Exploring Parallel and Angular Perspective

Some time ago, I took a weekend workshop in sketching led by an architect, which included a substantial section on perspective.  I have included some pages of mainly pencil notes from my sketchbook from this course below as log book evidence!   The course helped me to interpret any landscape and I have found that spending time looking around me to find my eye level and then considering the relative angles that the horizontal edges make with each other and to work out where various vanishing points lie can be a useful way to make use of time waiting for buses and trains… The following pages illustrate some simple points about perspective that I have tried to include in my drawings.  I am not always successful but I can usually see where I have gone wrong, even if I do not always go back and correct my mistakes…

We have a tendency when we begin to draw to draw things as we know them to be rather than as we really perceive them.  It is easy to misjudge the relative sizes of people and objects.  How trees or other objects appear to us from a distance and how other objects placed alongside them will appear, depends on where they lie in relation to each other as well as to ourselves as viewers. 



With regularly spaced trees or poles, the angles made by a line extending from the base of one tree to the midpoint of the next are equal when viewed head on but this angle becomes more acute when the line is viewed obtusely because the base line is no longer a horizontal line but tips up as it moves away from the viewer until it reaches their eye level.  However, the lines remain parallel and enable us to correctly space the objects in a drawing. All such lines meet at a vanishing point on our eye level. 



Buildings, boxes and other three dimensional cubic / cuboid objects have three vanishing points.   Edges below our eye level will appear to move up as they move away from us and those above our eye level will appear to move down.  Vertical edges will appear to move towards a vanishing point overhead. 



Circular objects such as wheels or formal ornamental ponds only appear as true circles when viewed from directly above, which is not usually practical for a pond!  Otherwise, they appear as ellipses.  Circles cause difficulty because the centre “moves” and has to be located according to our perception rather than in its actual physical centre.  The centre will appear closer to us and we will see more of the surface that is further away from us due to the angle at which we are viewing it.  Ellipses also occur in archways, bridge arches and other structures which describe a semi-circle or semi-ellipse.  All of this makes drawing a bridge, a bike or a series of arches a challenge!



In the drawings which follow, I tried to consider the above rules and often got into a muddle… I was supposed to begin with parallel perspective but instead drew things as the chances presented themselves.  For several days, I had a back problem that meant I could only sit bolt upright in a kitchen chair – hence, I drew the view through the kitchen door (see below), which involved using angular perspective. 

I started with a preliminary sketch in my A4 sketchbook using a sepia fine liner and noted various points about the angles and dimensions.  This was the first drawing made in an 18th century cottage with low ceilings and low doors, which seem wider than usual rather than shorter….  It took me some time to work out what the problem was….

The shadows from the banisters which are made by the light from the window behind them will also be moving towards their own vanishing point which must be somewhere between the drawing and me, and to my left.  

The door frame angles are underestimated in this drawing – this is addressed later on. 


                                                        28062012539 1


In the next A3 drawing made with a sepia artists’ lead, the door frame is still causing problems.  I am drawing from an angle but the frame is too square.  This can be seen in the smaller reproduction further in which the door frame has been redrawn in line with rules of perspective. Vertical lines are not very vertical…  The floor boards on the landing were confusing because they are actually flush with the doorway but the banister rail across the landing is not parallel to the door but actually at an angle of about 10 degrees from a line parallel to the kitchen door!  This was compounded by a rug on the floor that was not parallel to either!  Lots of pentimenti while I thought this one through… The lower door panels are not correctly drawn – their top edges should be angled slightly upwards, not downwards. Despite the odd perspective and untidiness, I like the light in the drawing below.  most of the surfaces are polished wood and there was a lot of reflected light from the window across the landing and from the kitchen light, and also a few corners of deep shadow.  

                                                              28062012541 2


I made one more attempt at this with a fineliner and the A4 pad.  The angle of the door frame is better judged this time but it is far too wide for its height… It It was after making this drawing that I decided to measure the door frame and find the width to height ratio, which I judged by a ruler to be about 1:2 but logically, this seemed unlikely.  I discovered that it was 1:2.25.  The misjudgement may have occurred because I was drawing the door frame incorrectly.  Because the angle wasn’t sharp enough, I interpreted the door frame as being much wider than it actually is and my own perception of the unusual door size (cottages have lower ceilings and smaller doors) also interfered with accurate judgment.   

                                                        28062012542 1



I drew a second view from the kitchen in this lovely old cottage into the hallway from a different angle. Here is the first drawing on A4 drawn without a ruler and making judgements about angles using a pencil and estimating the angles as times on a clock face. Looking at this again now as I log it, the eye level seems very high but I recall checking it at the time. Perhaps I wasn’t sitting properly… 

                                                01072012560 1              


I then redrew it paying attention to the adjustments noted on the page above: 


                                                 01072012561 1


I tried to check perspective and make corrections but it was difficult to do this accurately on an A4 pad with a 30 cm ruler… However, I had a go and then made the adjustments as judged necessary.  I clearly underestimated the angle made by the top and bottom of the door frame. 


                                                   01072012563 2  


The drawings this time appear to have door frames of more accurate dimensions but the door frames are still not correct so I have been adjusting the width to height ratio artificially because I was not really seeing the angles that the door frame make from where I was sitting.   

When I had access to a printer I printed out a smaller version and stuck this into my sketchbook.  I did the same for the sepia lead drawing, above, which is shown at the bottom of the page. I included a photograph taken from where I was sitting.  The light is poor but it shows the angles of the door frame clearly.






I now focused on parallel perspective.  The first drawing below is a view through a doorway into a bedroom.  I aimed to sit such that I was situated at the midpoint between the doorposts. All of the horizontal edges on the corners of the door frame, the rug, the cabinet next to the bed and the timber in the ceiling should be coming together at a single vanishing point at eye level.  The eye level is marked with an arrow to the left of the door.  I drew this in pencil and then went over the lines in ink to make them clearer to photograph.  I found it very difficult to judge vertical lines in an A3 format and these lines have been corrected and ruled.   The rug and the top and bottom edges of the door do not seem to share the same vanishing point…




I printed out a smaller version of this drawing in order to check its accuracy.  One thing that confused me was whether there are two vanishing points or only one.  I am still not sure…. Logically, it appears that all horizontal lines angled away from me should meet on the eye level at the midpoint within the doorframe.  However, the door is in front of the door frame and it appears as if its top and bottom edges are angled towards a vanishing point outside the frame…  If this is not the case, the door must be projected towards the viewer at a much sharper angle and must appear much larger than it does in this drawing.  This would be a distortion, it seems to me and not accurate at all.  So what is the answer?   One VP or two?   Parallel perspective looking through the door but angular perspective for the door itself?  This seems logical but I may be wrong.  I have looked in some books on perspective but have not so far found a drawing that helps answer this question.  

I made two copies of the drawing.  In the first, I identified the vanishing point(s) and drew lines to check the accuracy of the drawn lines.  The ceiling timbers were mainly OK but the front of the rug was too short and I had over-estimated the length of the door.   I redrew the lines in black pen on the second copy and added the door panels that for some reason I had omitted from the initial drawing.  While drawing the panels, I had the sense that the vertical edge of the door was not vertical.  Having check the width of the door, it seems to be OK.  Hence the gouache on the second copy! I also realised that I had used the wrong vanishing point (assuming there are two…) for the lock.  However, when I tried to alter this it didn’t seem right so I will have to investigate this further. 






I did a further study of parallel perspective in the Naumburger Dom.  I drew the north aisle and got into a mess trying to judge the distances between the arches and bring the pillars down to earth in an orderly fashion.  The bases of the pillars were not in a line but I misjudged and overestimated the misalignment..  I erased some pencil lines and redrew. The pillars are leaning inwards! Finally, I added some Ecoline to distinguish shadow and lighter areas.   




I liked the colours so I then redrew this a simplified version in an A5 watercolour sketchbook in order to work with the colours in a more subtle way.  They are a bit brighter in the original than they appear in this scanned copy! 




Subsequently, I have made many drawings in A4 and A5 formats in which I have attempted to tackle issues of perspective.  Below are some of the drawings made recently. Typically, when out and about, I use a black fineliner. I carry a water-soluble version for when I want to add a wash, and an insoluble one if I expect to add some sort of colour wash later.


Two views from opposite sides of an old stone doorway drawn at the monastery in Memleben in Thüringen. 







Below is a view of the interior of the parish church of St Lucia in Flemmingen near Naumburg, which dates from the middle of the 12th century.  It is an intimate space containing recently restored frescoes, which was my reason for visiting it.  I sat up in the lower gallery to make the drawing of the interior viewed from above.  I was sitting to the left, which I think is clear from the position of the arch but it was difficult to judge the angles of the side galleries in relation to the arch.   The angel on the altar front left is slightly too large.  I am quite pleased with the overall impression of altar detail without much actual detail…  I added the red colour to give an indication of the presence of the frescoes. Following the sketch is a photograph of part of the archway. 





In the drawings below, I attempted to address the problem of drawing arches.  These are not recent drawings but were made during the past two years during sketching excursions. The first is of the cloister in the Bonner Münster.  This structure is quite complex because there is ceiling vaulting and arches through the cloister which are perpendicular to those running around it.  I used a coffee wash to represent the colour of the stone. I attempted to incorporate atmospheric as well as angular perspective. From memory, I spent about 90 minutes on this, trying to place the arches correctly…  



The next drawing is of the remains of the Romanische chapel in Burg Are above Altenahr in Rheinland Pfalz.  The difficulty here was in depicting the arches meeting at 90 degrees to each other and extending in these two directions and then one arch “disappears” into the rock….  It is not entirely successful – one arch has been foreshortened a bit too much and appears squashed perhaps because the top of the pillar on the left is placed too low. 

                              Burg Are



This drawing is of the cloister in St Anthony’s Basilica in Padua, Italy.  I am quite pleased with the overall structure of the arches although the windows look a bit random but even they diminish in size with distance from the viewer.  This was drawn with a water-soluble pen and a wash was applied. 



There is a further example of a bridge in an earlier post on plotting space through composition and structure.  Further use of perspective will be evident in the documentation to follow on drawing townscapes.  


To remember in future drawing… 

  • Start with the eye level.  Note it carefully and mark it unobtrusively on the drawing.  Even consider drawing a horizontal line lightly in pencil across the drawing (a town planner I met recently does this on all of his drawings).  
  • Vertical lines are difficult to draw freehand but can throw off an entire composition if inaccurate.
  • Angles of objects close to the viewer are often sharper than at first perceived and must be carefully measured.  It can help to think of the “edges” as being distances from eye level rather than a certain distance from the viewer. 
  • Rulers are useful for guidance in drawing straight edges but too many ruled lines can give a drawing a technical rather than artistic appearance.  Taking care and time over a drawing might eliminate the need for overuse of rulers.
  • Thinking of angles as times on a clock is a useful way to judge them. 
  • Angles  become closer to the vertical the further a (in reality) horizontal line lies from the eye level.  




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