HNC CAD: Computer Graphics - 2D CAD Concepts - Elements - Circles and Ellipses

Circles and Ellipses

Definition

Circle
A Circle is drawn when a loci or path is marked out following some defined rule. In the case of a circle the rule is very simple. A point on the circles boundary, or circumference, is ALWAYS the same distance from one static point (known as its centre of origin).

NOTE: Circles and Ellipses ( and there part relatives the arcs) are ALWAYS drawn in an anti-clockwise direction.
Ellipse
An ellipse, like a circle, is a loci of points that follow some difinition. It is produced when points move gradually from the end of one radius distance to the end of a second radius distance 90deg away and then over the next 90deg it goes to the end of the first radius distance. This continues until a complete revolution has taken place. CAD programs don't place an enormous number of dots on the screen to trace out the outline of the circle or ellipse. They normally use a points, maybe 36, and join them up with straight lines to make it easier to draw
Drawing a circle and an ellipse
As with a line, CAD programs need some important information in order to construct circles and ellipses.
There are many ways to specify how a circle is to be drawn. You could start with either end of its diameter. Its centre and a point on its circumference or even just three points through all of which the circumference can pass. One exception is if the points lie in a straight line, that implies a radius of infinitely large size and so cannot be drawn.

circle
In the example below I have used the centre and a point on the circumference to define the circle.
Points 1 and 2

ellipse
An ellipse has two different radii and can be drawn on a slope. So we need to enter the direction that one of the radii of the ellipse is pointing and the length of each radius.

In the example below I have used the centre and a point on the circumference to define the direction and the length of the first radius and a point to specify the length of the second radius.
Points 1, 2 and 3

Drawing a circlular arc and an elliptical arc
As with the circle and ellipse there are many ways to specify the arcs.
The basic information is also needed but this time you also need a start and end point for the arc.
REMEMBER: Arcs and Circles and ALWAYS drawn ANTI-CLOCKWISE!!

circlular arc
In the example below I have specified the centre with point 1, the radius and start of the arc with point 2 and the end of the arc with point 3. Notice that the arc is drawn anti-clockwise from point 2.

elliptical arc
Drawing an elliptical arc is the same as a full ellipse with the addition of the start angle and end angle. In this instance I have specified the ellipse using the centre (point 1) and the end of that radius (point 2) to define the slope, and the end of the other radius (point 3) as before.
The additional information to draw the actual elliptical arc is given in points 4 and 5. Again, in an anti-clockwise direction.

Exercises

Shape
Draw the shape below which consists of a number of lines and a semi-circle. You do not have to insert the text at this point in time. We will cover text next.
The drawing consists of the details of the small piece of wood you could find on the bottom of a wooden window put there to help guide the rail water away from the wall.
You will have to consider where to start on this shape. You could try to draw the straight parts in on polyline and then inser the semi-circular arc. But you will have to work out the end points of the slope. It will probably be easier to leave the semi-circle till last.
When we cover snap features you will wind it much easier to positionparticular parts of an object.

For ease of calculation position the lower left corner of the drawing at 0,0.
Door
Draw the shape below which consists of a number of rectangles and an arc. You do not have to insert the text at this point in time. We will cover text next.
The drawing consists of the plan of a typical door you might find in your home. The centre of the arc needs to be fixed at the point where the rectangle of the door and the rectangle of the frame, where you normally find the hinge. The included angle of the arc is 90 deg.

You can complete the drawing using only rectangles and an arc. There are many ways of positioning each component which we haven't covered yet. So for now you can determine where to position each component point by using a combination of absolute and relative coordinates.
For ease of calculation position the lower left corner of the drawing at 0,0.