Last time, we considered the method of showing a proper shadow cast from a light source which is behind the viewer.  This lesson today will demonstrate the opposite situation, where the light source is before the viewer.

Andrew Loomis in his book Successful Drawing shows us the method of solving how to draw shadows in proper perspective.  The first point which needs stating is a concept hinted at from 2 postings past, which I hope to make concrete by the end of this lesson.  The aforementioned idea is that if the light source is Behind, the angle of light is below the horizon.  When the light source is before the viewer, the angle of the light is above the horizon.  Hold onto this thought, and I will review it at the end of the lesson, where I am sure it will form an integration for you.

Here are the steps for casting a perspectival shadow from a light source which is before.

1. Set up your horizon and the object using proper perspective.  Establish the Vanishing Points for the object’s sides, and draw the appropriate angles.  Draw the guidelines for the perspective on a separate layer of vellum or digitally, then remove the guidelines when the object is perspective. Save the layer.
2. Since the light source in this exercise is before the viewer, it is proper to next establish the position of where that light is coming from specifically.  This should be done with precision within the layout phase of your drawing.  Even if the light is not going to be within the boundaries of your finish crop for the illustration, you must lay it out with exact placement, or else your shadows will appear unconvincing.  Drop a line vertically down at 90 degrees from the centre of the light source to the horizon line.
3. The point where the vertical line crosses the horizon will be the VP of the shadows. This is a crucial step, so pay close attention to it.  As a rule, the Vanishing Point of shadows is directly below the light source when the light is cast from a Before placement.  The blue lines below represent the projection for the  Shadow VP.  Please not that these guidelines cross through the corners of the object you are drawing, laying on the ground plane.
4. Next we will cast the lines of light, which will fall like a triangle from the light source.  Each corner of the object you are drawing will interrupt the light, but the perspective you have chosen may conceal certain corners.  In this drawing there are 3 corners which will cast a shadow we can see, so there will be 3 lines.  If your object and perspective yields more corners which will cast a shadow, use the appropriate amount of lines.  Note how the light lines emanate from the centre of the light source, not its perimeter.  Cast the light lines further than where the Shadow VP lines lay on the plane.
5. Now, turn on the layer with the original perspective lines showing.  These perspective lines will give us the other half of the information we ned  regarding where the shadow’s perimeter will lay.
6. Where the red light lines cross either the blue Shadow VP lines or the black object perspective lines with demarcate the corners of the cast shadow your object will make, given the perspective you have chosen, and the placement of the light source.  I have numbered these 1-4.  Numbers 5 and 6 are the points where your object touches the plane it rests on, and from these points the shadow will originate.
7.  Outline the cast shadow perimeter, then fill it in with the value appropriate for the light intensity you are describing.  The darker the shadow, the brighter the light.  Add half-tones to the shaded sides of the object (the sides facing away from the light) Flat planes have even shading, curving planes will appear as a gradation.
8. Remove the guidelines to reveal your illustration of a properly done shadow, in perspective, with the light source before the viewer.  Congratulations!

As a last comment, think back the the idea of the angle of light above and below the horizon which I mentioned at the beginning.  If you think about it, it is natural to recognize that the angle will come from above when the light is before, because when standing on the earth, you perceive the horizon above you.  If the light is coming from behind, the angle must come from below for the same reason.  It is possible, tho rare that one’s point of view can be distorted, such that the horizon is perceived as below you.  This could occur if you are inverted or suspended in the air.  Such points of view will break this rule.  Luckily, there are limited calls for illustrations of that type.  I will cover such considerations at a much later date, due to their peculiarity.

There are many more subtleties related to cast shadows, but I believe I will go onto showing organic cast shadows in perspective next week.  It will be a difficult one!

Drawing the ‘Laying Square’

Technical Perspective Continued

Last posting quickly outlined the principles of one point perspective.  The key points included:

1. Every picture has a horizon
2. An object’s relationship to the horizon creates the illusion of a perspectival view of the scene to the viewer
3. The vanishing point is the point where a viewer’s sight is limited to

The previous posting used a simplified fir tree as the subject.  It is true that every picture has a horizon and involves the vanishing point, but it must be mentioned that natural phenomena, such as mountains, rivers, trees and bushes, are all very forgiving regarding perspective.  These forms are organic and do not involve straight lines, and furthermore, viewers will accept a very wide range of sizes and shapes in their representation.  This aspect of the inanimate, natural phenomena makes landscape painting and drawing much easier than works which involve architecture, humans or animals.  Traditionally, landscape painting has been considered the third lowest form of painting on account of the relative simplicity of the pursuit.

This posting will outline the fundamentals which lead to understanding how to draw geometric shapes in perspective.

As mentioned before, the initial step to drawing a geometric shape in perspective is mastering the ability to draw a perfect square, appearing as if it were laying flat on an imaginary surface.  This challenge is essential for revealing how an artist begins to create the illusion of space within a drawing.

Andrew Loomis does not break this task down for us, and many artists will be able to do this, merely with their eyes.  I personally find it very easy to draw a perfect square laying on an illusionary ground on any angle.  This is because I can visualize the correct placement and degree of the angles from the years of experience which I have integrated.

For the sake of the artists who do not find this easy, I have devised a simple method of finding the correct angles needed to draw a laying square from any position of perspective.

The Lesson

• Draw a horizon, and keep it towards the top third of your paper.  Every drawing has a horizon.

• This time, we will use 2 Vanishing Points.  Place them far apart.  Putting the V.P.’s too close together will create distortions in your perfect laying square.  The left hand V.P. will be “a”, the right hand V.P. will be “b”.

• Now, we draw a line at any angle from V.P. ‘a’, such that it crosses an imagined point between your two V.P.’s.  This line we will call the First Line.

• Now we will repeat the previous step, but this time using a different angle of trajectory.  We will call this line, Second Line.

• Now, for the next step, we measure 3cm from V.P. ‘a’, down the horizon line.  This point we lightly mark for reference.

• Using the 3cm mark as the starting point, measure the distance to the First Line, in a perpendicular to the horizon.  This will create a right triangle between the horizon, the First Line and the perpendicular measured.  In my drawing, the distance happens to be 2.5 cm.  This is not a set measurement, and it will always be different depending on the angle which the First Line was drawn at.

• The next step is to duplicate those points with exact measurements starting with V.P. ‘b’.  This will create an equal, but reversed right triangle with V.P. ‘b’ as the first vertex.

• From V.P. ‘b’, draw the Third Line, using the newly drawn low vertex point as the angular guide. Draw this Third Line such that it crosses through the First and Second Lines.  The crossing points with the First and Second Lines we will call Crossing ‘x’ and Crossing ‘y’.

• Measure the distance between Crossing ‘x’ and Crossing ‘y’.  My drawing happens to be 4.6 cm.  This measurement is relative to the angles of the First and Third lines, and is therefore not a constant measurement.

• Now, we measure that same distance up the First Line, from Crossing ‘y’, towards V.P. ‘a’.  Mark the point.  Again, my measurement of 4.6 cm is particular to my drawing.

• Draw Fourth Line back from that point to V.P. ‘b’ to complete the perfect laying square.

A Quick Way

There is a quick way to skip essentially from step 2 to step 8, but it involves having a tool with a set 90 degree to trace from (such as a drafting triangle or a t-square).  I will outline it here for those with such tools.

•  Draw horizon.  Choose vanishing points

• Measure length between the two V.P.’s, and half that number.  Measure that distance  over from one of the V.P.’s to find the mid point between them.

• Drop a 90 degree line down from the centre point, perpendicular to the horizon. Call this point the Centre Vertex
• Draw First and Third Lines from that point to either V.P.’s.

Drawing the Second and Fourth lines will work the same way if you choose a point above or below the Centre Vertex to create different angles.

Conclusion

Now with a laying perfect square in perspective, it is a simple thing to draw the perfect cube from the groundwork we have lain.   We will complete this 3 Dimensional cube in the next posting.