Class 2
Horizon Lines and Vanishing Points

In nature, the horizon line is where the sky and ground  meet.

But where is the horizon in pictures that have neither sky nor ground?  How do you find it?

The horizon line is eye level of the observer (and think of the “observer as the artist or photographer making the picture, not the person looking at the finished art).

Eye level is just that—it’s the straight line going from the observer’s eyes.  And as the observer looks up or down from a standing position, the eye level remains the same, but the picture plane (remember, this is basically the canvas or drawing paper) changes.

If the observer is looking straight out, the central line of sight is directly in the center of the cone of vision, so he can see equal amounts above and below the horizon line, and the horizon line is consequently in the center of the picture plane.

If that same observer were looking down, he’d see mostly ground and less sky, so his central line of sight (what he sees) would change and the horizon line would be up high in the picture plane.

If he were looking up, the opposite would be true. He’d see mostly sky, and the horizon line would be down low on the picture plane. So eye level determines the horizon line, but the central ray determines where that horizon is situated on the picture plane.

Vanishing points are tricky because they seem easy to understand, but difficult to place once you get to the drawing board.

If your vanishing points are too close together, your object will be too foreshortened and will appear distorted. Too far apart and the object appears too flat. So how do you determine where to put them?

In fine art, it really comes down to sketching the object roughly, then sharpening the lines and finding precise vanishing points to relate everything to from that point.

However, in some circumstances you can make a “plan” using the parallel pointing method by drawing a bird’s eye view of your set up, which will relate the object to the viewer and show you where the vanishing points fall.

This system will help cement in your mind the concepts of “picture plane,” “observer” and “object” and how perspective ultimately depends on the observers point of view.

Start your plan with a top view of the object, a line to indicate the picture plane, and a viewer standing in front of the object. Draw a line from the viewer’s eyes to all of the corners of the object.

Make a dot wherever those lines intersect the picture plane.  Next, draw lines that are parallel to the two sides of the object starting from the viewer’s eyes once again.

Where those parallel lines intersect the picture plane are the vanishing points.

Transpose those distances to a measuring line to determine their relative distances in relation to each other, and now you can draw your box in perspective by placing the vertical line and sides where they should be (you’ll need to guess at the height), then angling the sides through the vanishing points.

Those relationships are going to be the same no matter what vantage point you use; above or below the box.

So you can use the same vanishing points to draw the box anywhere on that vertical plane.

Class 3
The Three Kinds of Perspective

There are three kinds of perspective: one point, two point, and three point.

Each type derives its name from the number of vanishing points used for the object.    One point perspective is a head-on view of an object.

The vertical line is in the center, which is the same as the vanishing point, so all the sides converge to that center line.

If the line of the horizon shifted up or down (in other words, if the observer stands in the same place, but at different heights), the vantage point would change and you  would be looking down, into, or up at a box, but as long as the vanishing point is in the center, the box will remain  in  one-point perspective.

In two-point perspective, you can see two sides of a box converging to two separate vanishing points on the horizon line. Depending on how far apart the vanishing points are, the angle of the box will change and look either accurate or distorted.

Vanishing points that are too close together will make the front angle of the box too narrow and the resulting box unrealistic.

So before you mark your vanishing points, move your ruler to different angles to see what the sides will look like at different steepness.

You can easily change the vantage point of a box in two-point perspective. Just as in one- point perspective, the vantage point changes as the observer moves vertically up or down, but stands in the same position in front of the box.

Therefore, to change the vantage point of the box, just extend the vertical line, choose a new height, and use the same vanishing points to draw the box either above or below the first one.

You will then have a box from head-on, worm’s eye view, and bird’s eye view (or approximations of those).

Three-point perspective is looking up at a tall building (or down at something tall). In either case, the sides will converge to points on the horizon line as in two-point perspective, but the vertical lines will appear to converge to a vanishing point on the vertical axis as well.

From bird’s eye view, the vertical vanishing point will be far below the object; from a worm’s eye view, the vertical vanishing point would be far above it.

The principle is the same as the above situation in one and two-point perspective where the observer was standing in one place but moving up or down and so changing his point of view of the box; the only difference is that in three point perspective, the objects are tall enough that an observer below or above them would get a sense of vertical convergence or diminution as well.

Class 4
Techniques for Depth

Perspective is based on principles of geometry, one of which is that you can find a midpoint of any square or rectangle by drawing the diagonals and marking where the two cross lines intersect.

Using this principle, you can accurately place lines of objects that are diminishing in either vertical or horizontal lines.

If you have two posts running alongside a
railroad in one point perspective, you can determine the rate of diminution by drawing two guidelines for height that converge on the paper.

Place two poles within these height guidelines to mark how far apart the remaining poles will be, then treat those poles as two sides of a square and run diagonals from corner to corner  to find the midpoint.

Run a line from the midpoint to the vanishing point, and you now have the midpoint for every pole in that plane.

So to find the placement of the third post, draw a line from the top of post one through the midpoint on post two.  Where that line intersects the bottom guideline for height is the starting place for the third post.

Use a triangle to place that vertical line, and repeat this process for the remaining posts. Remember too that as colors and contrasts retreat in the distance, they lighten. In other words, the closer you are to objects, the brighter colored and higher contrast they are.

If you’re drawing irregularly sized or spaced objects, you can’t use the diagonal method. Instead, use the measuring line system to determine placement.

Begin with your shape drawn in two-point perspective and mark down the vanishing point, then draw a measuring line that extends outward from the lowest corner of the face.

On the measuring line, make hatch marks wherever you want the lines to be on the shape, and be sure to finish with a hatch mark that relates to the far corner of the shape.

Connect that hatch mark (it will be the farthest point on the measuring line) to the corner of the shape, and continue that line up to the horizon line to find the special vanishing point for the remaining hatch marks.

Connect the remaining hatch lines to that special vanishing point on the horizon line and make vertical lines on the face of the shape at those points where the hatch mark lines intersect.

You can also use the sliding ruler technique to find depth, determine height, and place objects on a larger shape (such as individual books on a block of books).

Draw a shape in two-point perspective, then run the ruler back and forth until you find a place anywhere on the shape that is evenly divided into the number of pieces that you need.

Run each tick mark through the vanishing point to complete the lines in perspective, and if you need vertical lines, draw a diagonal line across the shape and make vertical lines at each intersection.

You can use the sliding ruler method on vertical or horizontal planes; the only difference will be the direction of the vanishing point.

You can also apply this method in cases where you have objects retreating that aren’t evenly spaced.

For example, draw two lines that intersect and within the confines of those width guidelines, draw a table.

Draw a line for the beginning of the second table, and use diagonals to determine where to end the second table by extending the diagonal line to its vanishing point on the horizon line.

This is now the special vanishing point for all of the diagonals of the tables, so run a diagonal through the second table to this vanishing point to find the far end of the second table.

You can use the same system to draw a line of horizontal objects; the only change will be that the special vanishing point lies on a vertical line instead of a horizontal one.

Class 5
Techniques for Height

One common glitch in perspective drawing is that although the artist knows that objects appear smaller in the distance, he or she doesn’t know how small to make them.

This leads to finished pieces with people floating in space, standing on different planes, and looking unrealistically large or small.

The solution is to begin with a standard of comparison to determine heights anywhere in the picture plane.

If you’re drawing something with a fixed vertical plane such as a wall or a fence, use that as your standard.

If there’s nothing in the finished picture that will work, you can still draw a standard and then erase it when the various elements are placed.  For example, draw a cube in the middle of the paper and call it six feet.

With that block drawn, you need only extend the lines of the sides to determine several different places on the picture place that are also standards for six feet.

To draw a six-foot tall man in the picture plane, simply extend the guidelines for the box out to the point you want it to be (you may need to compromise and choose a place in line with the planes of your box).

Once you know where the head starts and where the feet go, you can simply fill in the body around those guidelines.

You can use that same standard to place other objects. If a little girl is standing beside the man and she’s three feet tall, you need only divide the man in half to find where her head should go; the feet will be on the same plane as his are.

Use this principle in drawing anything, and remember that the horizon line also works as a standard in many cases.

In a large group of people, if the horizon line is at the eye level of a standing adult male, all other adults of the same height who are standing on the same ground level will also hit the horizon line at eye level, so you can easily draw them in the correct perspective anywhere on the page by starting with their eyes at the horizon level and drawing their bodies proportionally from there.

Likewise, a five-foot tall person’s head may be just below the horizon line and can be similarly placed accurately anywhere in the picture plane.

Class 6
Drawing a Building

Using the measuring line system, you can add specifically placed doors, benches, and whatever else you may want in a scene.

For example, in this class we’ll draw a building in two-point perspective and add to it a sidewalk, door, window, and bench.

Once the building is sketched out as a box in two-point perspective, make a measuring line that extends horizontally from the lowest corner of the building.

The measuring line is a simple way to take the side of the building out of perspective for the sake of marking down where you want objects to go, then translating those objects back to the side of the wall in perspective.

Remember that the measuring line starts at one corner of the building, so place the door or window in as far as you want them to be from the corner of the wall, make hatch marks on the measuring line to show how wide you want them, and make one last mark to be the opposite side of that wall.

Make a line that connects that final hatch mark to the far side of the wall, and extend that line up to the horizon line to establish a special vanishing point for the door and window.

Use that vanishing point to connect every hatch mark on the measuring line. Where the lines cross the bottom of the building, draw vertical lines to show the width of the door and window.

Add the bottom and top of the door and window by using the vanishing point for the side of the house.

Since those objects are in reality parallel to the side of the house, in perspective, they will appear to diminish to the same vanishing point as the side of the house that they’re on.

Remember that depending on your point of view, you may be able to see some depth in the window and doors.

Add a top to the building (we’ll leave it flat in this class) by using the same vanishing points that you did for the sides of the building.  Remember that everything in the picture plane shares one horizon line.

If you’re placing objects to the house or even outside the house that are parallel to the sides, you use the same vanishing points on that horizon line as you did for the side that the object  is parallel to.

A sidewalk running in front of the door is parallel to the side of the house, so it shares a vanishing point with that side and all you have to do is choose a width.

A bench in front of the house may or may not be parallel to one side of the house.  If you choose to make it parallel, then you can draw it by using the vanishing point for the side of the house.

If you choose to angle it away from the house, the vanishing point will shift, but will still lie on the horizon line.

To add a chimney-type formation on the top of the building, you’ll need to carry the guidelines in perspective up the side of the building and then across the top.

Use a measuring line going to the left to determine hatch lines for depth, then build up the sides by drawing a box on top of your existing box.

Make sure to do the sight test as you work; it’s easy to draw lines through the wrong vanishing points. If it’s drawn in correct perspective, it should look correct.

If you want to add a 6-foot man, establish how tall the building is. If it’s twenty feet, dividing it into fourths will give 5-foot sections.

A line slightly above the five foot line will give the placement for his head, and the body can be drawn from there.

To draw him proportionally away from the side the building, extend the lines of the side of the building using the appropriate vanishing point to give yourself guidelines for his head and feet.

Class 7
Interior of a Room

Now that we know how to determine heights and width, we’ll tackle a room interior.

A room is really just a cube with two walls taken down, so to simplify, you can start by drawing a box.

When the box is drawn, erase all but the two walls (or three, depending on the viewpoint you’re using) that you’re looking at in your picture plane.

Mark your vantage points and horizon line, then place guidelines for height on the walls using the sliding ruler method. 8 feet is a typical room height; if you want an 8 foot room, tick off equally spaced marks on the wall somewhere in the room and run the lines through the vanishing point for that wall to give yourself a height grid.

If you only need guidelines for certain heights, don’t bother marking any except what you need.

If your room is drawn in one pt perspective, the system will be the same, but the vanisihgin point will be in the center of the back wall.

Start placing elements in the room as you need. You can use the measuring line system to place doors, windows and so on that need to be a certain size (five feet, two feet and so on), or you can sketch in the size that looks good to you.

Remember, things on the walls are sized according to the height guidelines that you’ve already placed.

If objects are in the middle of the floor, you’ll need to carry the guidelines across the room or ceiling to give yourself guidance for height in other places in the room.

If you started with a box, you can probably still see the ghost line of the corner of the room that is closest to the viewer, in which case you can run the height marks of the opposite wall onto that edge by running them through the vanishing point.

Using this method to determine relative size in different parts of the room, sketch boxes to stand for anything roughly square or rectangular; a couch, table, chairs, pictures, television and so on are all examples.

Refine the edges of the boxes and make sure everything goes through the correct vanishing point, then refine again to shape the boxes into the object that you want.

You can also add things on the ceiling, such as a lamp, by following the perspective lines across the ceiling and then using the triangle tool to make a vertical line hanging down for the chord.

Objects laying flat on any of the planes, walls or floor, can be drawn easily by simply using the vanishing points for whatever plane the object is on.

The final step is to erase all guidelines and shade the objects.

If you’re making a finished drawing or painting, you may want to trace the elements once they’ve been drawn in correct perspective, then transfer those shapes to your drawing paper using graphite transfer paper.

Class 8
Inclined Planes

To see what happens as a plane inclines, draw a box at a head-on view, then extend the center vertical line far above and below the box.

Draw a lid for the box. As you move its vanishing point either above or below the vanishing point of the box while staying on the same vertical line, the lid appears to open or close, or, incline.

So an inclined plane is a description of movement of the vanishing point.

You can apply this principle to putting a roof on a house.  Draw a house in two-point perspective and find the vanishing points and horizon line.

It’s also helpful to show the back walls. Erase your unnecessary lines, then you can begin adding the roof.

The first step is to find the center point of the walls over which the roof will come to a point.

Run diagonal lines corner to corner of the front and back walls, which will give the midpoint of those sides. Use your triangle to run a vertical line straight up from each point, and then decide how high you want your roof to be.

Mark a dot on the vertical line at that point, then run a line through that height to the vanishing point for the adjacent wall of the house, and the top line of the roof is established.

Connect the line of the roof to the front three corners of the house (the back side can’t be seen from this angle), and do a sight check to make sure the roof looks realistic. You may need to make adjustments in height or move your vanishing points for the side further apart.

To add eaves, extend the lines of the wide side of the roof up to their vanishing point. This point may be off the paper.

Widen the front and backside of the roof by using this vanishing point and choosing your preferred width. To close off the bottom of the eaves at the correct angle, continue the bottom line of the roof over.

Add a back eave in the same way.  First run a vertical line through the vanishing point that you used for the front eaves. This line may not go through the vanishing point for the side of the house.

The vanishing point for the back eaves, however, will lie on this vertical line. It is an inclined plane equivalent to the front slope of the house with a vanishing point that has shifted down on the vertical line.

Determine the width of the back eave, and close off the bottom by running a line through the vanishing point for the side of the house.

You can add doors and windows using the measuring line system or by randomly choosing the placement on the side of the house.

If you use the measuring line, make sure that the last hatch mark you place is where the edge of the house lines up; you need to run this line through the corner of the house and up to the horizon line to find your special vanishing point for the rest of the objects on that side.

Therefore, you need to know not only how far apart the door and window are from each other, but also how far they are from each corner of the house.

Add any horizontal elements (shingles, siding, brickwork) by running the horizontal lines through the appropriate vanishing points for the house, then dividing the lines vertically with your triangle as needed.

Class 9
Putting Irregular Shapes in Perspective

If you need to translate patterns from being drawn at straightforward views to perspective, you can do so by setting up a grid system.  Draw a picture of anything you want.

Next, you may choose to put the shape on a simple shape such as a rectangle to make putting it in perspective easier; you can always erase this rectangular frame once you’ve drawn the finished shape.

Place dots at every important point of the drawing.  This might be edges of the shape, places where the line changes direction, intersections of lines, the outermost point on a curve, and so on.

Next, set up measuring lines on two sides. Draw the important points straight down onto the measuring lines both horizontally and vertically to form a grid.

You’re transferring the relationship between the points to a numerical scale, which, because it’s on a line, can easily be put into perspective at whatever angle you need.

Don’t forget to include the edges of the card, or frame, on the measuring lines. When the grid lines are drawn, label one side numerically and the other side alphabetically.

Label one corner of the shape as “A” and the two corresponding sides “1” and “2” to make it easier to see how they line up on the shape in perspective.

Next, draw the frame shape in perspective at whatever angle you want the final picture to be and mark the vanishing points. Your drawing will lie on this frame. Label the frame sides “1,” “A,” and “2” to correspond to the initial drawing.
Page 18 of 41

Now draw a single horizontal measuring line that intersects the bottom corner of the frame drawn in perspective.

It should intersect the frame at point “A,” and be underneath sides “1A” and “2A.” If you’re not going to enlarge the shape, you can line up the paper with the original drawing on it directly over the perspective drawing and transfer the points from the measuring lines onto the new line.

Just make sure that “A” on the first drawing lines up with “A” on the perspective drawing.

Next, connect the farthest point on the new measuring line to the corresponding corner of the frame, and continue that line up to the horizon line to find the special vanishing point for that side.

To create the grid lines for the frame in perspective, run the hatch marks from the measuring line through that special vanishing point to find where they fall on the frame, then carry those lines through the vanishing point for the frame to put the lines in perspective.

Do the same for the adjacent side. This side will have its own special vanishing point.

Now the grid has been transferred to the plane in perspective, so all you need to do is label the new grid the same way you did the first one (numerically on one side, alphabetically on the other) and transfer the points from the original grid to the new one.

Connect the dots in perspective, and you will have drawn your pattern in perspective.  Erase the grid lines and frame (if desired,) and your drawing is complete.

Class 10
Putting It All Together
The Finished Drawing

The final challenge of this course is putting the techniques learned throughout the lessons together to make a finished drawing.

In this class we’ll be drawing a view through an airport window looking down on some railroad tracks, but the principles would apply to many scenarios, both natural and man-made alike.

Begin by finding the horizon line and vanishing point or points on the reference material. It may be helpful to put the photo on a blank sheet of paper first, then line up the main lines of convergence that you see and use a straight edge to continue them off the photo.

Where the converging lines meet is a vanishing point. Once you’ve found the vanishing point, draw a horizontal line through it to find the horizon line.

Translate the horizon line to your drawing paper.  You don’t have to place it in the same place as the reference photo; remember, the placement of the horizon line will affect the picture plane, but not the point of view.

If you shift it up or down you will be in effect cropping what the viewer sees of the photo, but the vanishing points won’t change.

When the horizon line is in place, draw the largest elements of the picture using the vanishing point.

As you lay out the picture, examine how the buildings fall in relation to the horizon line to give yourself a sense of space. Search for lines that fall on easy to define planes, such as the center of the paper, middle of the horizon line, and so on.

The tracks in this picture are curving to the right, so they will have multiple vanishing points on the horizon line.

Find the vanishing point for the section that runs fairly straight first of all, then mark points going through vanishing points farther and farther right to form a curve. A French curve template will be helpful in finishing the line.

When the large shapes are correctly placed, clean up the lines and begin shading. It will be helpful to have a selection of at least three drawing pencils on hand for the various tones: 5B or so for the blacks, H or B for the mid-tones, and a 2H for the lightest tones.

Start shading at the top and work your way down to avoid smearing the graphite as you work.

You may want to lay down a clean sheet of paper to protect the surface.

Lay down even strokes that follow the curvature of the form; in the case of the buildings without curves, add tone in the direction of the vanishing point.

Blend the tone in the same way, using long, even strokes that follow the curves. A stomp or tortillon are good options, but you can use a variety of blending tools for different effect.

Once the mid-tones are in place, darken the darkest areas by going over the grays with a much softer pencil and blend again.

Repeat until you have the range of tones that you’re looking for, remembering that the greatest contrasts will be closer to the viewer. Colors and contrasts diminish in the distance.

Class 11
Two-Point Box With Lid

Begin by drawing a “plan.” This will consist of the horizontal line of the ppo (overhead view of the picture plane), the flat object as seen from a bird’s eye view, and the station point.

Once you’ve drawn the ppo line, draw a square on it sitting at an angle and label your corners A, B, C, and D for clarity’s sake.

Draw a line on the AB side to indicate a lid, and label its two points E and F.

Choose a station point below the square. Once again, this is simply your choice, and indicates where the person looking at the object is standing.

Find the vanishing points relative to the station point by drawing a line that is parallel to the AB side of the square and then a second line parallel to the AD side. The points of intersection on the ppo are the two vanishing points of the object.

The picture plane is the area above the square where the three-dimensional version of the box will be drawn.

Measure the distance from the station point to A in the plan to determine where to place the horizon line in the picture plane.

Remember, vanishing points fall on the horizon. Since they’re already determined in the plan (the flat square, ppo and station point), you can translate them easily to the picture plane above.

Point “A” is determined with a vertical line from “A” on the ppo to the bottom of the picture plane. Draw vertical lines from the vanishing points on the ppo to find their intersections on the picture plane.

The height of the box is found by making a vertical line from point A in the plan to the point of intersection on the BC side of the square. Translate this same distance from point A on the picture plane, and you’ll have your height for the three dimensional object.

Once all those points are found, you can create the sides of the box by running a line through A and both vanishing points, and the height and both vanishing points.

To find the sides, go back to the plan and run a line through point B and the station point  and point D and the station point, then translate the points of intersection on the ppo straight up to the picture plane.

Extend those points straight up vertically, and the box has all of its sides.

To draw the lid, find where point E falls on the ppo by running a line through E and the station point.

Translate this point to the picture plane, then find the height of the lid by measuring the distance from E to where it intersects line EF on the plan. Translate that height to the picture plane.

Where the E line and the height of the lid intersect is point E for the object. Run that line through the vanishing point on the right.

Run a vertical line through the left vanishing point. Somewhere on this line is the AVP (accidental vanishing point) for the slope of the lid.

Find the AVP by extending the line that connects point E to the back of the box until you intersect the vertical line of the vanishing point. Use this AVP to run a line through the back corner of the box and find the front angle for the slope of the lid, and the box is complete.

Class 12
A Back-Lit Shadow On An Object

For the first class in shadow lighting, we’ll experiment with back lighting.

Of course you know the basic rules of light and shadows already, but this class will show you how to draw shadows in correct perspective regardless of where the light is coming from.

The station point, you’ll recall, is the eye of the
viewer (most perspective is drawn in monocular vision, and so assumes that the person only has one eye).

A projection ray connects the light source to the station point and creates a point of intersection on the picture plane that gives you the vanishing point of the light source. To find this point, draw a point to stand for the sun and draw a vertical line connecting it to the horizon line.

That point of intersection is the VS, vanishing light of the shadow. To draw the shadow, begin with the highest point of the object casting the shadow, which in this case is the uppermost corner of the open lid. This will be referred to as point A.

Draw a line connecting the light source to point A, and another line that connects the footpoint of A (the vertical line from the point to the lowest side of the box that corresponds to A) and the vanishing point of the light (VL).

Where these two lines intersect is the endpoint of the shadow. All other points of the shadow cast by the lid will come together at that point.

Follow the same steps to find the endpoints of the remaining points of the lid: first pass a line through the VL and the point itself, then the VS and the footpoint of the point.

When those lines jut out away from the shadow endpoint, make a mark at the point of intersection, then draw a line connecting that mark to the initial shadow endpoint.

When the shadow lines of the lid are in place, repeat the process for the body of the box.

The shadow cast by the box will, in this case, be within the shadow of the lid for the most part, but the points will not intersect at the same endpoint as was determined by the lid.

To find the point of convergence for the sides of the box, find the lines of intersection coming off the highest corner of the box first. The other points of the box will come together at this point.

The last step is to erase all the messy and unneccesary lines and shade the form of the shadow and the box. Remember, the shadow is darker the closer it is to the object casting the shadow and lightens as it moves away.

The object is light where it is light-struck, and dark where it faces away from the light.

In this example, the box is angled away from the sun, so rather than having one full side in shadow, a corner is in shadow and the two sides that make up that corner get lighter as they retreat toward the light.

Class 13
A Side-Lit Shadow on An Object

In the case of side lighting, light is parallel to the horizon line and the picture plane.

In this example, our object is identical to the other class for simplicity.

Draw the bottom of the picture plane, then choose the vertical line of light on either the right or left from the object.

Find the footpoint of “A,” the highest point of the lid on the box.

Do this by drawing a vertical line from “A” to the point of intersection on the corresponding bottom edge of the box.

Extend this line horizontally and you will have a line running parallel to and slightly above the picture plane.

There is only one point where A, a point on the vertical light source, and the horizontal line that goes through the footpoint of A can meet.

Draw this line and you will have a point of intersection on both the footpoint and the vertical line of the light source.

The point of intersection on the footpoint is the shadow endpoint of A, and since A is the highest point on the object, the endpoint of A is the longest point of the shadow.

Do the same thing to find the shadow enpoints of the other three points on the lid. For each point, mark the point of the corner as well as the corresponding footpoint.

Draw a horizontal through the footpoint, and then make a diagonal line that intersects the corner and is parallel to the diagonal that was already established (the one that passes through A, the footpoint of A, and the light source). The light rays in side lighting are all parallel to each other.

When the shadow of the lid is established, do the same steps to determine the shadow of the box.

Because the front corner of the box is touching the bottom of the picture plane, there will be a perfectly horizontal bottom edge to the shadow of the box, but then the shadow must blend into the shadow endpoint of A at some point.

To find exactly where, connect the top of the uppermost line of shadow to the horizonal shadow line running along the bottom  of the picture plane.

Clean up all the unneccessary lines and fill in the shadow shape. The shadow is darkest the closer it is to the object casting it, then gradually gets lighter as it moves away.

Add shading to the box in the usual way, keeping the light source in mind to determine which sides are dark and which are light. Because the lid of the box is raised, it will cast a shadow on the inside of the box as well.

Class 14
Angles and Proportions Of Observed Objects

In this class we’ll cover how to draw the angles of an obsevered object in correct perspective.

To begin, keep in mind that a protractor is designed to find the correct angles of lines, and so in rare instances, it can be held straight against the vertical line closest to you of the object and the receeding angles of the adjacent lines can then be physically measured and translated to drawing paper.

More often, however, you’ll have to determine the lines by guessing. Draw a horizontal line to establish the ground that the object is resting on, and take some time familiarizing yourself with common angles so you can guess more accurately.

Find the vertical line of the object that is closest to you and put a ruler or other straight edge against the point of intersection between the ground line and vertical.

Move the ruler up and down while looking between the object and the drawing until the angles appear to match, and mark them down.

The next problem in drawing from life is determining proportion. Use your thumb or a ruler held out straight in front of you to keep the distance consistent, and mark down where the length and height of one side of the object falls relative to your measuring device (thumb or ruler).

Transfer those proportions to the drawing by sketching them in roughly to begin with, and then straightening the lines once they look correct.

Once you have the height and sides of the box, you can find your vanishing point by extending them out until they intersect.

When you have one vanishing point, you also know the horizon line (eye level), which is the horizontal line that goes through that vanishing point.

Place the lines of the opposite side of the box by using that horizon line. The steeper the angle is, the closer the vanishing point will be.

Double check your horizon line by noting what of the object you can see when you look straight at it.  If you can see some of the top, the horizon line must but above the object and you (the viewer) are looking down on it slightly.

To quickly check your lines, tie a knot in a piece of string and loop it around a push pin stationed at the vanishing point.

When you pull the string taut, the line in correct perspective will appear. You can also use this technique to cut down on time and erasing by using the string to determine where the line is placed in the first place.

Finish the box by placing the vertical sides where they look correct and using a triangle to place them.

Complete the back side of the box by running each corner through its respective vanishing point, erase the unneccesary lines, and then add the details that you want the box to have.

Remember, every line that is straight on the box will have to be placed using the appropriate vanishing point to keep it in perspective.

Class 15
Two and Three Point Perspective of Observed Objects

We’ve drawn a picture from observation in two-point perspective, so to finish off the study we’ll do the same thing in one and three point perspective.

Start with a one-point perspective study.  Draw a ground line to establish where the object is sitting.

In one point perspective, only one side of the object appears to be diminishing, so after determining which sides have a vanishing point, draw the vertical line closest to you to serve as a starting point.

Guess or use a protractor to measure one of the angles that is adjacent to the vertical line and draw it in.

The second line you draw should be the one that determines the vanishing point for the object.

Wherever the two diminishing lines converge is the vanishing point. When you know one vanishing point of the object, you can draw in the horizon line by passing a horizontal line through that point.

Draw the sides of the object in proportion to the height, erase any unneccesary lines, and the object is complete.

To draw in three-point perspective, follow the same steps but add one more.  Remember that three-point perspective is the effect of looking up at something high, or having an extreme bird’s eye or worm’s eye view of an object.

In such cases, the two sides that would normally appear to be diminishing in two-point perspective have their respective vanishing points, and a third vanishing point exists on the vertical axis of the object as well.

Begin your drawing of the object in three-point perspective by establishing a ground line and the vertical line of the object that is closest to you.

Guess at the angles of the sides to find one vanishing point and run the horizon through that point. Use the horizon to help find the second vanishing point (so far, the process is just that same as drawing an object in two-point perspective).

The third vanishing point can be found most easily by extending the vertical line that you started with and using a piece of thread attached to a push pin to mark a point somewhere on that line.

Experiment by running the thread from one side of the object to the other. Your vanishing point will look best when placed somewhere that doesn’t make the angle of either side of the object too extreme.

When you’ve found a point that works well for both sides, use a ruler to draw in the sides angling toward that vanishing point.

Complete the box by drawing the bottom and/or top through the necessary vanishing points on the horizon, then erase the excess lines and add detail if desired.

Class 16
Cylinders and Ellipses

Now we’re going to start looking at how to put round things in perspective.

Remember that to draw a circle in perspective, all you need to do is draw a square in perspective, mark off the diagonals, horizonal center and vertical center, and sketch the circle within those guidelines.

The circle will touch the square at each intersection, and will curve at the upper third of each diagonal.

To draw a series of ellipses in perspective, draw a center line and mark off equal distances above and below it.

Close in the edges to form a rectangle, find the center of that rectangle, and draw a vertical line through that center. That center intersection is the central vanishing point.

Also on that vertical line of the central vanishing point is the diagonal vanishing point.

Choose whatever place you want for it, keeping in mind that the angle of the ellipses will  vary depending on how close the bottom edge of the rectangle is to the diagonal vanishing point.

Divide the rectangle into as many evenly spaced pieces as you want ellipses. They don’t have to be evenly spaced, but it will make the process faster if they are.

Draw the vertical lines straight up from the points of intersection and you now have several side-by-side rectangles on the larger, horizonal rectangle.

Draw a line through the bottom corner of each rectangle and the central vanishing point, then determine the diagonal of each rectangle by running a line through the upper corner of each rectangle and the diagonal vanishing point.

The second side of each rectangle is found by drawing a vertical line straight up from where the diagonal line intersects the lower line of each rectangle.

Complete each rectangle, then begin drawing the ellipses within the reference points that you have determined for each.

Notice that they will become more “squashed” the closer they are to the central vanishing point.

Now that you know how to draw ellipses in perspective, you can also draw cylinders.  Begin with a horizonal line for the horizon line, mark a vanishing point on the horizon, and draw a square anywhere you like on the picture plane.

Attach the corners of the square to the vanishing point, and you have a cube in one-point perspective.

From that point, all you need to do to make the cube into a cylinder is find the diagonal of the squares on both the front and back end of the cube, mark off the horizontal and vertical center lines, and sketch the circles within those guidelines.

Then drawn a line from the top of one circle to the other, making sure that the line goes through the vanishing point. Erase the guidelines and square edges, and the cylinder is finished. If you want, you can shade the form as desired.

Class 17
Drawing Cylinders from Direct Observation

Now apply the lessons on cylinders and ellipses to a still life and try drawing it from life. The first thing to determine is the placement of the horizon

Sketch in the objects roughly, in their approximate placement relative to that horizon.

If you can see the top of an object, then it is below the horizon line (eye level) and if you can see the bottom, the object is above the horizon and so on.

Use the proportions and lines of the first object to place the second and third so that they remain in correct placement and size relative to each other.

When the objects are roughly sketched, clean up the lines with a ruler, then move the straight edge from the corner of the most tilted object to different points on the horizon line until the angle of the receeding side looks correct.

That is the vanishing point for the first object. If the object is in two-point perspective, you will need to find a vanishing point for the second set of parallel lines by following the same process.

Complete the top and sides of the first object using those vanishing points, then move on to the second object.

Keep in mind that unless the objects are angled the same direction, they will each have different vanishing points on the horizon. Those vanishing points may be hidden behind or within an object (as in the bottle of ink in this example).

Once you’ve found the vanishing points and drawn in the sides, guess at the depth (use the methods for determining proportion to help you), and stand back to make sure everything looks correct.

Complete the front and back squares for each cylinder, and draw in the diagonals, vertical, and horizontal centerpoints to use as guidelines for drawing the ellipses within each square.

When the largest shapes are drawn in correct perspective and the sizes are correct in proportion to one another, start to develop the detail work each object.

Make sure that you run the details on each object through the necessary vanishing points as you work.

A piece of thread attached to a push pin will be a good time saver here.  A good rule of thread is to sketch roughly first, clean up the lines with precision, and then darken the lines freehand so that you keep correct perspective but don’t get too bogged down with precision in cases where it’s not necessary.

Erase sketch lines and perspective guidelines, then start working on the shading and details  of each object. Don’t forget to add shadows both on the ground and on the rounded edge to add that much more realism.

Class 18
Drawing Horizontal Reflections in One-Point Perspective

Drawing reflections can get complicated in a hurry, and you’ll see why when you start playing with a simple cube in a mirror.

Depending on the angle of the mirror, you’ll be able to see different sides of the cube, and the cube in the mirror will appear farther or closer, higher or lower depending on the distance from the original cube and the angle of the mirror.

There is always a fixed relationship between the object and its reflection, but it isn’t always easy to translate that relationship to the drawing board.

So begin with the most simple reflection: an object reflected on a straight horizontal plane.

Begin by drawing an object in two point perspective.  To make it easy on yourself, make the sides a simple measurement, such as two inches.

If you want to add a top to the box and make it a bottle or liquid dropper, build a second and third cube on top of the first cube in two-point perspective.

Keep the lid centered on the bottle by measuring a constant value from the outer sides of the bottle and drawing the sides straight up.

Add details as desired; a label is a nice touch if you’re drawing a bottle as in the example.

To make the reflection, carry the vertical lines straight down.

The central height of the bottle will be the same on the reflection, but because the reflection has a different point of view than the object, you need to take the measurement for the heights of the parts of the bottle (bottle itself, lid, and nipple) from the center of the bottle, not the outer line of the bottle.

The outer length of the object is going to change when put in perspective, but the distance from center to tip will not.

So find the center of the bottle to measure from by completing the back side of the square and dividing that square into diagonals. The point of intersection is the center.

Mark down the necessary lengths of each part of the bottle in that same way.  Keep in mind that the reflection will share the same vanishing points as the object, it will just appear to be upside down.

When you add text and the design on the label, draw the design as a mirror image in the reflection.

The lines of text will be upside down and backwards in the reflection, but the lines will still go through the vanishing point for the side of the bottle that they’re written on.

If the bottle were being reflected only partially (in a lake, for example), draw the shape of  the lake over your reflected image, then simply erase whatever doesn’t show up anymore.

It is easiest to draw the entire reflected image first and get rid of what you don’t need than to draw a partial  reflection.

Class 19
Drawing Horizontal Reflections in Two-Point Perspective

To draw a tilted, one-point perspective object with a horizontal reflection, first draw a horizon line, then sketch the most basic shape of your form in the size and at the angle that you want.

Once you have an approximate angle for the sides, you can use a ruler to straighten the line and find the vanishing point of the object at the same time. Remember, in one-point perspective, you’ll only have one vanishing point.
To determine the angle of the top of the rectangle, you need to measure the angle that your object is rising at, and match that angle to complete the top.

The easiest way to do this is to use a protractor and measure the angle from the horizon line to the closest line of the object going through the vanishing point.

Draw a vertical line (90 degree angle) that passes somewhere through the top of the rectangle that you’re trying to find.

You’ll use it to line up against the vertical line of the compass. This vertical line together with the t-square that gives you a true horizontal line will give you the lines you need to measure an accurate angle of rise.

Once you’ve found the top of the rectangle with the compass, follow the same steps to find the bottom, which should be rising at the same angle.

Make the line longer than you need, and you can use a triangle to find the perpendicular sides of the rectangle coming off of it.

Draw a line for the depth of the rectangle by using the previously drawn sides to measure against.

The lines should be parallel to each other. Next, measure the long side of the rectangle and find the center, then run that point through the vanishing point to determine your center.

Run a line through the lower left corner of the box and the point where the horizontal center intersects the right side of the box.

Where this diagonal line intersects the upper vanishing point line of the rectangle is the depth of the reflection.

Draw a line from this depth line that is parallel to the lines of the object, since the reflection in this case shares the same vanishing point and sides as the object.

Finally, erase the guidelines and clean up the form, then add details to the object and reflection shapes.  Remember, the reflection in this angle will be smaller than the object, but proportionally the same.

Keep in mind which parts of the object are being reflected as well.  You won’t be able to see the side closest to the viewer in the reflection, but you will be able to see the front of the sharpener in either case.

Feel free to fill in details freehand if you’re drawing for fine art purposes, which is faster than finding the perspective angles for every line.

Class 20
Drawing Vertical Reflections in One-Point Perspective

To save time in this class, the original object being reflected into a mirror on a vertical axis has been drawn beforehand.

Choose the angle of the mirror wherever you want it, making sure it has a back and bottom side, and then you’re ready to begin transposing the object into the mirror.

The first step is to establish a common ground between the mirror and the object.

This will entail making lines that coincide with the edges of the object, but are perpendicular (90 degrees) to the mirror plane.

To find those lines, use a triangle butted up against the back of the mirror’s edge, and lay a straight edge against the bottom of the triangle.

Move the measuring tools up and down on that mirror edge until the straight edge goes through the upper back corner of the bottle, and draw this line.

Repeat the process for the lower corner of the same plane of the mirror, and you have the tilt of the reflection correctly transposed.

The length of the reflected sides should be consistent with the bottle’s distance from the mirror, so measure each length (using the correct horizontal line for each measurement) from the corner of the bottle to the corner of the mirror, and translate that distance onto the reflection in the angle that you have already established for the reflection.

Once you know the length of each side of the reflection, connect them, and you have the first side of the bottle. As you repeat the process to find the lengths of the other lines of reflection, keep in mind that the slopes of the lines have to go through the horizon line.

Therefore, it’s not enough to merely match the distances from object to reflection; you need to mark off the distance from the bottom corner of the mirror to the line in perspective and make sure the length is correct between those two endpoints.

You can save time by using one set of parallel lines to eyeball the second line against, but don’t forget to check yourself by moving a ruler up and down the two lines to make sure the lines are indeed parallel.

Once the bottle is drawn, you need to add the top and nipple to the reflection.  Do this in  the normal way, but completing the front and back squares of the bottle, finding the center of each square by using diagonals and horizontal and vertical lines (remember to keep those parallel to the reflected bottle, not the original bottle), and then measuring on the original where to place the lid. If the original lid is half an inch from either side, for example, it should be similarly placed in the reflection.

Clean up lines and then round the corners of the bottle by using the method you already learned for turning a cube into a cylinder, add shading if desired, and the reflection is complete.

Then select the location you wish to save the files to (either your DESKTOP or MY DOCUMENTS e.t.c.)

Once finished, simply unzip the files (PC use winzip, MAC use stuffit) and your files will be there.

All written material can be opened as a PDF.

All videos files can be opened with VLC Media Player.

Select your download option below …

• Click Here To Download PC Version
• Click Here To Download MAC Version