# Computer-aided design/Objects

*Part of:*

## Introduction

editA three dimensional (3D) computer model, for example a gear box, consists of many objects. These objects are of several types, for example solid and surface types. We will look at 3D model types and briefly discuss when to use them.

## Workplane

editAlso called reference plane or coordinate-system. The workplane acts as a reference from which the model data is calculated.

## Point

editA point represents a position in the 3D workspace and so is defined by x,y,z coordinates. Points are usually used as reference to snap other objects onto.

## Wireframe objects

editExamples are lines, circles, arcs or curves in 2D or 3D space. Wireframe objects are defined by control points and equation.

For example circle has center a,b (control point), radius r and equation defining set of all x,y circle points.

Implicit function:

- .

Parametric equation can be written using the trigonometric functions sine and cosine:

*x*=*a*+*r*cos(t)*y*=*b*+*r*sin(t), where t is parametric variable.

CAD systems use parametric versions of equation.

Some wireframe objects like Beziér spline cannot be defined by control points and simple function only. These objects are defined by many control points, vectors in control vertices that define shape and set of x,y is is calculated by algorithms (instead of simple equations).

Commonly used wireframe objects are:

- Line
- Arc
- Circle (full arc)
- Ellipse
- Polyline - set of connected lines and arcs
- Rectangle (special case of polygon)
- Regular polygons
- Polygon
- Bézier curve (special case of B-spline)
- B-spline (special case of NURBS)
- NURBS - Nonuniform rational B-spline

## Surfaces

editYou can understand surface as a part the the outer shape of an object or as an idealized sheet metal with zero thickness. Surface can be represented in several ways, but the most common is as a Parametric surface.

Types of surfaces:

- Regular (or canonical) surfaces include surfaces of revolution such as cylinders, cones, spheres, and tori, and ruled surfaces (linear in one direction) such as surfaces of extrusion.
- Surface mesh
- Facet surface
- Voxel surface
- Freeform surfaces (usually NURBS) allow more complex shapes to be represented via freeform surface modeling.

## Solid objects

editA solid represents a complete physical body, usually part that can be manufactured from one piece of material. Most CADs use method called Boundary Representation (abbrev B-rep or BREP) , to represent solid in computer. The object is represented by connected surfaces forming a closed solid volume. Surface elements create boundary between solid and non-solid. Solid objects have a volume and other physical and optical properties (mass, density, opacity ...).

Solids can be constructed from primitives or by sweeping base 2D shape along a path. Complex shapes are constructed by boolean operations as union, subtraction or intersection of two or more solids.

Sets of predefined solid primitives differ in various CADs. Commonly used are:

- Box, Cuboid
- Wedge
- Cylinder
- Cone
- Sphere
- Torus
- Sweeping

Imagine that you want to model bent pipe. You can create it, by draw two concentric circles that will form a doughnut shape. The doughnut shape is the profile. Then you will draw and axis of the pipe. Axis can be straight line, arc or any other curve. Then you will sweep the doughnut along the defining path (pipe axis).

Extrusions or rotations are special cases of sweeping. You can create a solid box from a 2D rectangle by extrusion along the Z axis, or you can draw a 2D circle and rotate it 180 degrees to create sphere.

You can use boolean operations to create more complex solid objects. Subtraction is similar to drilling. Draw a box and a cylinder inside it. By subtracting the cylinder from the box you will get a box with a hole. Unions are similar to welding in that it joins two solid bodies together.

## Feature

editMany modern CADs use features.

Features are for example a hole or slot applied to solid object. Often features are used with parametric geometry constraints. For example a hole must be in the center of the disk.

Features are applied to base solids one by one.

## When to use wireframe, surface or solid objects

editWireframe objects are typically used for drawing construction lines and basic 2D shapes from which you will create solid objects by sweeping.

Solid modelling should be used for models that consist from relatively regular shapes. Engines, gear boxes and machinery like lathe are typical examples. Parts are usually put together by assembly modelling. Making changes is usually fast, especially when features and parametric modelling is used.

Surface modelling is used for models with non-prismatic features, mainly freeform, doubly curved surfaces. Airplane body and bodies of consumer goods like electric razor are typical examples. Making changes is usually more difficult and time consuming than with solid modelling.

## Tasks to do

editLearn about CAD math background. Learn more about parametric equations.

Use examples and on-line demos:

## Achievements

editYou now have a basic understanding of CAD objects. You also have an idea of how these objects are represented in a computer. You also know some math behind the construction of these objects.

## Deliveries

editParametric equations for some simple 3D surface (cylinder, sphere, ellipsoid).

You will need:

- Internet access and browser (with enabled Java applets)

## Further Reading

edit- Excellent introduction to computer graphics math and OpenGL programming (Børre Stenseth; Østfold University)