Perspective

Dividing a line into parts

• From one endpoint, draw a line creating an angle around 45 degrees.
• The second line is measured into the exact number of parts that is desired for the first line.
• From the endpoint of the second line (the one that is not the corner), draw a line back to the endpoint of the first line.
• From each measuring point, draw a line parallel to the third towards the first to intersect it.
• The intersections divide the first line in the desired amount of parts.

Dividing an object into equal parts horizontally.

• 2 point perspective
• Measure the equal parts on the vertical and then bring the lines back towards the VP.
• OR using a ruler, place the ruler so that it aligns with the top and bottom of the line to be divided. Align it with ruler measurements that fits with the amount of parts or a multiple of it.
• Vertically
• 2 point perspective
• Measure the equal parts on the vertical and then bring the lines back towards the VP.
• Then draw a diagonal and the intersection denotes where the verticals go.
• OR create a RP on the EL.
• Run the RP to both bottom corners of the wall.
• Project a horizontal line from the nearest bottom corner. This is a measuring line.
• The intersection of the reference orthogonal with the measuring line denotes one unit.
• Measure another unit on the measuring line.
• Bring the end of it back to the RP. 

To translate a point situated in a rectangle.

• 1 point perspective
• From the point, trace two lines pass both back corners of the rectangle to the EL making two RPs.
• To make the new rectangle, decide on where a corner of the rectangle will go.
• Then trace from the original corner to its new counterpart to find a third RP.
• Trace the other corners back to the third RP.
• From the new corner, trace back to the VP, and using the information, you can replicate the first rectangle.
• From the first two RPs, trace back through the back corners and the intersection is where the point will be on the second rectangle.

To translate a square.

• 2 point perspective
• Pick the closest corner of the square and trace back to both the VPs.
• Find the DVP. Trace from the first corner to the DVP.
• Decide on how long one side will be and then from there, trace back to the opposite VP.
• The moment you hit the DVP line, follow the other VP out. That's a square.
• With a square in place already, decide where a corner of the new square will be. From the old to the new, trace a line through to the EL. That is now a RP.
• Trace the old corners and from the first new corner, extend to both VPS. Now you have all the information to make the rest of the square.

To translate a height onto a slope.

• Translate the height to the edge in which the slope begins.
• Find the auxiliary eye line.
• Determine the x-coordinate of the desired location on the slope.
• Run a line from the height at the slope's edge toward the desired point.
• The intersection of the line and the auxiliary eye line is a RP.
• The RP will determine the height on the slope.

Building a cube with pre-determined measurements.

• 2 point perspective
• Have the closest corner and the vertical length for that corner.
• In ratio and relation to that line, draw a perpendicular line that extends to both the left and right side of the bottom end (for grounded cube).
• The lines should measure out to be the measurement for those sides.
• Find MPs for both VPs by measuring the distance of one VP to the SP and then marking that distance off on the EL starting at that same VP.
• From the ends of the perpendicular line drawn, go to the opposite MPs.
• From the bottom corner, extend to the VPs. The point at which it intersects the MP lines is where the sides end.
• Proceed as usual.

Diagonals can also show where a point's mirror point is on the other side of a rectangle. From the point, trace a line up to where it hits a diagonal, bring it over to the other diagonal, and then down to where it hits the orthogonal.

To find a DVP, you trace a 45 degree angle in between the 90 degree of the VPs from the SP. The DVP help to determine if a shape is a square are not.

Ellipses

• Major and minor axise always bisect at a 90 degree.
• The minor axis goes to the VP.

EL = Eye line

SP = Station Point

VP = Vanishing Point

DVP = Diagonal Vanishing Point

RP = Reference Point
MP = Measuring Point