Inasmuch as we discuss about drawings in orthographic projections
or 2D drawings, the single most important feature of a CAD Drawing is the plane of the drawing. For an object of
Euclidean or non-Euclidean geometry being represented by a drawing, the plane
of drawing may cut across the object (Section
Drawing) or view the object from outside (View Drawing).
All drawings (sections and views) consist of sets of lines
(polylines, multi-lines, arcs, curves) that form closed/open figures at section/view.
These figures may be detailed by renderings
such as hatches and annotations such
as dimensions and texts. A set of figures along with necessary rendering and
annotation, used as an interchangeable unit constitute a block.
The figures on drawings/blocks can be distinguished into real
and reference figures. Real figures
such as walls, furniture, doors and windows represent objects that do exist or are
created in reality. The set of lines that form the real figure represent the edges of the real object in the plane of
the drawing. Reference figures such
as grid lines, centrelines, axes, dimensions, tables serve as references to
real figures and do not exist in reality. We shall make few observations about
real figures here.
- For a real figure as it represents a real object, any point on the drawing represents a point either inside or outside of the real object, in the plane of drawing. Hence, we shall postulate that all real figures are indeed closed figures (closed polylines or curves) as all real objects are bounded. Exceptionally, a real object may be represented by an open figure on a drawing if and only if one of the dimensions of the object is negligible by the scale of the drawing.
- An important corollary of this observation is that, when two real objects or figures interfere, there has to be an even number of points of intersections. As interference of two objects is a Boolean operation, this observation is equally valid for Boolean subtraction. Any cut-outs or openings thereof should also have even intersections with the real figure.
- Another significant observation about real objects is that, two objects cannot occupy the same space on a drawing, as it is in reality. This means that when two real figures meet, one of the figures needs to be trimmed to accommodate the other and the edges of the figures coexist at the interface.
- The plane of drawing is a fixed coordinate along the normal to the plane, hence in a way the edges of the real object represent the edges at that coordinate or elevation. Therefore, a real object can have only one set of closed edges, on a given plane of observation. Multiple closed or open edges represent themselves as duplicating/overlapping collinear lines, which does not have a corresponding mapping in reality.
- Foregoing discussion shows that two collinear lines can co-exist if and only if they represent edges of two different objects. This introduces an important imperative on drawing standardization – that different or discontinuous objects should be represented differently on the drawing. CAD drawings enable the differential representation by layers, line-types, colours and line-weights.
- A drawing may represent lines that are not necessarily on the plane of drawing (beneath or above the plane of drawing). Out-of-plane lines are of two types: hidden lines on view drawings and section drawings represent real edges that are invisible in the plane of drawing, and view lines on section drawings, also representing real edges that are visible from the plane of drawing. Although most draftsmen place hidden line on separate representation, they keep view lines in same layer/line-type/colour/line-weight as real figures.
- For same object, the layout of hidden and view lines depend on the plane of drawing. Consider the difference between architectural key plans, drawn just below of just above window sill levels. For plans drawn below sill levels, the sill lines are part of real figure, there are no view lines and lines on either side of the windows are hidden lines. For plans drawn above sill levels, the window side lines are part of real figure, sill lines are view lines and there are no hidden lines.
- For out-of-plane lines, hidden and view lines together constitute the closed figure. A view line may be closed by a hidden line and vice-versa. However, when the configuration of a view line or hidden line falls exactly on the real figure (that is the edge surface overlays on a different plane), it is conventional to leave the view/hidden line unclosed.
To summarize, following types of lines (polylines and curves
including) may be seen on a 2D drawing.
- Reference lines
- Closed real figure lines
- Open real figure lines
- Coexistent collinear edge lines of interfering objects
- Closed hidden lines
- Closed view lines
- Closed view-hidden lines
- Open hidden lines
- Open view lines
