Variable Perspectival Spaces within a Single Block

On page 43 of Successful Drawing, Andrew Loomis shows a very useful mechanic for artists to know in order to convincingly draw architectural details or features on mechanical objects in perspective.  This example demonstrates how to project a sequence of repeating sections, found within a whole, using a vertical and a horizontal scale. This is similar to previous lessons, but it expands the skill set so that the artist can draw repeating sections which are varied in sequence.  For example, imagine a condominium building in perspective.  The viewer can see the front of the building going off down the block.  This viewed side features a set of 4 windows, followed by  a portico with a double entryway in the middle, then another set of 4 windows.  Each of the openings of the windows need to be identical in size; but naturally, of a different dimension than the portico, which again is different than the two sets of double doors within.  This then is an example of Variable Perspective Space, Within a Single Block.

Let us begin.

Suppose you are an illustrator, and you are asked to draw the Egyptian temples at Abu Simbel.  Let us say that you are drawing the small temple, and you have (for whatever reason) a restriction as to the perspective you must use.  You search through the internet for reference, and let us say that there is nothing in the correct perspective which you need.  Short of traveling to Nubia, you cannot get a reference shot of the correct perspective.  This is how it is done.

Here is the small temple at Abu Simbeltumblr_nrqdlqhwMT1tkairwo1_1280

  1. Lay out the image in the angle you want, establishing the horizon and the perspective which you need to draw the site at.  This can be done with any angle of perspective that you wish.  2
  2. At the wide edge, establish the vertical and horizontal planes which will be used as your measuring lines.  (see last posting for further use of the horizontal and vertical lines as measurement guides)3
  3. Mark the VP and a new point, called the Measuring Point, just to the left or the right of the vertical scale.  The MP can be on either side, but it must be close to the vertical line.real4
  4. Now, looking at the reference shot of Abu Simbel, one can see that there are 5 different sections in the sequence of Variable Spaces.  They are as follows:
    • Green Bracket: we will call these the FRAMES
    • Red Bracket:  we will call these the NICHES
    • White Bracket: we will call this the PORTICO
    • Purple Bracket: we will call these the JAMBS
    • Blue Bracket: we will call this the DOORWAY5spaces
  5. Now, estimate the ratio of widths between the 5 spatial elements in the picture.  For simplicity, let us say that the Frames to Niches are a 1:2 ratio in width, and the Jambs to Frames are also 1:2.  (this means that the Niches are DOUBLE as wide as the Frames.  So too is the relationship between the Jambs to the Frames; the Frames are DOUBLE as wide as the Jambs).  Let us say the Jambs to the Doorway is 1:1.75.   Once you have established a ratio of the sizes by eye, decide upon a base unit for the Frames (since most of the ratios refer to these). We shall say the Frames are 2 cm.  Thus each section width is as follows:
    • Frames: 2cm
    • Niches: 4cm
    • Portico: 3.75cm (two jambs + doorway)
    • Jambs: 1cm
    • Doorway: 1.75cm
  6. Starting at the (0,0) point on the Vertical and Horizontal scale lines, lay out the measurements in the order that the sequence appears on the reference.  The full sequence is not measured in this example, in order to accommodate the size of the image, and readability.  In reality, one must layout the entire sequence on the horizontal Measuring Line.real5
  7. Through the points on the Horizontal Measuring Line, cast new lines of measurement to the MP (Measuring Point)6real
  8. The points where the cyan coloured Measuring Lines cross the bottom Perspectival Line will be the Variable Spaces on the monument, projected into perspective.  A secondary (red) line of perspective is cast to accommodate for the sloping nature of the temple’s face, i.e. it is not 90°. 8
  9. Erase the guidelines and the new temple is drawn in the new perspective. Finish it to the level of detail that you desire.1inal

In closing, I would like to apologize for not posting this on Sunday as per usual.  I hope you are able to use this technique of projecting Variable Spaces within a Single Block.  I also hope to see you next week.

Drawing To Scale

It is amazing how much information Andrew Loomis packs into each of the pages of his books.  His method of instruction is to constantly expand the uses of techniques outlined on previous pages.  In so doing, he also expands the learner’s set of drawing mechanics in a straightforward way.  For example, on page 39 of Successful Drawing, the method of depth by diagonal is elaborated upon, and here Loomis shows the reader how to use the technique in order to execute a scale drawing.  He says:

Every artist should know how to draw to a scale.  Scale drawings require the division of vertical and horizontal planes into square feet or square units. 

Let us then examine the method.

  1. We must first establish a vertical and horizontal measuring line, like an X and Y axis, where the lines touch at right angles at point zero.  Both lines must have equal division of unit, which represent feet in the drawing. The size of the unit which you use is done by eye.  A horizon line is established and the measuring lines are placed upon the scene.1
  2. From each of the ends of the measuring lines, and from point zero, lines are drawn to the VP.  Set the VP where you want by eye.2
  3. Now, a fourth Line of Perspective is cast to the VP, this time from the mid point (at the 5) of the vertical line.  This line is represented as a black and white dotted line in the example below.  We shall call this line the Halfway Line.3
  4. Next, gauge by eye the optional depth of the first foot of measurement along the low Line of Perspective going from the zero point to the VP.  4
  5. When the first unit is established, cast a Line of Perspective from point one on the vertical scale (yellow checker in this sample), as well as a second vertical line at the point where the first unit terminates (red checker in this sample).  This first square unit will represent one foot. 5
  6. Ascending diagonally from the  low near corner (point 0, 0), cast a diagonal measurement line (cyan coloured in this sample). Make sure it crosses exactly through the upper furthest corner of the first square foot.6
  7. Where this diagonal measurement line (cyan coloured) crosses the top Line of Perspective, draw another vertical down to the bottom Line of Perspective.  This is 10 feet deep into the image from point 0,0.  Cast Lines of Perspective (yellow here) from each remaining vertical measurement points to the VP.  Where the  diagonal (cyan coloured) measurement line crosses the many interior Lines of Perspective (yellow), additional vertical lines are drawn.  These represent 1 foot sections receding into the distance.8
  8. Next, draw horizontal lines on the horizontal plane, each at 90 degrees from every incremental foot measurement determined in step 7.  This divides the ground plane also into ten 1-foot sections in perspective. 9
  9. As in last week’s posting, cast a descending diagonal line from the top near corner of the vertical plane, crossing through the far mid point delineated by the Halfway Line (black and white line) on the plane.  This shows where the next ten foot wide plane will terminate.  10
  10. Draw the vertical for the twenty foot mark, and then diagonally bisect this new plane, from corner to corner (purple diagonal in this sample).  Where that diagonal line crosses the Halfway Line is the centre of the second vertical plane.   12
  11. At the centre point where the newly drawn diagonal (purple diagonal in this) crosses the Halfway Line, draw a new vertical.  This will show the point of 15 feet in depth, as it is exactly between the 10 foot and 20 foot markers. 13
  12. Repeat this process of descending diagonals from upper near corner through the Halfway Line, and ascending from corner to corner to determine as much depth as needed.  Each line that descends from top corner through the Halfway Line shows us 10 more feet in depth.  15
  13. Now suppose we were asked to place these two men of different heights, on the field 20 feet away from each other.  Furthermore, we want to place two Greek columns of equal height also on the plain, 30 feet away from each other.  We want to place the tall black man beneath the near column, and the short white man 20 feet behind, and 9.5 feet over to the left of the black man .  The black man is 6 feet tall, the white man is 5 feet tall, and the columns are 10 feet tall.  Frontier
  14. With this method of Drawing to Scale, the task is simple.16
  15. Erase the guide lines and add some shadows, and the task is complete.  Notice how the short white man looks proportionately still like a short guy -even way back in the field.  Because the perspective is correct, and our Intelligent Perception is so fine tuned to seeing people in distances, we can tell he is a small man even though he is not standing directly beside any reference point.  This is the power of perspective.  17

Thank you for reading this week’s posting.  I hope you will subscribe and learn more about Andrew Loomis by keeping up with this blog.

A More Precise Method

Previously in Understanding Loomis, I have shown several ways of determining depth by diagonals.  The method explained today is another method of finding depth by diagonal, but this one is a more accurate method than those previously covered.  Today’s method should be used when the illustrator is seeking to draw to scale; i.e. when he must divide the vertical and horizontal planes into square units for measurement in perspective.  The previously outlined methods are fine when the illustrator is seeking to represent visually realistic perspective, but when mathematical precision is necessary -as in the cases of scale drawings-  a more precise method is needed.

Today’s post will explain the method of laying out the precise division of vertical planes.  How this is used in the creation of scale drawings will be covered in the next posting.

  1. First establish the horizon and the V.P. for the first plane.  Cast perspective lines back from the VP to establish the height of the plane.  Determine height by eye.2 precise
  2. Establish the First Unit depth also by eye. This establishes a Base Unit Plane, which will be cloned in perspective.  Next, cast a new line from the centre point on the nearest edge of the Base Unit Plane to the VP.  This will bisect the plane perfectly in half.  We shall call this new line the Middle Line. 3 precise
  3. When the first unit is established, it is cloned by using diagonals.  Create a Vertical Line by bisecting the horizon at the original VP.  Make certain to draw the Vertical Line long enough to accommodate the diagonals which you will draw in the next step.  4 precise
  4.  Cast the first diagonal (green in this example) from the near bottom corner through the far top corner to the Vertical Line (the pink line in this example).  At the place where the (green) diagonal line crosses the (pink) vertical, make a secondary VP5 precise
  5. This step is where the method tightens up the measurement.  Cast a downward diagonal (yellow in this example) from the top near corner of the plane, through the point where the bisecting Middle Line (from step 2) crosses the midpoint on the far edge of the plane.  This line does not go corner to corner. Extend this downward diagonal far enough for it to meet the (pink) Vertical Line.  Mark a tertiary VP at the low crossing point.  6 precise
  6. Again, as in step 4, cast a new ascending  diagonal from the next bottom corner (where the next plane will be) up to the secondary VP marked on the Vertical Line in step 4.7 precise
  7. Where the ascending diagonal (green) and the descending diagonal (yellow) both cross the original perspective lines (red), draw a vertical line to indicate the depth of the second plane.  This will be a more accurate representation of the First Unit Plane’s width in perspective, than that which was shown in previous postings. 8 precise
  8. Repeat the procedure by casting ascending lines corner to corner, and descending lines from corner through the Centre Line to establish the further planar depths. 9 precise
  9. Erase the guide lines to reveal the four planes receding into the distance, with more precise perspectival depth.10 precise

Conclusion

Readers will have noticed that with the introduction of a secondary guiding point, i.e. the bisecting Middle Line, the illusion of correct perspective is tightened.  For the sake of interest, compare the planes of today’s post with the divisions of depth created with the earlier methods in previous postings.  You will be able to see the subtle difference by eye, and how this method creates a more accurate representation of repeating planar depth in perspective.  This is especially true in the perspectival plane sections which are shown far off in distance.  The previous methods tend to shorten the depth incrementally, such that the distant planar sections become much too close together.

Next week, we will investigate how to use this method of depth by diagonal to set up for the creating of scale drawings.

A Specialized Method of using Diagonals

This week’s posting will be a very straight forward one.  Andrew Loomis’ third example in this section of Successful Drawing shows how the artist can use diagonals to create a checkerboard pattern in perspective.  This is useful for drawing repeating windows of uniform size, or bricks on a wall receding into the distance.  The example I will use is of a brick wall.

This is how it is done.

  1. Create the perspectival plane which will be the brick wall.  Locate the Vanishing Point. Use any angle that you wish.1
  2. Divide the near vertical edge of the wall into equal separations.  The size you choose will represent how tall each brick will be.2
  3. Cast lines to the V.P. from the points indicated by the vertical spacing you created with the brick heights in step 2.  We shall call these lines the Brick Height Lines.3
  4. Here is where the diagonal comes in.  Cast a diagonal line from corner to corner on the face of the wall you are drawing.  The diagonal can go up or down. 4
  5. Where the diagonal (blue line in this example) crosses each of the multiple Brick Height Lines, draw a 90 degree vertical from the bottom of the wall to its top.5
  6. Repeat this at each crossing point, and the wall plane will be divided perfectly in perspective.6
  7. Erase the guide lines to reveal the wall.7

Uses

This method can be used for drawing multiple series of drawers, such as in a morgue or a bank vault, architectural or vehicular designs, it can be used as a grid for aiding the placement lettering or imagery on signage, or as a way of drawing bricks and checkers.

The diagonal is the key to being able to measure the depth of the sections.  Next week, I will explain how the diagonal can help in measuring, and thus correctly drawing a repeating panel section in perspective.

Thanks for reading, and I hope to see you next posting.