Principles of Orthographic Projections: Lines and Planes in Descriptive Geometry

Line Projections in Descriptive Geometry

Oblique Line Projections

For oblique line projections, both the horizontal projection (r1) and the vertical projection (r2) intersect at the reference line (LT).

Frontal Line Projections

A frontal line is straight and parallel to the Vertical Plane (PV). Its horizontal projection (r1) is always parallel to the reference line (LT).

Lines Parallel to the Reference Line (LT)

For lines parallel to the reference line (LT), both horizontal (r1) and vertical (r2) projections are parallel to the LT.

Vertical Line Projections

A vertical line is perpendicular to the Horizontal Plane (PH). Its vertical projection (r2) is perpendicular to the reference line (LT).

Edge View Projections (Perpendicular to PV)

When a straight line is perpendicular to the Vertical Plane (PV), its vertical projection (r2) appears as a point. Its horizontal projection (r1) is perpendicular to the reference line (LT).

Profile Line Projections

A profile line is contained within a profile plane. Both the horizontal (r1) and vertical (r2) projections of the line are perpendicular to the reference line (LT).

Special Lines Within Planes

Horizontal Lines in a Plane

A horizontal line within a plane has its horizontal projection (r1) parallel to the horizontal trace of the plane.

Frontal Lines in a Plane

For a frontal line (a1) within a plane, its horizontal projection (r2) is parallel to the horizontal trace of the plane.

Line of Maximum Slope (Gradient Line)

The line of maximum slope (a2) within a plane forms the largest angle with the Horizontal Plane (PH). Its horizontal projection (r1) is perpendicular to the horizontal trace of the plane it belongs to.

Line of Maximum Tilt (Steepest Line)

The line of maximum tilt within a plane forms the largest angle with the Vertical Plane (PV). Its vertical projection (r2) is perpendicular to the vertical trace of the plane it belongs to.

Plane Representation and Classification

Fundamental Principle of Plane Membership

For a line (r) to belong to a plane (A), its horizontal trace (H1, H2) must lie on the horizontal trace (A1) of the plane, and its vertical trace (V1, V2) must lie on the vertical trace (A2) of the plane. Similarly, for a point (X) to belong to a plane, it must be possible to draw a line (r) through X that also belongs to the plane.

Types of Planes

• Vertical Plane Parallel to the Vertical Plane (PV)

  Its horizontal trace (A1) is located below the reference line (LT).

• Horizontal Plane Parallel to the Horizontal Plane (PH)

  Its vertical trace (A2) is located below the reference line (LT).

• Oblique Plane

  An oblique plane (A1) is a general plane not parallel or perpendicular to the projection planes.

• Profile Plane

  A profile plane is perpendicular to the reference line (LT).

Projecting Planes

Projecting planes are named based on the projection they contain. They are planes that contain all the projections of a given object or element.

• Horizontal Projecting Plane

  A horizontal projecting plane is perpendicular to the reference line (LT). Its vertical trace (A2) is perpendicular to LT, and its horizontal trace (A1) is also perpendicular to LT.

• Vertical Projecting Plane

  A vertical projecting plane is perpendicular to the reference line (LT).

Bisecting Planes

• Bisecting Plane Parallel to the Reference Line (LT)

  This plane contains two parallel projections to the reference line (LT).

• Planes Containing the Reference Line (LT)

  These planes contain the reference line (LT). To define them, an additional point is needed.

• First Bisecting Plane (Perpendicular to the First Bisector)

  Its traces are perpendicular to the reference line (LT) and are equal in length.

• Second Bisecting Plane

  Its traces lie on the reference line (LT).