Constructing a Perfect Cube in 2-Point Perspective

Set up a Station Point and 2 Measuring Points.

Draw a vertical line parallel to the picture plane.

Draw a horizontal line the same length as the vertical line starting the base of the vertical line and extending to the left. This is a Foreground Measuring Line.

Draw another horizontal line the same length as the vertical line starting the base of the vertical line and extending to the right.

Draw a line from the Left Measuring Point (LMP) to the right-most end point on the Foreground Measuring Line.

Draw a line from the Right Measuring Point (RMP) to the left-most end point on the Foreground Measuring Line.

Draw 2 lines, one from the bottom of the vertical line to the Left Vanishing Point (LVP) and the other from the top of the vertical line to the LVP.

Draw 2 lines, one from the bottom of the vertical line to the Right Vanishing Point (RVP) and from the top of the vertical line to the RVP.

Draw a vertical line starting at the intersection of the line to the LMP and the bottom line to the LVP that continues until it meets the top line to the LVP. This is one of the visible vertical back edges of the cube placed correctly in perspective to form what would be a square face.

Draw another vertical line starting at the intersection of the the line to the RMP and the bottom line to the RVP that continues until it meets the top line to the RVP. The is the other visible vertical back edge of the cube, also placed correctly in perspective to form what would be a square face.

Connect the tops and bottoms of the vertical lines to construct the foreground vertical faces of the cube.

Draw lines from the bottoms and tops of the back vertical edges of the cube to the left and right vanishing points, respectively.

Assuming that the cube is placed below the horizon line, The visible horizontal face of the cube will be created by the intersection of the top lines receding from the back edges to the vanishing points.

The most distant vertical edge of the cube is placed between the intersection of the bottom lines receding from the back edges to the vanishing points and the most distant point of the visible horizontal face of the cube. This edge is not visible when the cube is opaque.