Marshall sells a reasonably priced set of videos on perspective. Here are some personal notes about them. These are not a replacement for watching the videos, but will hopefully make them easy to review.

Click a title to jump to that section.

1. Intro To Perspective

2. Right Angles (Part 1)

3. Right Angles (Part 2)

4. Right Angles (Part 3)

5A. Circles & Ellipses (Part 1)

5B. Ellipse Construction Demo

6. Circles & Ellipses (Part 2)

7. Circles & Ellipses (Part 3)

8. Right Angles & Circles Combined

9. Inclined Planes

10. Depth Measuring (Part 1)

11. Depth Measuring (Part 2)

12. Plan Projection

**1. Intro To Perspective**

Parallel Lines

Perpendicular Lines, Right Angles

Oblique Lines, Acute & Obtuse Angles

Create Depth:

• Diminution (overall size getting smaller as it moves farther back)

• Foreshortening (length of a single object getting shorter as it recedes)

• Convergence (parallels seem to meet at a distance)

• Atmospheric Perspective (objects getting lighter or more hazy in the distance)

• Overlapping (objects cover one another when one is in front of the other)

Width X

Height Y

Depth Z

We need more than one view to get perspective.

Shapes = 2-D

Forms = 3-D

Squares → Cubes

Circles → Spheres

Rectangles + Circles or Ellipses = Cylinders

Triangles + Circles or Ellipses = Cones

Master cubes, then reduce objects to cubes.

**2. Right Angles (Part 1)**

Diminution causes Convergence

Beginner Problems:

• No Convergence or Convergence in the wrong direction

• Arbitrary Convergence (lines that should share a VP do not)

Every set of parallels moving away from us seems to converge, and every parallel going in the same direction has the same vanishing point. Therefore, always either draw from the vanishing point to a non-converging edge of the shape that you are drawing, or aim converging lines at a vanishing point. You will probably do the latter much more than the former.

POV:

How high am I from the ground? Eye Level and the Horizon Line correspond because it is huge! Something that is super far away from us does not seem to move much as we move.

HL low = looking up

HL high = looking down

Station Point forms a vertical axis, while HL forms a horizontal axis in our field of view.

When drawing a cube, there are only three sets of lines (i.e.: parallels along X, Y, and Z).

1-point = one set of parallels seems to Converge

2-point = two sets of parallels seem to Converge

3-point = all three sets of parallels seem to Converge

Each set has its own VP.

3-point is usually used for large things (like skyscrapers), or when we are close to something.

What do you do when VPs are so far apart that they are off of the page?:

• Work small and use a grid or blow it up with a photocopier

• Pins and strings

• Off-set T-Square

In 2-point, the vanishing points get closer together the closer you get to something.

**3. Right Angles (Part 2)**

A square in 2-point turns into a rhombus with 2 obtuse angles and 2 acute angles.

[The angles of a quadrilateral always add up to 360 degrees.]

Think about what you want to convey and how to position things before you start to apply perspective to it (i.e.: Composition is more important than Perspective).

POV is made up of three things:

• Horizon Line (Eye Level)

• Station Point

• Cone of Vision (distince between VPs in 2-point)

Notice how this accounts for all three axes, X, Y, and Z!

Ask these questions:

How high (looking down at it or up at it)?

Orientation (is it to your left or right)?

How close (near it or far away from it)?

Focal Length of Lenses in Photography:

1. Telephoto - 500mm

2. Standard - 50-80mm

3. Wide Angle - 28mm

4. Fish Eye - 8mm

Notice how the telephoto lens extends out like a telescope while they get progressively closer to the camera body as you go down the list. The longer the length, the more acute the angle of the cone of vision!

Make things look huge by using a wide-angle lens and getting close to it.

Around 80mm is used for portraiture. You do not want the face to look "big".

One can distort perspective to give different effects (e.g.: to exaggerate the size of things closest to the viewer).

**4. Right Angles (Part 3)**

Hard Edges for Hard Plane Changes

Gradients for Soft Plane Changes

Look at a corner to find X, Y, and Z.

Exterior Corners for exteriors (e.g.: outside of buildings)

Interior Corners for interiors (e.g.: rooms inside of buildings)

If the former is in 2-point, then parallels to the right Converge to the right and parallels to the left Converge to the left. If the latter is in 2-point, then parallels to the right Converge to the left and parallels to the left Converge to the right.

Always keep X, Y, and Z in mind and whether the set of parallels going in each direction is true or Converges. Always be sketching along these lines, like you are a tram being guided by rails.

Notice how primitive forms build on each other:

Cubes → Rectangular Prisms → Cylinders → Cones

Cubes → Spheres

Stack, cut away, and extrude primitive forms to "scuplt" the form that you want. Draw through to make sure that they take up the right amout of space and do not conflict with one another.

Seeing how things line up along the X, Y, and Z is how we get "x-ray vision". It helps us to understand how forms rotate in space (e.g.: at what point do we start to see the ear on the far side of the head as it turns?).

Transfer distances to find the sizes of things throughout a scene.

If things are in different orientations, they could have a set of vanishing points different from another thing, even though both are level with one another.

Finding the center points, extending lines from them, and transfering distances along surfaces can help you find out how things line up, in both interiors (e.g.: chandelier's over tables, characters looking out of windows, etc.) and exteriors (e.g.: where the back ear is on a head in three-quarter view, how the handles line up on a treasure chest, etc.).

Composition comes before Perspective. In other words, you will figure out what is in the scene and how it relates before you try to make it spatially accurate. Sketch draft views and thumbnails.

Part of Composition is Gesture, giving things dynamism, particularly Figures.

**5A. Circles & Ellipses (Part 1)**

Circles become ellipses in perspective. An ellipse is symmetrical horizontally and vertically. It is not an oval, which is an egg-shape. It is not pointed on the ends like a football, nor is it simply a rectangle with rounded edges like a sausage-shape.

A circle is a 90-degree ellipse. The degree of that ellipse becomes smaller as it nears the horizon, until it becomes a straight line at Eye Level. The same is true for ellipses moving left and right. One that is right in front of us is a vertical line.

We can imagine the head as a cylinder, so that the lines that divide it into thirds in a front or side view become ellipses as the head tilts forward or back.

**5B. Ellipse Construction Demo**

2. Draw a Minor Axis.

3. Take another paper and mark off half of the Major Axis (i.e.: from the ellipse center, A to the end of the Major Axis, C).

4. Place point C on the end of the Minor Axis and use the ellipse center to find point B.

5. Move the paper while keeping both point A on the Minor Axis and point B on the Major Axis. Point C will trace out the curve of the ellipse.

6. Do this to get one quadrant, then mirror it to get the others.

**6. Circles & Ellipses (Part 2)**

1. Knowing the center of the ellipse

2. Finding the degree

To find the center of a square, take its diagonals.

Whenever we draw an ellipse by using a circle inside of a square, we have to keep in mind that the center of the ellipse does NOT coincide with the center of the circle in perspective. Remember, all four of quadrants of an ellipse are of equal size.

Build cylinders out of boxes.

To give an ellipse the right orientation for a cylindrical object: First, draw the axis of a cylinder in the direction of the vanishing point. Find the line that is 90-degrees away from it on the paper. This is the Major Axis of the ellipse. The Minor Axis of the ellipse coincides with the axis of the cylinder. Use this crosshair to make the ellipse on the end of the cylinder. We might use the analogy of an axle. [The axle is perpendicular to the wheel surface.]

An ellipse will fit perfectly within a surrounding trapezoid/rhombus if it represents a circle and square in perspective. Therefore, we can check if a trapezoid/rhombus represents a square in perspective by finding the ellipse that should fit within it, and/or we can use ellispes to draw true squares in persepective.

An interesting exercise for practicing ellipses is to slice a sphere in different directions.

**7. Circles & Ellipses (Part 3)**

1. If you want to place something within the center of a circle in perspective, do not use the center of the ellipse. Again, they do not coincide.

2. Since the Minor Axes of ellipses point towards a vanishing point, the ellipses can tip depending upon where the vanishing points are placed.

Find ways to take things in and out of perspective. For example, divide up a circle into the desired number of increments, and then carry those divisions back over to the ellipse that represents it in perspective. We have to connect the points that we've made on an unchanging axis (such as a horizontal line in 1-point) to the vanishing point as necessary.

This technique can be used to make wheels, gears, clockfaces, staircases, wrap graphics around cylinders, put longitude and latitude lines on globes, etc.

It can be used to make equal or unequal divisions on any surface that seems to curve away from you.

Learn how to do a grid of cross-contours along the surface of every primitive form (like a "wireframe")! This is super useful (e.g.: how to wrap drapery with designs around forms, how light moves along the surface, etc.).

An interesting exercise for practicing this is to put letters with proper Convergence on the surface of spheres, both convex and concave.

**8. Right Angles & Circles Combined**

Remember, the top and bottom edges of the door are parallel to one another and will seem to converge in perspective.

Pay attention to the degree of each ellipse! They might be different depending on how the door is orientated (in the same way that we might look down on one end of a cylinder while also looking up at the other end at the same time). This is determined by how far each of them is from the HL.

Because the door has thickness, it will be in 2-point unless we are looking at it head-on (wether we are talking about the long skinny side or the wide flat side).

Anything that rotates in a circular motion can be taken out of perspective by turning it into a square. Use the diagonals of the square to find the center of the circle. Then, put it back into perspective.

Master circles and squares (shapes), and then master cubes, cylinders, and spheres (forms).

All of these ideas apply to the joints of the body too. Notice when a motion makes a circle! It will form an ellipse in perspective.

**9. Inclined Planes**

When a box rotates, it moves from 1-point, to 2-point, then and back again. The VPs seem to slide along the HL. Tiling is the same thing, except the HL is vertical!

Always ask yourself: "What is closest to me, and what is farther away?" "Which lines are moving away from me, and which ones are parallel to the Picture Plane?" "Are these lines level or are they tilted (and if so, which way, up or down)?"

**10. Depth Measuring (Part 1)**

1. "X finds the center"

Connect the diagonals of a quadrilateral to find its center. Repeat to divide it up into even segments. However, you have to know the front and back edge.

This is good for dividing up surfaces quickly and simply.

2. "Diagonals find far corner"

Extend a line through the midpoint of a side in the direction of the vanishing point. However, like the previous, you need a front and back edge to start with.

This is good for items that receed infinitely.

3. "Vanishing Trace diagonal"

Given a quadrilateral, take its diagonal to a vanishing point. This vanishing point will be above or below the one for the quadrilateral. Same limitations as the previous method.

Tip: Cut the quadrilateral into a smaller size so that the angle of the diagonal is more shallow. This makes the vanishing point of the diagonals closer to the vanishing point of the quadrilateral.

This works for multiple sizes next to one another, so long as they are already in perspective.

**11. Depth Measuring (Part 2)**

4. "Checkerboard measurement"

Divide up the non-Converging axis into how many ever parts you need. Then, extend a line from those markings to the vanishing point. Split the quadrilateral with a diagonal. Any point where the diagonal crosses the previously made lines shows the same divisions with Convergence. Use the other diagonal to flip the measurements.

This can be used for regular or irregular divisions.

Tip: As long as you keep it parallel to a non-Converging axis, the ruler can be moved along the quadrilateral until it reads a measurement that is convenient for dividing it up into how many ever parts that we need.

Quick Division of A Line: Starting on the same end point as the line you are trying to divide, draw another line that is a length that can be divided easily into the number of parts needed. Connect it to the other end point by another line, and through the divisions draw more lines that are parallel to the previous. These lines will split the original line into equal parts.

5. "Measuring Line & Special Vanishing Point"

Take the edge of the quadrilateral that you want to divide out of perspective. Make sure that both of these lines share an end point. Divide it into the number of parts that you need. Draw a line through the end point of this line to the one in perspective until it hits the horizon line. This forms a "special vanishing point". Connect the divisions to this same vanishing point with more lines. They will divide the original quadrilateral into parts.

This can be used for regular or irregular divisions.

**12. Plan Projection**

"Elevation" = Front or Side-View that gives heights

Neither of these have perspective (i.e.: no Convergence).

1. Put a plan into a square or rectangle.

2. Make a corner of the plan touch a picture plane at whatever angle is desired.

3. Draw lines from important points on the plan to a viewer. Remember, the farther back that they are, the further the vanishing points are from one another and the flatter their view is. This also makes the cone of vision larger.

4. Find the vanishing points by making lines that are parallel to the square or rectangle. They meet at the viewer and are 90-degrees from one another.

5. Make vertical lines starting wherever the lines made in steps 3 and 4 cross the picture plane.

6. Set the horizon line somwhere over these vertical lines.

7. The front corner is a non-Converging axis, so we can run lines from an elevation that lines up with it to find the heights of things.