Skip to content

Projection of a Plane -- VektorCAD Tutorial

This exercise shows how to draw the projections of a plane (lamina) using VektorCAD. You will build the XY reference, construct a true-shape polygon, impose the inclination to HP (theta) and the inclination of an edge to VP (phi), then generate the final top and front views.

What you'll learn

  • Constructing a true-shape polygon using the Edge method
  • Projecting from top view to front view (edge view on XY)
  • Tilting to impose inclination to HP (theta)
  • Rotating to impose inclination to VP (phi)
  • Obtaining final front and top views by intersection

Problem Statement

Draw the projections of a regular pentagon of side 25 mm, having its surface inclined at 30 degrees to the HP and a side parallel to the HP and inclined at 60 degrees to the VP.

Given Value
Shape Regular pentagon
Side length 25 mm
Inclination to HP (theta) 30 degrees
Edge inclination to VP (phi) 60 degrees
Condition One side parallel to HP

Objective:

Requirement Details
Commands used XYLine, UCS, Polygon, Line, Arc, Ray, Point, DimLin, DimAlign, Text
Construction lines Normal thickness
Final plane edges Thick thickness
Entity Snap ON throughout

Step-by-Step

1) Prepare Drafting Settings

  1. Set Line Thickness: Select Normal from thickness options (Thin / Normal / Thick)

  2. Entity Snap ON: Turn on snaps -- recommended: Endpoint, Midpoint, Perpendicular for accurate alignment

2) Draw the XY Reference Line

  1. From the Line dropdown, click XY Line
  2. Draw a horizontal line approximately 300 mm long

3) Construct the True Shape in Top View (Plane Parallel to HP)

Since the plane is initially assumed parallel to HP, the top view shows the true shape.

  1. Switch to Thick thickness
  2. From the Rect/Polygon dropdown, click Polygon

  3. At the prompts:

    Prompt Action
    Number of sides Enter 5
    Method Choose Edge
    First endpoint Pick a point below XY
    Second endpoint Enter @25<-90 (25 mm edge perpendicular to XY)

  4. Label the vertices a, b, c, d, e using Text

Pentagon

Note

The Edge method lets you control the exact position and orientation of one side. The pentagon is drawn with one edge perpendicular to XY for the initial construction.

4) Project the Initial Front View (Edge View on XY)

Since the plane is parallel to HP, the front view collapses to a line on XY.

  1. From each vertex (a-e), draw projectors perpendicular to XY upwards using Line (Normal thickness)
  2. Mark a' and b' on XY where projectors from a and b meet
  3. Optionally mark c', d', e' on XY for reference

Projection

Tip

When a plane is parallel to HP, its front view is always an edge view (a straight line on XY).

5) Impose theta = 30 degrees to HP (Tilt in Front View)

Rotate the plane about hinge a'b' so the surface is inclined at 30 degrees to XY.

  1. Click Line on the toolbar
  2. Right-click, choose Nearest, and snap on XY near c' for the start point
  3. At the prompt, choose Angle and enter 30
  4. Pick a point some distance away to finish the line

  5. Using Cutting Arc, transfer distances from the top view to the inclined line:

    Distance to transfer From To
    a/e to c' Top view measurement Inclined line
    a/e to b'/d' Top view measurement Inclined line

  6. Mark and label the new points along the inclined line

Inclined Pentagon

6) Draw Horizontal and Vertical Projection Lines

  1. From the Line dropdown, click Ray
  2. Enter 0 -- draw horizontals through a, b, c, d, e (top view points)
  3. Run Ray again, enter 90 -- draw verticals through a', b', c', d', e' (front view points)
  4. Trim excess rays outside the required intersections

HV Projections

7) Obtain the Top View After Theta

  1. Mark the intersection points of horizontal and vertical projection lines
  2. Label them a, b, c, d, e
  3. Connect with Thick lines to form the tilted pentagon (top view after theta)

Top View

8) Impose phi = 60 degrees to VP (Rotate Top View About AB)

  1. Click Line on the toolbar
  2. Right-click, choose Nearest, snap on XY
  3. At the prompt, choose Angle and enter -60
  4. Pick a point below XY to finish the line
  5. Using Cutting Arc, transfer distances from the tilted top view to the new line
  6. Mark points a-e and connect with Thick lines

Inclined Pentagon

Note

This rotation ensures the specified edge makes the required angle (phi) with VP while maintaining the surface inclination (theta) to HP.

9) Final Front View (After Both Tilts)

  1. From the new top view points a-e, draw projectors upward (perpendicular to XY)
  2. From theta-tilted front view points a'-e', draw horizontals

  3. Intersections give the final front view positions

  4. Redraw final edges in Thick:

    View Vertices to connect
    Top view a-b-c-d-e-a
    Front view a'-b'-c'-d'-e'-a'

Final Front View

10) Dimensions and Labels

  1. Switch to Normal thickness for dimensions

  2. Add dimensions:

    Dimension type What to dimension
    DimAlign Side length = 25 mm
    DimLin Vertical offsets from XY
    Angular Angle of surface with XY (theta, phi)

  3. Label angles and key points using Text

Dimensions

Result Checklist

Item Status
XY drawn (Normal) and labeled
Entity Snap ON; UCS positioned conveniently
True-shape pentagon drawn in top view with edge on XY (Thick)
Projectors built; initial front view lies on XY
theta = 30 degrees imposed: front view after tilt obtained
Back-projected top view after theta
phi = 60 degrees imposed: top view rotated about edge
Final front view obtained by projection
Final plane edges in Thick; all construction in Normal
Dimensions (side length, angles) and labels added

Variations (Practice)

Variation What to try
Hexagon Regular hexagon, side 25 mm -- repeat with 6 vertices
Equilateral triangle Side 40 mm -- simpler shape, fewer projectors
Swap order First set phi, then theta -- compare results
Perpendicular to VP Plane perpendicular to VP initially (true shape in front view)
Different angles theta = 45 degrees, phi = 30 degrees

Commands Recap

Command Purpose
xyline Draw XY reference line (Normal)
ucs Reposition origin near work area
polygon True-shape lamina in top view (Edge method, side = 25 mm)
line Projectors, reference lines, and final edges
ray Horizontal and vertical projection rays
carc Transfer distances using cutting arcs (impose theta/phi)
point Mark auxiliary points if needed
dimlin / dimalign Linear and aligned dimensions
text Labels and angle annotations
Format Normal for construction; Thick for final plane edges

Complete

You've completed the projection of a plane using auxiliary construction and rotation: clean final views in Thick with all supporting geometry in Normal for clarity. Export to PDF to verify and share.