1: In the demonstration on 2PP you where shown how to layout the plan, elevation and where to position the picture plane & horizon. In a 2PP the height of the horizon is as a rule sited within the height of the object.
2: Where the 3PP differs from the 2PP is primary in the height of the horizon. However, if the object is not very high and rather wide, and the horizon is drawn above or below the object, it maybe better to treat it as a 2PP. The main reason being that the regression of vertical lines will probably be too small to warrant the effect.
3: Here we see a typical artistic 3PP where the 3rd vanishing point is positioned by eye to create a perspective that will probably emphasize an aspect of the design. But if you wish to take it further and create a real 3PP we have to do more than that.
4: Lets start this demo by looking at how we see ‘things’. Suppose you where sitting on an upper floor and looking out the window at an office block across the road. This is probably similar to what you would see.
5: Then if you went to the window and took a photograph looked up at the same office building, we would see how the perspective changes. The vertical lines appear to get closer the higher they go and the floors become lower.
Note 1. 
6: Then if you took another photograph looked down on the building you would see the opposite. Obviously, it is not the building that changes, but the way we look at it. So, lets look at how this happens.
7: Here we are across the road opposite the 50th floor. Our line of vision is at 45 degrees and the picture plane is set-up perpendicular to that. A construction line is drawn from the viewing point (eye) to each floor. Where those lines intersect the picture plane a reference point is made that indicates the level of each floor in perspective.
8: Now lets return to our office and make a copy of those floors from the building across the road.
9: Because the picture plane was anchored at the floor line of the 50th floor, we know that that line is to scale. So we can use it as the start to the regression and all the remaining floors will diminish in size to match the projection lines. In this example the line of vision is placed in the center. Then VP 3 is positioned at the intersection of the regression line and the line of vision.
10: Before we move on lets see how to map the regression. Because the line A-B is the anchor of the picture plane it is to a true scale. To get the ratio of how the above floors will be affected by the regression we set-up a base line A-C. Parallel to that draw a construction line from the intersection of each level & the line of vision. The path of the regression line are those points where each construction line intersects the projection lines.
11: With VP 3 in place, the vertical lines (columns) can be added. That is basically the method used to determine the position of the third vanish point. Before looking at how to draw a 3PP we need to look at a few variations and options you have when plotting the VP 3.
12: Firstly, the line of vision can be positioned anywhere. However, it is advisable to link it to a point that is related to the object or a point that can be measured. In fact there may well be times when the line of vision is beyond the side of the object. But in all cases VP 3 will be linked to the line of vision and always be on the horizontal line.
13: Here we have an example similar to the pervious where instead of the line of vision being +45 degrees this is set at –45 degrees. (Looking down)
14: Except for the fact that VP 3 is now below the object the methods used and result is much the same
15: In this example the viewing point (eye) is further from the building, and the line of vision has been reduced to 15 degrees. The picture plane is always perpendicular to the line of vision and in this case is linked to a set point on the building. Then as with the previous example the construction lines are added and the projection levels are drawn from the intersections.
16: In this example the picture plane is not linked to the building. Moving the picture plane closer to the viewing point will reduce the size of your 3PP but will not change the regression to VP 3. The picture plane can be moved forward or backward, and, if need be can be moved beyond the building or object.
17: Here we have to result of how the diminishing projected line create a regression line to VP 3, which is ‘off the page’.
18: When comparing the two results of the 45-degree 3PP (Near) & the 15-degree 3 PP (Far) we can see how much they differ from each other. Furthermore, it is important to know the exact position of the third vanishing point. Using the artistic 3 PP will be useful when drawing a comparatively simple object. But when you are doing a complex or mutable objects it will become difficult to coordinate the variations.
19: To demonstrate how to do a 3PP of a building, we need the Plan and Elevation. Both must be to the same scale. Because this example is relatively simple in design one elevation will do the job. However, in more complex projects 2 or more elevations may be required.
20: Here the viewing point is at a set distance.The focal point has been set at top of the base structure on the elevation line. Centred on the focal point an arc is drawn from the base of the building to the upper structure. This will create 2 equal portions to plot the regress to the third VP. From the viewing point a construction line is drawn to those points. Where the construction lines intersect the picture plane 2 projection lines are drawn.
21: On the right a copy of that portion of the building was made to plot the regression. The diminishing ratio is applied to each copy to match the projection lines. Once the regression has been plotter a parallel line is drawn from the viewing point to the elevation line. VP3 is at that intersection.
22: This is an example of how the regression can be plotted by projecting the floor levels as per previous examples. Both methods will produce the same result.
23: Once the regression and VP 3 has been set-up the viewing point can be raised or lowered to suit. The horizon is always at eye level (viewing point). Here the horizon is set at the forth level and VP 3 will be moved up by the same dimension.
24: Here is how you layout your desktop. On the side of your working drawing (WD) place the elevation. Add the
horizon &
viewing point. Perpendicular to the
horizon add the
line of vision to the plan placed above your WD. Rotate & position the plan to suit. It is advisable but not essential to link the line of vision to a point on the plan. In this example that point it has been set-up on the 2nd column. Add the
picture plane perpendicular to the
line of vision.
Note 2. 
25: With the layout complete you need to set-up the VP’s. Parallel to horizon move VP 3 to line of vision. Parallel to the face of the building draw a construction line from viewing point to picture plane. Do the same on the other face. Thereafter, drop those 2 points to the horizon. These points are VP 1 & VP 2.
26: Okay, lets start the 3PP. We will do this in stages so you can see how it is done step by step. From the
viewing point draw a
construction line Note 3. to the corners of the building. If the point is in front of the
picture plane, extend it to the
picture plane. These points are referred to as being the
PP intersection. (PPI)
27: From the PPI, draw a perpendicular line to the horizon. Referred to as the H intersection. (HI) In a 2PP these lines would be vertical lines to your object. However, in a 3PP the lines are linked to VP 3 to create that diminishing affect.
28: From the HI, add a construction line to VP 3. In a 3PP these are the vertical lines to your 3PP.
29: Next we need to determine the height of theses columns. From the viewing point draw a construction line to the column top on the elevation line. Where that line intersects the picture plane add the horizon projection line. This is intersection is referred to as the being elevation intersection. (EI) Then do the same to the base of the column.
30: The height of the 2nd column is where the 2 projection line intersect the line of vision. Referred to as (VI). Next we have to set-up the regression to VP 1 & VP 2. From the 2 VI draw the construction lines to VP 1 and VP 2.
31: With all the construction lines in place, the 2nd column can be drawn. Thereafter, extend the VP 1 construction lines to the 1st column and draw the construction lines to VP 2, and draw column 1.
32: Now lets return to the remaining columns and do the same. From the viewing point draw a construction line to the building corners.
33: From the picture plane intersections add the perpendicular line to the horizon.
34: From the horizon intersections, add a construction line to VP 3. Then extend them to base regression lines and draw the outer face of the columns.
35: Then add the regression lines to the sides of the columns and draw the remaining faces.
36: Now we add some of the lateral structure. From the viewing point draw construction lines to the first floor slab on the elevation line and extend to picture plane. Then from the PPI add the projection lines and extend them to the line of vision. Because these are measured from the outer face of the column we have to add the regression to VP 2 to find the its true location on the inner face.
37: From those points on the inner face draw a construction line to VP 1. Thereafter, draw in the first floor slab and glass.
38: The same method is used to add the remaining floors. First add the construction lines from the viewing point to the structure on the elevation line.
39: Where they intersect the picture plane add the projection lines. Then add the regression to VP 2 from the outer to the inner face.
40: Then add the regression to VP 1 and draw the remaining floor slabs and glass.
41: With the lower portion of the building complete we need to add the upper portion. First set-up the construction lines to the right face of the building and add the PPI’s. The near corner to the upper portion is the far corner of the 2nd column. To this scale it is a little obscured.
42: Thereafter, draw the perpendicular lines and add the HI’s.
43: Next add the regression line from the horizon to VP 3.
44: To get the height of the glass front, draw a construction line from the top to the viewing point. Where it intersect the picture plane add the projection lines. Add the regression to VP 1 & VP 2, and draw the columns.
45: With the columns in place, add the floor levels and glass to the left face.
46: Finally, do the same with the right face. That’s it.
That is how to draw a real 3-point perspective.
