## 3D basic functions

### 3D basic functions

3D tips from CADD Primer

User-defined Coordinate System:

We discussed in Chapter 2, “The CADD Basics”, how a user-defined coordinate system can help to work with odd-shaped diagrams. Here is an example of using it in 3D.

Let’s say you want to draw an arched object on the inclined surface of the model as shown Fig. 7.14. It is very difficult to calculate the 3D coordinates for a drawing object on the inclined surface. By creating a user-defined coordinate system, you can align the XY plane with the inclined surface of the model. Indicate the origin of the coordinate system at one corner of the inclined surface and indicate the sides of the inclined surface to be the X and Y axes (Fig. 7.14). Now the inclined surface becomes the XY plane. You can draw anything on this plane just like 2D. You don’t need to worry about entering any Z coordinates. Whatever you draw will be directly drawn on this surface.

Displaying Views:

You can rotate a 3D model on the screen and display different views by specifying an exact viewpoint. The viewpoint represents the position of the camera from where a picture of the view is to be taken. You can define a viewpoint with the help of any of the coordinate methods discussed earlier.

There are two main protocols used to display views:

• View coordinate geometry
• Object coordinate geometry

View Coordinate Geometry:

View coordinate geometry assumes that the camera (viewpoint) remains stationary and the 3D model is rotated to display a desired view. The model can be rotated around the X, Y, or Z-axis (Diagram A, Fig. 7.15). You need to specify around which axis the rotation will take place and by how much. When you rotate the model around the Z-axis, the model rotates in the XY plane; when you rotate it around the Y-axis, the rotation takes place in the XZ plane.

Object Coordinate Geometry:

Object coordinate geometry assumes that the model remains stationary and the camera (viewpoint) is moved to display a desired view. You can use any of the coordinate methods to specify an exact viewpoint. Spherical coordinates are particularly helpful to indicate a viewpoint (Diagram B, Fig. 7.15).

Comparison: View coordinate geometry can be compared to holding a small model in your hand and rotating it on its sides to get a desired view. Object coordinate geometry can be compared to viewing a building from the sky. The building remains stationary, while the camera is moved to get a desired view.

Note: Most CADD programs provide both view coordinate geometry and object coordinate geometry options to display views. Depending on how you want to view a model, you can use either method.

Displaying Isometric Views:

To display an isometric, you need to specify the direction from which the view is to be taken. The most appropriate method to indicate direction is with the help of spherical coordinates. You need to specify two angles: an angle in the XY plane (longitude) and an angle from the XY plane (latitude). The longitude determines the orientation of the model in the XY plane and the latitude determines the height of the viewpoint.

To display isometric views of the 3D model, consider the model to be lying on the XY plane (Diagram B, Fig. 7.15). The model can be viewed from four isometric positions: 45, 135, 225 and 315 angles.

The following chart shows the values to display the views shown in Fig. 7.16:

View Longitude Latitude
A 45 35
B 135 35
C 225 35
D 315 35

Displaying Plans and Elevations:

You can display standard 2D views such as plans and elevations by specifying the direction of the view. To display a plan view, you need to view the model from the top, that is, enter the angle from the XY plane (latitude) as 90. To display an elevation, you need to view the model parallel to the XY plane, that is, enter the angle from the XY plane (latitude) as 0. You can view an elevation from any angle by specifying an exact angle in the XY plane.

The following chart shows the values to display the views shown in Fig. 7.17:

View Longitude Latitude
A 0 90
B 270 0
C 90 0
D 180 0

Note:

The diagrams created in Fig. 7.16 and Fig. 7.17 show a symbol of a tripod. In most CADD programs, this symbol automatically appears when you display a 3D view. It shows the positive direction of the three axes, and acts as a guide when drawing in 3D and displaying views. The shape of the tripod is changed according to the angle of the view.

Displaying Perspective Views:

CADD allows you to display perspective views from any angle of the model. You can display a true perspective by specifying an exact distance between the viewpoint and the model. (Specifying a distance is not necessary to display parallel projection views such as plans, elevations and isometrics.) When you specify an exact distance, it causes the lines of the view to converge and display a true perspective (See Fig. 7.18). The closer the viewpoint, the greater the conversion takes place.

CADD programs use one of several methods to display perspective views. A common method is to establish a line of sight between the viewpoint (camera) and the model (target). You can specify any distance along this line of sight to display an appropriate perspective view.

Fig. 7.19 illustrates some examples of displaying perspective views of a model from different angles. Diagram A shows the plan view of the model created in Fig. 7.13 (some grid lines are added at the base of the model). The point V1 is entered as the camera position (at a certain height), and point T1 is entered as the target. This establishes a line of sight between the two points. Views B and C are displayed along this line of sight by specifying different distances. In Diagram D, a different target location is entered. This changes the direction of the line of sight. View E and F are displayed along this line of sight.

Note:

To display the model so that the lines in the background (hidden lines) are not visible, you need to convert it into a surface model. You need to draw total seven surfaces: top, bottom, four sides and one inclined surface.

Important Tips:

• You can manipulate the views of a 3D model in a number of ways. You can rotate the view, cut a section of the view along a plane, reduce or enlarge the view, change the focus of the view, hide and display certain lines, etc.

• You can display more than one view of a model on the screen at the same time. You can create a number of viewing windows (viewports) that can be used to display different views. For example, you can display a plan view of the model in one viewport, elevation in another and a perspective view in another. When you draw something in one viewport, it is automatically shown in all the viewports.

• Advanced CADD programs enable you to create animated images. You can create perspective views and store them in the computer memory. You can display a number of these images within seconds to create an animation. You can create a presentation that simulates walking through a building or the functioning of a machine.
3D Drawing-Aid Functions

The common 3D drawing-aid functions of CADD are described as follows:

• Linear extrusion
• Shading and rendering

CADD allows you to draw a number of 3D ready-made shapes (primitives) in a few simple steps. To draw a cube, you don't need to draw all the lines or 3D faces for each of its sides. You can draw a cube just by specifying its dimensions. Similarly, you can draw a number of commonly used geometrical shapes by specifying their shape and size.

Fig. 7.20 illustrates some common 3D shapes available in CADD such as pyramid, prism, dome, vault, cylinder, cone, sphere and torus. To draw a pyramid, you need to specify the number of sides and the height. To draw a sphere, specify its diameter and the number of longitudinal and latitudinal divisions (if needed). A cylinder can be drawn by indicating the height and the diameter. Similarly, you can draw other objects just by specifying their dimensions.

Important Tip:

Specialized engineering programs provide a number of additional 3D objects and techniques to facilitate a 3D drawing. You can combine a number of 3D objects to form a single object or subtract one 3D object from another. This technique is referred to as "boolean operation". You can create a skeleton of the model using boolean operation and build the rest of the model based on it.

Extruding Objects in the Linear Direction:

CADD allows you to extrude 3D shapes from 2D profiles. You can extrude a square to form a cube, a circle to form a cylinder, or a triangle to form a prism. When you use the linear extrusion function, you are prompted to select the objects to be extruded and specify the direction of extrusion (axis of extrusion). You can select any profile made of lines, arcs, polylines, or other objects and extrude it in any direction by specifying the axis of extrusion.

Fig. 7.21 illustrates how you can extrude an elevation profile of a house to make a 3D block of the house. The profile is extruded in the horizontal direction.

Fig. 7.22 illustrates how you can extrude the drawing objects in the vertical direction. In this illustration, the walls of a house as shown in the plan diagram (A) are extruded vertically to create a 3D model (B).

Extruding Objects in the Circular Direction:

CADD allows you to extrude drawing objects along a circular path (called radial extrusion). For example, you can draw a section of a cylinder and extrude it to form the complete cylinder. To perform a radial extrusion, you are prompted to select the objects to be extruded, indicate an axis of revolution and an angle of extrusion. The axis of revolution acts as a pivot point of the revolution and the angle of extrusion determines how much revolution will take place.

Fig. 7.23 illustrates how you can extrude a 2D profile of a flange to form a 3D model of the flange. To complete the diagram, you need to draw the section of the flange as shown in Diagram A. Indicate a vertical line as the axis of revolution. To draw only half the flange as shown in Diagram B, enter the angle of extrusion as 180. To draw the complete flange as shown in Diagram C, enter the angle of extrusion as 360.

Note:

CADD provides options for drawing the dividing rib lines as shown in Fig 7.22. You can specify any distance for these lines to create a 3D rendering effect.

There are a number of shading and rendering programs available that can be used to make 3D drawings very realistic. These programs allow you to create colors, shades and shadows exactly as they would appear in a picture. These programs are quite large and complex and require powerful computer hardware.

With the help of rendering programs, you can specify a number of shading and rendering parameters and create a 3D scene. You can assign colors and textures to different surfaces of a model. You can specify light sources in a scene and specify what kind of light is used and how it is directed. You can create a special setting for the model, such as a landscape or interior.

The computer analyzes all the factors specified in a scene to create a rendering. It determines how a ray of light will travel from the indicated light source to all the surfaces of the model. It determines how a surface will be lighted and where it will cast a shadow. This procedure is known as “ray tracing”, and a number of rays must be traced to determine the exact lighting and shading pattern of a model.

The program determines how a color or texture will look in a certain type of light.
John D

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