0

Vertex (3, 0): 25, 1, 0

Vertex (3, 1): 25, 5, 0

Vertex (3, 2): 25, 10, 0

Example of a rectangular mesh – a terrain model.

Creating a polyface mesh is similar to creating a rectangular mesh. To create a polyface mesh, you specify co-ordinates for its vertices. You then define each face by entering vertex numbers for all the vertices of that face. As you create the polyface mesh, you can set specific edges to be invisible, assign them to layers, or give them colours. 

To make the edge invisible, enter the vertex number as a negative value. For instance, to make the edge between vertices 5 and 7 invisible in the following illustration, you would enter the following: 

Face 3, vertex 3: -7

In the figure below: 

• face 1 is defined by vertices 1, 5, 6, and 2. 
• face 2 is defined by vertices 1, 4, 3, and 2. 
• face 3 is defined by vertices 1, 4, 7, and 5, and 
• face 4 is defined by vertices 3, 4, 7, and 8

To create a ruled surface: 

1. From the Draw menu, choose Surfaces > Ruled Surface

2. Select the first defining curve. Then select the second (1, 2) 

3. Erase the original curve if necessary 

You can specify any two points on closed curves to complete RULESURF. See the figure below. 

FIGURE

TABSURF icon

To create a tabulated mesh: 

1. from the Draw menu, choose Surfaces > Tabulated Surface

2. Specify a path curve (1)

3. Specify a direction vector (2)

4. Erase the original objects if necessary.

FIGURE

The surface is defined by a mesh which, in turn, is defined by a matrix of M and N vertices. M and N specify the column and row locations of vertices. Two system variables, Surftab1 and Surftab2 , control the mesh density: 

• Surftab1 controls the mesh density in the M direction; it controls the density of the mesh for Ruled Surfaces because they are always a [2 X Surftab1 + 1] mesh
• Surftab2 controls the mesh density in the N direction

To set the value for Surftab1, for example, enter the command surftab1

For the new value for Surftab1, enter 40

REVSURF icon

To create a surface of revolution: 

1. from the Draw menu, choose Surfaces > Revolved Surface

2. Specify a path curve (1) 

The path curve, which defines the N direction of the mesh, can be a line, arc, circle, ellipse, elliptical arc, 2D polyline, 3D polyline, or spline. 

3. Specify the axis of revolution (2) 

The direction vector can be a line or an open 2D or 3D polyline.

4. Specify the start angle. Then specify the included angle. 

5. Erase the original objects if necessary. 
The SURFTAB1 and SURFTAB2 system variables control mesh density in the M and N directions. 

EDGESURF icon

To create an edge-defined surface patch mesh: 

1. From the Draw menu, choose Surfaces > Edge Surface

2. Select the four edges in any order (1-4) 

The first edge you select determines the mesh's M direction. 

FIGURE 

The SURFTAB1 and SURFTAB2 system variables control mesh density in the M and N directions. 

The elevation of an object is the Z value of the XY plane on which the object base is drawn. The thickness of an object is the distance that the object is extruded above or below its elevation. 

Thickness changes the appearance of certain geometric objects, such as circles, lines, polylines, arcs, 2D solids, and points. The user sets the thickness of an object with the THICKNESS system variable. Once you have set an object's thickness, you can see the results by going to any view other than the plan view (see figure below). 

Not all objects can have their thickness set: 3D faces, 3D polylines, and 3d polygon meshes cannot be extruded. 

The CHANGE command is used to change an object's THICKNESS property. The ELEV command is used to establish the current elevation. The current elevation remains in effect even as you change from one UCS to another. ELEV defines the drawing plane of the current UCS.

1. Choose Modify > Properties

2. In the Modify dialog box, enter the thickness settings, then choose OK

3. Draw the desired objects. 
 

To change the thickness of EXISTING objects: 

1. Enter the command chprop

2. Select the objects to change 

3. Enter t (i.e. "thickness") 

4. Enter the new thickness in units 

5. Press Enter to quit the command

• from one of the basic solid shapes of box, cone, cylinder, sphere, torus, and wedge or 
• by extruding a 2D object along a path or 
• by revolving a 2D object about an axis.

Once you have created a solid in this manner, you can create more complex shapes by combining solids. You can: 

• join solids,
• subtract solids from each other, or
• find the common volume (overlapping portion) of solids
• fillet or chamfer solids' edges
• slice a solid into two pieces
• obtain the 2D cross-section of a solid

Like meshes, solids are displayed as wireframes until you hide, shade, or render them. By exploding a solid, you can break it down to mesh and wireframe objects.

To create a solid box: 

1. Choose Draw > Solids > Box (or choose the icon) 

2.Specify the first corner of the base (1) 

3. Specify the opposite corner of the base (2) 

4. Specify the height (3) 

To create a solid cone with a circular base: 

1. Choose Draw > Solids > Cone (or choose the icon) 

2. Specify the base centrepoint (1) 

3. Specify the radius or diameter of the base (2) 

4. Specify the height (3) 

With procedures similar to those for creating box and cone (see above) other 3D solid primitives such as cylinders, spheres, wedges, and tori may be generated.

You cannot extrude 

• 3D objects
• objects contained within a block (explode the block first)
• polylines that have crossing or intersecting segments, or
• polylines that are not closed

You can extrude an object along a path (see figure below). You can extrude objects you've created in profile. If you create profile using lines or arcs, then you must either: 

• use the JOIN option of pedit command to convert them to a single polyline or
• make them into a REGION before you use EXTRUDE

1. Select Draw > Solids > Extrude (or choose the icon) 

2. Select the objects to extrude (1) 

3. Enter p (i.e., "path") 

4. Select the object to use as the path (2) 

After the extrusion, AutoCAD deletes or retains the original object depending on user's wishes. 

To combine objects: 

1. Select Modify > Boolean > Union (or click tool icon)

2. Select the objects to combine (1,2) 

To subtract one set of solids from another: 

1. Choose Modify > Boolean > Subtract (or click tool icon) 

2. Select the object to subtract from (1) 

3. Select the objects to subtract (2) 

To create a solid from the intersection of two or more other solids: 

1. Go to the menubar and choose Modify > Boolean > Intersect (or click tool icon) 

2. Select the objects to intersect (1,2) 

1. extrude it into 3D, and
2. use surface modelling to turn it into 3D

Then, you will turn it into a block, and copy it to each column grid location. The use of blocks provides efficiencies and simplifies updating when there are repeated elements.

The command will prompt you to select the object to extrude. Click on the column circle. Enter 3000 as the height of extrusion. Press Enter or the Return button on the mouse (right mouse button) to select the defualt value (0) for the taper angle. 

From the View menu, choose Zoom, then All (or choose the Zoom All tool on the Standard toolbar to display the entire 3D model. It should resemble the figure below. 

Although very quick and effective, extrusion produces very simple 3D shapes. Let's look at surface modelling methods for producing a more interesting form. 

You may produce a different profile if you prefer. Think about how it will look as a 3D object, in later tutorials. 

Set drawing layer back to grid (See earlier exercises for method) 

Zoom in to give magnified view of one column: 

Command: z (Shorthand zoom command) 

ZOOM All/ etc / Window/ etc : w (for Window) 

Note that there are a wide range of other zoom options in the selection line. The standard method of selection to key the character or characters shown in upper case. 

First corner:

Pick a point about 6000 (3 grids) above floor, and a similar distance beyond the left edge of the floor 

Other corner:

Pick a point below the floor lines, and beyond second grid line 

Draw construction lines for half column

Command: l (Line) 

From point: int (intersection) 

Pick intersection of left grid and floor.

Object snap locational names (like int) can either be: 

• Typed, as shown
• Selected after pressing the mouse right (Menu) button when the pointer is in the drawing area 
• Selected from Assist/Object Snap Sub-menu. 

To point: @300<180 (300mm to left) 

To point: @3000<90 (3000mm up) 

To point: @300<0 (300mm to the right) 

The examples above demonstrate how points, like movements shown earlier may also be specified by the polar coordinate method. (ie. distance from an origin and angle relative to the X axis). 

Offset the top of column line up 200 to draw the construction line for the top of the capital. 

Command: Offset

Offset Distance: 200

Select object etc:

Pick the 300 long horizontal line you have just drawn 

Side to offset:

Pick above the selected line

Draw half column profile - using arc command: 

Set drawing layer to col

The method below is suitable for drawing an arc, by eye: 

Command: arc

Center/: int

of

Pick point where column vertical construction line crosses floor 

Cen/End/:

Pick bulge point, part way up shaft 

End point: near

to

Pick position along horizontal top of column line. Arc will be drawn fitting the points.

Evaluate the result: 

Does it look like a column? If you wish to redraw it you could consider two options: 

• Undo. Make a clean start. Undo command is u
• Repeat process. Use the first attempt as a guide, then erase it on completion. Erase command is e

Once you are satisfied, try a similar or another method, and draw a profile for the column capital. 

Command: qsave (save your work) 

Draw other half of column - using mirror: 

Command: mirror

Select objects:

Pick all of the half column. Press left button and drag window from left to right, fully enclosing all column elements, but allowing other lines to extend beyond the window. The left-right selection window, selects only items that are fully within the window.

First point of mirror line: near

to

Pick any point on vertical, column centreline

to Second point: near

Pick another point on same column centreline. 

Delete old objects?<N> :n (we want both sides) 

Other side will be drawn after 

Finish your column, using commands you have employed earlier: 

• change the layers of the construction lines you intend to keep, to col. (eg. column and cap tops)
• trim and/or erase unnecessary linework Trim command was usedabove. Erase command functions like copy or move. 

Now zoom back to the wider view 

Command: z (Shorthand zoom command) 

ZOOM 

All/ etc / Window/ etc : p (for Previous) 

Command: copy

Select objects:

hold down left mouse button. Drag window from left to right to select the column, as described in the previous section for the mirror command.

<Base etc>/Multiple: m (for multiple copies) 

base point: near

to

Click on grid line of column to copy

Second point etc: perpendicular

Pick from Object Snap menu i.e. by pressing left mouse button or using toolbar.

Move cursor to right and click on the next grid line. Another column will be drawn after 

Move cursor to the next grid line, select Perpendicular again, as above, and four more times until the other columns are copied. 

Command: qsave (save your work so far)

Command: z (Shorthand zoom command) 

ZOOM 

All/ etc / Window/ etc : w (for Window) 

First corner:

Pick beyond top left 

Other corner:

Pick beyond bottom right 

Draw 600 deep x 400 wide beam: 

Set drawing layer to beam

Command: layer

?/Make/Set/etc: s (for set) 

New current layer <col>: beam

?/Make/Set/etc:(to exit command) 

Try the next steps without detailed instructions. The following approach, using the commands in bold, is but one of many possible methods: 

• offset the floor line, up by the height of the column and capital - ie. 3200 
• offset new line, up by 600 - ie. 3800 above floor 
• offset both end column grids outwards by half the beam width - ie. 200. Observe that the offset command repeats. You can offset both with the one command. 
• Use trim (see above) to cut the overhanging ends. Observe that all lines can be selected and cut off with the one trim command 
• Change layer of the newly drawn beam to beam. 

• Set the drawing layer to roof
• offset the top beam line, up to the top of gutter level 300 above beam 
• offset the new line, up another 1200 
• offset both end column grids outwards by the roof overhang plus beam width - say 450 to form the roof edge. 
• change layers of newly drawn lines to roof 

Extend the horizontal roof lines to meet the vertical edge of the roof. For this operation a new command is best suited. 

Command: extend

Select boundary edge(s)...

Pick both new vertical roof edge lines 

<select object to extend>/Undo:

Pick both new horizontal lines, near all 4 ends. Each line will extend when picked

(to exit command) 

To finish off roof: 

• offset the lower roof line 300 down, to form bottom edge of roof, level with top of lintel beam
• trim ends of vertical lines to form ends of roof.

Command: qsave (save your work regularly) 

To position the elevation, assume its right hand edge will be 13000 to the right of the corresponding edge of the side elevation. 

You may need to zoom out, before proceeding, in order to fit the extended image on your screen. 

Copy right hand elements and 4 column bays: 

Command: copy

Select objects: 

Move pointer to just beyond the bottom right of the side elevation, press Pick button and drag window from right to left and up beyond the roof line, to include four right-most columns and the horizontal lines.

<base etc>/Multiple:

Ignore location of cursor and simply click left button. Polar co-ordinate method.

Second point etc: @13000,0 (13m to right) 

Second point etc: (to exit command) 

Copy left hand elements: 

Command: copy

Select objects:

Select left hand ends of roof, beam and floor, either by directly picking the lines or by windowing (ie. by making a window as above) from left to right.

<base etc>/Multiple:

Simply click left button as above

<base etc>/Multiple: @17000,0 (17m to right) 

Second point etc: (to exit command) 

Trim off horizontal lines: 

The roof lines will first be trimmed to act as construction lines for the drawing of the gable end. 

Try zooming in closer at this point, for better visibility. Use z command and w option. 

Command: trim

Select cutting edge(s)...

Select objects:

Pick left vertical roof line 

<select object to trim>/Undo:

Pick each of the three horizontal roof lines, near their left hand ends, one at a time. Each line should disappear as it is picked.

(to exit) 

Next, trim the beam lines: 

to repeat last (trim) command 

Select cutting edge(s)...

Select objects:

Pick left vertical beam line 

Select objects: 1 found 

<select object to trim>/Undo:

Pick top and bottom horizontal beam lines

(to exit ) 

Next, trim the floor lines: 

(to repeat last (trim) command) 

Select cutting edge(s)...

Select objects:

Pick left vertical floor line

Select objects: 1 found 

<select object to trim>/Undo:

Pick over-extended horizontal floor lines

(to exit ) 

Remove any unwanted duplicated items: 

There could be some currently invisible, accidentally duplicated lines, that need to be deleted. Use the Redraw option which you can access via the menubar, View menu. The screen will also be redrawn if you use either zoom or pan commands, but often it is better to finish cleaning up before moving on to another view. 

If any duplicate lines appear erase them: 

Command: e

Select objects:

Pick unwanted objects

Command: qsave (save your work) 

Draw gable end of roof: 

Change zoom if necessary.Change current layer to roof

The construction lines will enable the sloping roof line to be drawn from the intersection of the edges and gutter line across to the mid point of the ridge level construction line. 

Command: l (i.e., line) 

..From point: int

of

Pick intersection of gutter line and left or right roof edge.

The other side may be drawn equally well by either of the following methods: 

• Repeating the above process.
• Using the mirror command. The mirror axis (requested if this command is used) is the vertical line through the mid point of the ridge level construction line, or the top end of the previously drawn sloped edge

Any remaining construction lines can now be removed with the erase (e) command.

Command: end (to save and exit) 

Remember to log off before leaving.