Measuring & Proportion / Drawing with Accuracy & Precision | Brent Eviston | Skillshare

Measuring & Proportion / Drawing with Accuracy & Precision

Brent Eviston, Master Artist & Instructor

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7 Lessons (1h 26m)
    • 1. Measuring & Proportion Trailer

      1:39
    • 2. Welcome to Measuring & Proportion

      3:33
    • 3. Introducing Proportion

      16:32
    • 4. Plumb Lines

      15:28
    • 5. Angle Sighting

      14:13
    • 6. Triangulation

      15:43
    • 7. Putting it all together

      19:10
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About This Class

Drawing is not a talent. It’s a skill anyone can learn. Designed for aspiring painters, graphic designers, illustrators and artists of all types, The Art & Science of Drawing series will teach you the foundation of art and design of all kinds: drawing.

MEASURING & PROPORTION is the third course in The Art & Science of Drawing series designed to take students from the absolute basics to advanced drawing techniques like perspective drawing and shading.

In this course you’ll learn how to draw using a series of measuring tools and strategies that will take the guesswork our of the drawing process. You'll learn how to determine the proportions of any subject and draw them accurately on the page. You’ll also learn how to use angle sighting to triangulate the location of any point on your subject to make sure your drawings are always accurate and in proportion.

This course is perfect for artist of any medium looking to improve their accuracy and a great primer for painting and figure drawing.

MEASURING & PROPORTION is a remarkable course that will teach you how to draw one day at a time. Here’s how it works: Each day you’ll watch one video lesson that will introduce an essential drawing skill, and then do the recommended practice. 

During this course you’ll create a series of drawing each focusing on a different measuring technique.

This course is overflowing with powerful insights into the drawing process and offers some of the clearest, most accessible drawing instruction available.  Many of the tools and techniques you'll learn here are rarely taught outside of private art academies. 

If you're a beginner, we recommend going through the entire series in the following order:

The Art & Science of Drawing:

The Art & Science of Figure Drawing:

If you've got some drawing experience, feel free to mix and match The Art & Science of Drawing courses to suit your personal needs as an artist!

Transcripts

1. Measuring & Proportion Trailer: The focus of this week is on measuring and proportion. Learning to measure takes all of the guesswork out of drawing. This week you're going to learn a series of measuring tools and strategies, that are going to allow you to quickly and easily evaluate the proportions of your drawing subject, and get them on the page. The strategies we are going to learn this week are going to include: Proportional measuring, where you're going to use your pencil to evaluate proportions of a subject. You're going to learn how to use plumb lines, which are using vertical and horizontal lines to compare points of your subject to one another. Finally, you're going to learn angle citing, which will allow you to actually extract an angle from your drawing subject, and bring it over to the page. Learning how to measure will dramatically increase the accuracy and believability for your drawings. After this week, you'll have a whole series of strategies that you can use, and you can mix them and match them depending on what your subject is, what measuring strategy you're most comfortable with. You'll be able to design your own approach to evaluating the proportions of your subjects in getting them to your drawing. Learning to measure takes a good amount of discipline and dexterity. But once you've mastered the techniques, you'll be amazed at how quickly your drawings will improve, and how easily you'll be able to actually capture the proportions of your subjects accurately on the page. 2. Welcome to Measuring & Proportion: Welcome to the measuring and proportion course in the art and science of drawing series. I'm your instructor, Brent Davidson. There are a few things I'd like to share with you before you start the first lesson. The first thing is that I absolutely love working with students. Teaching drawing is a joy and a privilege that I take very seriously. Before creating the art and science of drawing series, I taught drawing for 20 years in studios, schools, museums and universities. While working with students, I would constantly ask myself, what are the teaching tools and techniques that really connect with students? What tools and techniques show the most improvement in their drawing skills? How can I teach these techniques in a way that really speeds up their skill development? This course is the answer to those questions. The courses in the art and science of drawing series contains some of the most powerful teaching tools and techniques that are proven to teach students how to draw. Here's how the course works. Each day, you're going to watch one video lesson and then be given a project to do. Once you've completed that day's project, you're ready to begin the next video lesson. This course was designed so that you can watch one video lesson each day and do one project each day. But you're welcome to adapt the structure of the course to fit your schedule. If you can only get to one video lesson in project a week, that's fine. Feel free to make this course work for you. This is a project based course, which means that every lesson is going to come with a specific project that it's designed for you to get the most out of the skills you've just learned. The practice that these projects provide is absolutely essential to your learning how to draw. If you're not practicing, if you're not doing these projects, you will not improve. Having an intellectual understanding of these ideas is great, but practice is required to really get good at drawing. Now one of my great joys as a teacher is to see students evolve and grow over time. I encourage you to share your work. You can share it with family and friends, you can share it on social media and of course, you can share it right here on Skillshare. When you share your work on social media, I encourage you to include the hashtag, evolve your art. Building a community when you're learning to draw is a great way to be inspired to practice and get feedback on your work. Now this course is one of the seven in the art and science of drawing series. Each course in the series focuses on a different essential drawing skill. If you're a beginning student, I highly recommend going through this series in order. But if you've got some experience drawing, feel free to mix and match the courses to suit your own needs and interests. Now while you're taking the course, I recommend watching it on a larger screen. You're welcome to take the course on your phone if that's what you have available, but by watching it on a larger screen, you'll have a richer experience, you'll be able to see more detail in the drawings. If you'd like any other information on other courses in the art and science of drawing series, drawing resources or a detailed description of what materials to use, I encourage you to visit the website, EVOLVEYOURART.COM. It's a great place to go for further drawing resources. Well, thank you so much for joining me. It's an honor and a privilege to have you as a student. Let's get started with our first lesson. 3. Introducing Proportion: Learning to measure takes all of the guesswork out of drawing and this week you're going to learn a series of measuring tools and strategies that are going to allow you to quickly and easily evaluate the proportions of your drawing subject and get them on the page. The strategies you're going to learn this week are going to include proportional measuring, where you're going to use your pencil to evaluate the proportions of a subject. You're going to learn how to use plumb lines, which are using vertical and horizontal lines to compare points of your subject to one another. Finally, you're going to learn angle sighting, which will allow you to actually extract an angle from your drawing subject and bring it over to the page. Learning how to measure will dramatically increase the accuracy and believability of your drawings. Before we get into today's subject, I wanted to address a couple of things. The first, is that measuring, just like any other skill in drawing, requires a huge amount of practice. The second thing is that it's important to remember that learning to measure will get us much closer to the actual proportions of our subjects but no measuring strategy is without its faults. While you're learning the different strategies, I'm going to talk to you about the benefits and drawbacks of each one. The idea is that after this week, you'll have a whole series of strategies that you can use and you can mix them and match them depending on what your subject is, what measuring strategy you're most comfortable with and you'll be able to design your own approach to evaluating the proportions of your subject in getting them to your drawing. Learning to measure takes a good amount of discipline and dexterity but once you've mastered the techniques, you'll be amazed at how quickly your drawings will improve and how easily you'll be able to actually capture the proportions of your subject accurately on the page. Before we get into technique, let's take a look at some theory. So what exactly is proportion? Proportion refers to the size relationships between various parts of your drawing subjects. When you're drawing accurately depicts the proportions actually found in your subject, we say that that drawing is in proportion. But if parts of your drawing are either too big or too small, particularly if it's recognizable to the viewer, we say that that drawing is out of proportion. So to do drawings that are in proportion, we need to measure as many parts of our drawing subject as possible and compare them to one another. Now before we apply these ideas to the drawing process, let's just talk about what proportion is on its own. Let's start off by introducing what proportion is and how you can think about it. Here you can see a simple square. The distance from one side of the square to the other is called its width. The distance from the top to the bottom of the square is called the height. On a perfect square, the width and the height are equal to one another. Meaning that the ratio of width to height is one-to-one. Let's change this proportion by adding another square on top, thereby doubling the height of our shape. Now, the height of our shape is two times the width of the shape. Therefore, this rectangle has a proportional relationship of one to two. It is twice as tall as it is wide. It's important to remember that the number for the width is on the left side of the colon and the number for the height is on the right. Now let's return to our simple square. Instead of increasing the height, let's double the width of our shape. This creates a rectangle that is twice as wide as it is high, giving it a proportional ratio of two to one. Let's return once again to our simple square. When you're drawing, it's actually pretty rare for the proportional relationship of the width to the height to be solvable using whole numbers. Let's take a look at some very simple fractions. So instead of simply doubling the height of our shape, let's only add half of the height of our square. Now, our rectangle is one-and-a-half times higher than it is wide, giving us a ratio of 1 to 1.5. Now most of the objects you're going to measure, well actually drawing won't even be this clean. So you should get comfortable with approximating. You can see here that if we increase the height of our box just slightly, even though it's no longer exactly one-and-a-half times as high as it is wide, it's still approximately the same proportion. So let's apply these ideas to an actual subject. As always, it's critical when you're learning a new idea to start off as simply as possible. So our subject here is going to be a simple upright egg. First, let's evaluate the width of the egg. The initial evaluation of the width on any drawing subject should be taken at the subjects widest point. We will assign the width as our unit of one. Now let's see how the width of the egg compares to its height. We can clearly see that the egg is taller than it is wide but most people can make that evaluation without measuring at all. So the question becomes, how much taller is the egg than it is wide? To figure this out, let's imagine our unit of one as being divided into thirds. Now if we take one-third of the width of our subject and add it to the height, it gets us very close to the height of our egg. So now we know that our subject is approximately one and one-third times as high as it is wide. It's important to note that this is still just an approximation, but proportional measuring will usually get you closer to the actual proportions of your subject than just looking with your eyes alone. Now let's take a look at the tools and processes you'll use to measure your subject while actually drawing. So now that you have some basic ways to think about proportion, let's learn how to actually measure our drawing subjects so we can bring the measurements to our drawings. To start, you're going to select a measuring tool. Now, I tend to just use my pencil, but you can use knitting needles, you can use a paintbrush, really anything that is straight, lightweight and rigid. The next thing you want to think about is your posture. Now while you're measuring, it's critical that you put yourself in a single position and don't move. I would recommend sitting up straight and you want to make sure that you're not moving at all. You really want to watch to make sure that you're not moving forward or backward or side to side. Even subtle shifts in your relationship to your drawing subject will invalidate the proportions. Here, you can see me in my studio actually measuring the subject. While taking measurements, I keep my body in the same position. I'm using my pencil as my measuring tool. You'll notice that my arm is held straight out in front of me with my elbow locked. You'll also notice that my head is tilted towards my shoulder. I'm using my right eye to measure and keeping my left eye closed. Bringing my head closer to my shoulder brings my measuring eye in line with my arm. This can help minimize distortions, particularly if you're sighting a large subject like a figure and you're moving your arm great distances up and down or side to side. Now let's take a look at the sight lines. First, let's follow the side line at the top. You'll notice that it moves from my eye, touches the top of the pencil, and moves until it hits the top of my subject. Now take a look at the sight line on the bottom. It moves from my eye and hits the tip of my thumb, which I'm using to mark the bottom of my subject on the pencil from my point of view. This is done by placing the top of my pencil so that it appears to be touching the top of my subject from my point of view, and then sliding my thumb up and down the pencil until my thumb marks the bottom of this subject from my point of view. You'll use this technique regardless of what proportional measuring tool you're using. Now, let's apply all of this to an actual drawing of an egg. Here, you can see me capturing the width of the egg by holding my measuring tool at arm's length with my elbow locked, putting the tip of it at one edge of the egg and my thumb on the other edge. We'll use this measurement as our basic unit of one. Now, let's see how that measurement compares to the height. Whenever you compare one proportion to another, you must make sure that your elbow remains locked and that your posture hasn't changed. Remember, any shift in your posture or your arm will invalidate the proportions that you've captured. Here, we can see that the width of the egg gets us about three-quarters of the way up of the height. One of the things you're trying to do is train your brain to visualize these kinds of proportional dimensions. Another way this can be done is to find the height of the egg first and then compare it to the width. Once again, you can see that the width is roughly three-quarters of the height. Next, I'll show you how to actually use these proportions in your drawing. Here, you'll see me making a vertical line that will roughly establish the height of the egg. You can see me make two marks, one at the top and one at the bottom. We know from measuring that the width to height ratio is one to one and one-third, or to understand this another way, if we divide the width into thirds and add one of those thirds onto the height, we'll arrive at a proper proportions. What this means is that I can divide the height into quarters and only use three of those quarters to establish the width. You'll see me do this by first dividing the height in half and using my pencil to compare the two halves together to make sure that they are the same. Next, you'll see me divide the lower half of the height in half again. I'm also using my pencil once again to make sure that the two halves are equal. We know from measuring that it will take three of those smaller units to equal the width. Using my pencil, with a dimension marked with my finger, you'll see me bring this dimension across for the width three times. Now I've established the width and height at a ratio of one to one and one-third, or, for those of you who are comfortable simplifying fractions, we could also say that the width to height ratio is three to four. With our width and height established, we can easily complete the box and then, using the skills we explored during weeks 1 through 4 of the Art and Science of Drawing, I can lightly draw in the egg. You'll remember that when we measured the egg, it was actually slightly taller than the one to one and one-third box that we have here. You can see this reflected in my final drawing. Now, let's apply these same ideas to a slightly more complex object. In this demonstration, you'll be introduced to a variation on the width to height ratio. Instead of starting with the largest width to height box, I'll begin measuring this subject by finding the width of the rim of the vase. With the width marked in my measuring tool and with my arm outstretched, elbows locked, I'll measure the height by figuring out how many of those units it takes to get from the top to the bottom of the vase. You can see that it's approximately three and one-third. With the width of the rim still marked in my pencil, next, I'll see how many of those units it takes to get across the vase at its widest point. You can see here that it takes exactly two of those units to get across. On these rare occasions when your proportional ratios occur in whole numbers, it makes measuring and drawing the subject much easier. Now we know that the width to height ratio of the entire vase is two to three and one-third. To draw this box, you'll first see me make a box that has a width to height ratio of two to three. Next, you'll see me divide the top third of the height into thirds. Finally, you'll see me place one of these thirds on top, arriving at a box that has a width to height ratio of two to three and one-third. Finally, at the center of the top of the box, we can place the rim, which is half of the overall width of the box. To do this, you can see that I've divided the width into quarters in marking the location of the width of the rim. With the essential proportions measured and marked, I can lightly draw in the basic shapes and volumes of the vase. You can even use the width to height comparison to arrive at the proportion of the rim of the vase, although measuring items this small can be cumbersome. You might have better luck just assessing it using your eyes alone. But while you're practicing today, I would encourage you to try both. Once you're comfortable capturing a width or height on your pencil and comparing it to others, you can apply this skill in a countless number of ways. Here's your project for today. You are going to select a minimum of five simple subjects and explore their proportions. You're going to do this by applying the proportional measuring technique that you learned today. While you're doing this, be creative. You want to evaluate as many proportions on your subject as possible and compare them to as many other parts of the subject as you can. Just like you saw demonstrated today, for each of your objects, I'd like you to draw the box that is derived from the width and the height of your subject found at its highest and widest points. Once you've lightly drawn your simple box, go ahead and use the skills and strategies that you've learned in the previous weeks to draw a light volumetric foundation for your subject. There's no need to go into any detail today. Remember, the focus of this week is on measuring. Remember, producing these five drawings is the bare minimum amount of practice. The best thing you can do if you really want to expediate your learning is to do more practice. Double, triple, quadruple the amount of practice you're doing. Remember, your development is directly linked to how much you're willing to practice, and when we're dealing with fundamentals like measuring, you cannot practice too much. One of the things I'd like you to notice is how familiar the object becomes to you after you've really explored its proportions through measuring. One of the greatest benefits of practicing these proportional measuring techniques is it trains your mind to start to make these evaluations before you even pull out your measuring tool in order to measure things. Well, go to your practice, and I will see you here for the next session where you're going to learn about plumb lines. 4. Plumb Lines: Today, we're going to talk about plumb lines. Plumb lines are vertical lines that we're going to use to figure out how different parts of our drawing subject line up with one another. In order to do this, the first thing we need to do is get comfortable determining true vertical. The first tool I'd like to introduce you to is the plumb bob. A plumb bob is where plumb lines get their names. It is a line with a weight or a bob attached to the bottom of it that pulls the line perfectly down, creating a true vertical. How artists use this is they hold it up in front of their drawing subject so they can see actual vertical line and how it lines up on different parts of their subject. Another tool you can use is a level. Some levels will help you determine verticals. Some levels will help you determine horizontals and some do both. This level will help you find horizontal lines, which are also very useful when determining alignments. Now the last tool we'll talk about is your pencil. How you use your pencil to determine true vertical is simply to hold it out in front of you so that you can put it right in front of your drawing subject and you want to keep it perfectly vertical. This means that you have to recognize what perfect vertical looks like, but as it turns out, human beings are actually pretty good at determining true verticals. Let's try an experiment. Take a look at the line on your screen. Is this line perfectly vertical? Many if not most people can immediately tell that this line is leaning slightly to the right. If this is difficult for you to see, don't worry, you'll learn a whole series of measuring tools and strategies over the next few days that will hone this skill. What I'm hoping you'll take away from this demonstration is that you're already pretty good at determining whether something is perfectly vertical or not. Assuming that you can see that this line is almost, but not quite perfectly vertical. Go ahead and watch as I shift this line to a true vertical and note how slight the difference in angle really is. The fact that human beings are so good at determining verticals makes plumb lines a powerful measuring technique, even without any tools. Now, It's completely up to you to figure out what tool you want to use, whether it's a plumb bob, a level, your pencil, or simply your eyes. While you're learning, I would encourage you to try as many of these as possible just to see which ones you prefer. Plumb bobs and levels you can get at any hardware store, but one thing to remember is that it's useful to just be able to do this using your pencil because if you're drawing, you always have your eyes on your pencil. If you're reliant on tools, that means you'll really struggle to draw if you don't have them with you. Before I show you how to use plumb lines in a still life, I want you to realize that using plumb lines requires a certain level of complexity in your subject. If you think back to the previous session when we were measuring an egg, plumb lines wouldn't make sense with the subject that simple. There's not enough information there to search for the kinds of vertical or horizontal alignments that we're looking for. For simpler subjects, a proportional box is probably going to be your best way to measure them. As your subject gets more and more complex, plumb lines are an excellent way to manage and organize all of the different pieces you'll be grappling with. Let's begin by locating the highest point on our butternut squash. You can see that it is the right tip of the stem of the squash. Now let's drop a plumb line all the way down to the bottom of the image. What does this line tell us? First of all, you'll notice that it lines up exactly with one edge of the marble bookmark. When specific pieces of information perfectly line up like this, I usually call it a happy accident. They're incredibly useful, but not very common. Even though those two pieces of information are the only things that line up perfectly, we can still learn more from this vertical plumb line. For example, you can get a sense of how far to the right the ceramic coffee pour over is from this plumb line. Next, let's try dropping a plumb line from the right side of the upper portion of our squash. You can see that it lines up perfectly with the left side of the ellipse at the base of the ceramic coffee pour over. Once again, when you're using plumb lines, you want to get in the habit of not only finding out what lines up exactly on the line, but also what is near it. Take a moment and look for what other pieces of information are directly to the left and right of the plumb line and approximately how far they are from it. Next, let's drop a plumb line from the highest point of the marble bookmark. We now know that it lines up perfectly with the lowest point of the marble bookmark. This is incredibly valuable information that we may have missed if we hadn't used plumb lines for measuring. One thing you may have noticed is that I started off using long plumb lines that went from the top of the image to the bottom, and I'm slowly working my way down with my plumb lines getting smaller and smaller with each evaluation. You almost always want to work from big to small and from general to specific. Measuring is no exception. It's critical that we find the biggest and most important relationships first before moving on to smaller ones. Once we've used plumb lines to determine some of the larger vertical alignments, we can start to find smaller ones as well. For example, you can see that the right side of the ellipse of the coffee pour over lines up with the edge of the handle at the exact moment where the side of the handle becomes the top. It's important to remember that you can use plumb lines at any location in your subject. We've just taken a look at a few of them here, but take a moment and ask yourself where else you can use vertical plumb lines to discover alignments. While you're doing this, remember, even if two points don't vertically align perfectly, you can still get a sense of how close they are together. In addition to using plumb lines vertically, we can use all of these same principles with horizontal lines. The human mind is just as good at determining true horizontals as it is at determining true verticals. Here, we can see that the tip of the bookend perfectly aligns with the bottom of the handle. Just like before, the alignments don't have to be perfect to be useful. For example, if we take a horizontal line from the highest point of the bookend, we can get a sense of where it intersects the ellipse at the top of the coffee pour over. Plumb lines combined very nicely with proportional measuring, which you learned about in the previous session of the art and science of drawing. When working with multiple subjects in a still life, you can start by finding the width to height box derive from the highest and widest points of the entire still life. By applying this strategy, we can immediately tell that our still life is slightly wider than it is high. Of course, you should find the width and height box derived from the widest and highest points of every individual object in your still life. With some practice, you'll be able to visualize and compare each of the proportional boxes to one another. I'll start this drawing by first placing the largest vertical alignment. You can see in the reference photo in the bottom right corner that this line goes from the right side of the tip of the stem, all the way down to right tip of the marble bookend. You'll see me make two marks on this vertical line; to establish the placement of these two points. It's important to note that these two marks establish the scale of the entire drawing. By placing the points closer together on the vertical line, I would make the drawing smaller and by spreading them further apart, I would make the drawing larger. My main goal with the placement of these two points on our vertical plumb line, is to make the drawing big enough so that it fills the page, but not so big where it goes off the page. I've left some room at the bottom of the page so that I can finish the bookend. Now you'll see me begin to sketch in my first light attempt at the forms. Assuming that you're going through the art and science of drawing series in order, you will remember that these first attempts at the forums are almost certainly going to be inaccurate and will need to be revised again and again. With each new measurement we take and evaluation we make, we should expect to change the drawing to incorporate this new information. It's important to remember that incorporating measuring into your drawing process is not a strict set of rules. You get to choose how and when you measure. With these basic forms blocked in, I can begin to incorporate the horizontal and vertical plumb lines that are shown in the diagram on the right. In this demonstration, you'll see me actually drawing in the vertical and horizontal plumb lines. The more experienced with plumb lines that you get, the less reliant you'll be an actually drawing them. You'll be able to simply make the evaluations using your eyes. On the left of the drawing, you can see that I've drawn the vertical plumb line that goes from the uppermost point of the marble bookend down to the lowest. To place the uppermost point of the bookend, I compare it's height to the initial vertical plumb line we used that ran from the top of the squash down to the far right point of the bookend. You can see the drawing slowly evolve as I carefully draw in the vertical and horizontal alignments that we mapped out earlier. You can also see that I'm moving back and fourth between taking careful measurements and simply sketching in the basic forms. I'd also like you to notice that I'm not lingering for too long at any single object. I'm moving around the entire drawing, so it develops as a hole. This allows us as artists to see the relationships between all of the objects instead of getting focused in on details prematurely. With each new piece of information I'm drawing in, I'm always comparing it to what I've already drawn and paying particular attention to the vertical and horizontal alignments we discovered earlier. In every drawing I do, at some point, I become comfortable with the size and placement of all of the individual objects. My uncertainty about the drawing begins to lift and I can begin to focus more on drawing and less on measuring. Now that I'm satisfied with the size, shape and placement of all of the primary objects in the still life, I can begin to work up the lines using darker marks that I want to be seen by a viewer. Confident, that my measuring has given me a proper foundation. Now for some students, measuring comes pretty easy, but a lot of students really struggle with how to incorporate measuring into their drawing process. I just want to remind you that it takes a lot of practice. If after you do just 3 or 4 drawings and it still not making sense to you, that's okay. Keep doing more and more drawings. I promise you it really is worth getting good at this and getting good at measuring requires a huge amount of practice. Don't get discouraged. Once you put in the practice to get good at measuring, it'll really improve the accuracy and believe-ability of your drawings. The better you get at applying these measuring tools and strategies, the less reliant on the physical tools you'll become. You'll start to notice that when you draw your drawings or more accurate or believable sooner before you actually even pull out your measuring tools to measure. In this sense, you can think of the actual measuring tools themselves, kind of like training wheels. They're great while you're getting your bearings but ultimately you'll become less reliant on them. Now it is entirely up to you as an artist to figure out how much measuring you really want to do in a drawing. If accuracy is really important to you, you can do a huge amount of measuring it at drawing. But if accuracy isn't as important to you, you can measure just a little bit or not at all. It really depends on what kind of drawing you want to and what your subject is. While you're learning, here's a great rule of thumb. If you're feeling uncertain about the size or placement of anything in your still life, measure it. Here's your project for today. I want you to find three objects of moderate complexity. Nothing too complex, but certainly more complex than a simple egg. First, I'd like you to draw each of these objects on their own, so you can get used to applying plumb lines to a single object. Next, I'd like you to do a minimum of two drawings where you're grouping all of these objects together and you want to find as many vertical and horizontal relationships between different parts of your subjects as possible. I'd also encourage you to start experimenting with how to combine proportional measuring with plumb lines. Remember, how you incorporate measuring into your drawing process is entirely up to you. Remember which measuring tools you use and how often you use them really comes down to the level of accuracy you're looking for in your drawings and what the subject requires. The best way for you to figure this out as an artist, is to start using these different kinds of measuring techniques to figure out their benefits and drawbacks, how comfortable you are with them, and how to combine them or not. In fact, many artists only use a single kind of measuring tool for everything. Thank you so much for joining me today and I look forward to seeing you on the next session where you're going to learn how to evaluate angles. 5. Angle Sighting: Today we're going to focus on angle citing. Angles citing allows us to find the specific distance and direction between any two points on our subject, measure it, and then transfer it over to our drawing. Every point on whatever subject you're drawing has a specific distance and direction from every other point on your subject. What a well measured drawing does is accurately arrange all of these points so that the distances and directions between all of the points in your drawing accurately map out what is really going on in your subject. As an example, take a look at this still life. There are numerous corners and intersections where two lines come together. We can think of each one of these intersections is having a specific point in space. Every single point on your still life, is a specific distance and direction from every other point. To illustrate this, let's select one point on the orange. From this one point on the orange, we can create a line going to every other point on the still life. Each one of these lines has a specific distance and directional relationship with the point on the orange and of course, we can do this with any discernible point on the still life. Every subject you're going to draw has a dense network of relationships between the various points on the subject. When we angle site, we're going to select two points and use our pencil or another measuring tool to extract the angle between those two points and bring it over to our drawing. Your only goal today is to get good at taking an angle between two points and your subject in transferring that angle accurately to your paper. Once you're good at angles citing, you can use it in numerous ways. Angle citing can be a challenge to learn, but it is well worth the investment of time and effort. Angles citing is the most effective and versatile measuring system out there. I would say at least 70 percent of the measuring I do is angle sighting. I use it more than any other single form of measuring out there. The tools are going to use for angle citing are pretty simple. The vast majority of the time, I simply use my pencil. Now, if you are using your pencil for angles citing, you're going to want to make sure that it is a newer pencil, that it is at full length because it's much easier to transfer an angle with a longer pencil than it is with a much shorter one. For some subjects, the pencils simply isn't long enough and in that case, I switch over to using a knitting needle. Knitting needles are great because they are straight and they are lightweight. Just like with other forms of measuring, you could really use anything that's straight, lightweight, and rigid. But again, being able to just take measurements with your pencil is a really powerful thing to be able to do because you always have your pencil with you while you're drawing. One of the reasons angle citing can be a challenge to learn is because it takes a good amount of setup. You really need to position yourself well in order to extract angles accurately, get them transfer to your page accurately. Before I teach you the actual technique of angles setting, let's take a look at how you need to set up your drawing board, your still-life subject, and yourself. This is a bird's-eye view of me in my studio. This is my drawing board, and this is a table with a still-life object on top of it. Angle citing is most effectively done at an easel. Imagine that the drawing board is propped up on an easel, notice that my cone of vision is towards the left side of the drawing board. This is because my still life is on my left side. I would highly recommend that if you're right-handed, you put your still life to your left. This way, you don't have to strain your back and neck to look over your drawing arm to see you're still life. Conversely, if you're left-handed, I would recommend putting the still life to your bright. You'll notice that with this setup, when I turn to face the still life, it is immediately to my left. This means that from my point of view, my still life appears right next to my drawing surface. This setup minimizes the distance I'll have to swivel back and forth while drawing from my still life. This next bit of information is critical to successful angle citing, so please pay close attention. For angle citing to work, your line of sight must be exactly perpendicular to your drawing surface. The angle between your drawing board and your line of sight must be a perfect 90 degrees. If you're drawing surface is not perpendicular to your line of sight, one part of the paper will be closer to you than another. This will distort all of your angle measurements. You want to avoid this setup at all costs. This perpendicular relationship between the line of sight and the angle of your drawing board is just as important from a side view as well. It's critical that the top of your drawing surface is no closer or further away from your eye, then the bottom is. This perpendicular relationship between your line of sight and you' re drawing board is important, no matter how you decide to prop up your drawing board. A great way to make sure that you are drawing board is propped up exactly perpendicular from your line of sight, is to hold your pencil out perpendicularly in front of you and to place it right next to your paper. You'll notice that my arm is completely outstretched and my elbow is locked. Maintaining a straight arm is important to the skill of angle citing. With your pencil perpendicular to your line of sight, you're drawing surface should run parallel to the pencil, as you see demonstrated here. This location on the page when your paper and your pencil are running parallel to one another, is where your drawing should be focused. You'll notice that when I move my arm left to right, the pencil moves in and out of being parallel with a drawing surface. You want to make sure to focus the heart of your drawing right in this sweet spot where the pencil and paper are parallel with one another. You can repeat this process, holding the pencil vertically in order to make sure that your drawing board is perpendicular from your line of sight, both from side to side and from top to bottom. One quick note before we move on, if you are drawing from a drawing horse or a chair setup, you can position your still-life subject so that it appears above your drawing board instead of to the side. Just remember that while your angle citing, it's important that you follow all of the rest of this set of principles that you've just learned. Don't underestimate the importance of setting up properly for angle sighting. All the time I see in the studio students attempting to angle sight without being properly set up and it simply doesn't work. In order for angle sighting to be effective, you have to be set up properly. Once you're all set up, you're ready to extract an angle from an actual drawing subject. To do this, you want to think of your measuring tool, like the hand of a clock. Always keeping your pencil perpendicular to your line of sight, hold your pencil out in front of you with your arms straight and your elbow locked. You'll see that I use my left hand to brace my arm while I'm angle citing. This provides extra stability. Keeping one eye closed, you want to tilt the pencil until it matches the desired angle from your drawing subject. In this case, it's the lower angle of the book. With the angle locked on your pencil, you want to slowly transfer it to your drawing surface. While holding the angle in front of your drawing surface, you'll get a sense of what the angle looks like on the page. Practice moving the angle back and forth. It's critical that while you're transferring the angle from your subject to your drawing surface, that you're not accidentally changing the angle. Watch your pencil very closely to see if you can detect any change in the angle as you move it from your subject to your drawing. If you do see the angle change, patiently bring your pencil back to your drawing subject and recapture the angle on the pencil. After some practice, move in the angle from the subject to your drawing board. Once you've got a sense of what the angle will look like drawn on the page, you're ready to make your first attempt at drawing the angle that you've captured on the pencil. After making your first attempts at drawing the angle, you'll need to cite the angle on the subject once again and compare it to what you've drawn. Keeping the angle on your pencil, you'll want to move it back and forth. While comparing the angle taken from your subject to the angle you've drawn on the page, you'll most likely discover that your first attempt was not completely accurate. After making a mental note of how you'll need to change your drawing so that it will reflect the angle of your subject, go ahead and make a second attempt at drawing the angle on the page. If it's helpful, feel free to erase your first attempt. After each new attempt, you'll want to recapture the angle of your subject on your pencil and compare it back to what you've drawn. If the angle taken from your subject and the angle that you've drawn match, you've accomplished your goal. If not, repeat this process until the angle you've drawn on your page accurately reflects the angle that you've measured from your subject. Remember, there's no right amount of attempts that it should take you. Sometimes you'll get it on the first try, other times it will take you multiple attempts. The only thing that matters is accuracy. During your practice today, you're going to repeat this procedure 50 times, extracting different angles from your subject and transferring them to your page. Now you'll see me repeat this process, this time focusing on the bottom left angle of the book. First, I will extract the angle from the subject by capturing it on my pencil. Next, I'll carefully move the angle from the subject to my drawing board to get a sense of what it will look like on the page. Now I can make my first attempt at drawing the angle. Finally, I'll check the angle that I've drawn by recapturing the angle on the pencil and comparing it back and forth from the subject to the drawing, making any necessary changes. Here's your project for today, you're going to select a simple rectilinear subject, like a book or a box. Once you've done that, you're going to set up your drawing station in the way that I showed you earlier today, and you want to make sure that you're drawing board is perpendicular to your line of sight. Once you're set up to angle sight, you're simply going to practice extracting an angle from your subject and bringing it over to your drawing board. Remember, you want to follow these simple steps. First, make your best guess. Draw the angle as best you can before you measure it. Next, actually measure the angle using your measuring tool, whether it's a pencil or a knitting needle, actually measure it from your subject and then you want to carefully transfer that angle back to your paper and compare the angle you have drawn to the angle on your pencil. Next, you want to make any adjustments necessary and then repeat this process. Every time you change an angle, you want to re-measure. It's important to do this as many times as necessary in order to get the right angle on the page. I would like you to accurately transfer 50 different angles from your subject to your paper. What you're doing today's practice. Feel free to move your subject around as many times as possible to generate as many variations and angles as you need. While you're learning to angle sight, I would recommend once you have the angle on your pencil or knitting needle to just slowly transferred back and forth from the subject to the drawing to see if you arrive at each location with the same angle still on the pencil. You really want to make sure that you're not seeing any subtle drift in your pencil while you're doing this. I want to be very clear about this today. You are not actually drawing your subject. You are simply practicing selecting two points and getting the accurate angle between those two points to your page. You'll probably go through many pieces of paper today while practicing, and that's fine. Remember, all that should really be on your paper are a series of slanted lines. You don't need to attempt to draw the subject. Not only are you not actually trying to draw the subject, I wouldn't even worry about how big or small the lines are. You want him roughly the size of your pencil. Remember, we're just getting a direction down on the page, we're not dealing yet with length or distance of the line. As always, if you want to do more than 50 angles, that's great. Remember, angle sighting is extremely effective and versatile, but you have to be able to accurately transfer an angle first. Well, you've got your practice cut out for you today and remember, be patient. This takes time to learn. I look forward to seeing you during the next session where you're going to learn how to actually apply angle sighting in a whole series of ways that it'll take all of the guesswork out of the measuring process. 6. Triangulation: Today you're going to learn how to use angle citing to triangulate how this is going to work is you're going to use two known points taken from your subject and your going to use those two points to triangulate a third, we're going to take the skills you learned in the previous session and apply them to an actual subject. Now before I show you how triangulation actually works, I want to make it clear that this method of measuring is only going to be successful if you can accurately transfer an angle from your subject to your page. Hopefully, this is a skill that you've developed some comfort and some competence with while practicing angle citing from the previous session. Both angles citing and triangulation take a good amount of practice to learn in today's project is going to be an excellent opportunity for you to continue to hone those skills as you probably learned while practicing angle citing, it takes a number of attempts to get the right angle on the page. While you've practiced angle citing, you've probably learned that it often takes a number of attempts to get the right angle on the page. During today's demonstration, you're going to see me go through the same process that you've gone through. Sometimes I get my angle sites right quickly, but other times it takes a number of attempts. You'll see me start every initial line, i'm trying to draw extremely lightly and I only darken the correct line that I want seen by a viewer. That means i'm waiting until i'm fairly confident that the accuracy of any line before I darken it up. Now you'll often see me racing my unsuccessful attempts at angles before I arrived at the correct one. That way those unsuccessful attempts don't add visual distraction while i'm trying to measure or draw new lines. Let's get right into a demo today. Now you're going to see how to use angle citing to triangulate. In this demonstration, you'll learn to use angle citing to construct a box from observation. The first thing we need to do is place a point from our subject onto the page. We could start with any point and still have this process work, but i'm going to select the top front corner of the box. The reason i'm selecting this point is because I have a good sense of how much room I'll need to leave above it for the top of the box, and how much room I'll need to leave below it to complete the bottom of the box. The wonderful thing about placing the first is that we can place it anywhere on the page. In order to make this demonstration easy to understand, i'm going to try and draw the box at the same size and placement as the box in our reference photo. I've placed the point, leaving plenty of room on the page at the top and the bottom to construct the rest of the box. The next thing I'll do is draw the front vertical line. At this point, my goal is simply to get the direction right, i'm not concerned about the length. After angle, citing the front vertical line from the actual subject, I'll carefully transfer the angle on the pencil over to the drawing. Once I've got a good sense of the direction of the line, I'll lightly make my first attempt. You'll notice that i'm drawing the line longer than I need it to be. At this point, my only goal is to get the direction correct. I'm not concerned about the length of the line. Now let's compare the line I've drawn to the actual line in the reference photo up the box. It's critical to check and double-check all of the angles do draw to ensure accuracy. That being said, it's important to remember that perfect accuracy is nearly impossible in a drawing, but we want to make sure we get reasonably close. You can see that the line I've drawn isn't perfectly straight, nor is it going at the exact right angle, but it's extremely close and I feel comfortable moving on. Next, I'll draw the left front edge of the box. To do this, I'll need to angle cite from the actual subject and slowly transfer the angle on the pencil over to the drawing surface. As always, While i'm transferring the angle, i'm making sure that there's no shift in the angle on the pencil. Once I've got a sense of what the angle should look like on the page, i'm ready to make my first light attempt. When we compare the angle I've just drawn to the angle and the reference photo, you can see that my angle is off. The best way to see if your first attempt is correct is to angle side from the actual subject, carry the angle over on the pencil and compare. You want to make a mental note of the difference between the angle you just drew and the angle on the pencil. Now that I've got a good sense of the difference between the angle that I just drew in the angle on the pencil, you'll see me make my second attempt. I'm confident that this new line is closer, but every time I make a new attempt, I double-check to see if it's correct. When I compare the angle taken from the actual subject to my second attempt, I can see that it's still a little bit off. Now it's completely up to you to decide how accurate you want to be while you're measuring. Even though my second attempt is close, it's still off enough to warrant a third attempt. Once again, I'll double check to make sure that the new line I've drawn is as close to the original angle as I can get it. Let's take stock of what we have on the page, we have one fixed point in our drawing, which represents the top front corner of the box. From this point, we have two lines extending indefinitely out into the drawing. We know that these lines accurately represent the direction of the edges of the box were drawing. We know this because we've measured them and checked them for accuracy. Next, we'll establish the scale of our drawing. With only these two lines on the page we can still make our drawing as big or as small as we want to. The only thing that is currently locked in our drawing is the location of the front top corner of the box. Whether we decide to draw our box big, small, or anywhere in between. You can see that the direction of the two lines that we've drawn, as well as the fixed point remain the same. In order to establish the scale of our drawing, all we need to do is to establish the length of either of these two lines. During today's demonstration, I'll try and draw my box at the same size as the one in the reference photo you see on your screen. Once I place the location of the bottom front corner of the box, the entire scale of the drawing is locked. Every new measurement we take will be in relationship to this vertical line segment. The line representing the vertical front edge of the box now has a specific starting and stopping point. However, the line projecting diagonally out to the left just goes on indefinitely. We know that somewhere on that line is the correct location of the top left corner of the box. In order to figure out exactly where, we're going to angle sight across the left front plane of the box. In other words, we're going to use the two known points of the front vertical edge of the box to triangulate the location of the top left corner. Here, you can see that I've cited the angle going from the bottom front corner of the box to the top left corner of the box. Once I've got a sense of what that angle will look like drawn on the page, I'll make an attempt. As always, after I've made my first attempt, I'll check it for accuracy by comparing the angles sighted from the actual box to the line I've just drawn. I'm now satisfied that this angle is correct. Where this angle intersects the front left edge of the box reveals the location of the top left corner of the box. It's important to remember that we as human beings, are not perfect measuring machines, our hands shake, we can't draw perfectly straight lines and we often accidentally change angles on our pencil without us even noticing. But with patients and practice, we can learn to minimize these challenges. Upon inspection, you can see that there are numerous subtle differences between my drawing and the reference photo of the box. However, even though my drawing is imperfect, It's remarkably close to the reference photo of the box and much closer to the actual angles and proportions of the box, then I would have been able to capture using my eyes alone. Because we are imperfect measuring machines, we'll want to base as many measurements as possible off of this initial line segment representing the front vertical edge of the box. Because every line we measure and draw will most likely be just a little bit off by using this very first line segment for our triangulation, we can avoid compounding any inaccuracies. Now, you'll see me use triangulation to find each of the remaining points of the box. Every line I draw will begin with me sighting the angle from the actual box, getting a sense of what it looks like on the page, making my first attempt at the line, and then checking and rechecking, making any adjustments necessary until I've arrived at the accurate angle of that line. You can see here that through careful triangulation, I found the location of the top right corner of the box. Now I can begin constructing the sides of the box. Each new point I draw is being carefully triangulated using two existing points. You can see that by triangulating the bottom right corner, the entire right front plane of the box has been drawn. A great way to check for accuracy is to angle sight each new point in relationship to the existing points you've already drawn. If your drawing is accurate, the angle between any two points on your drawing should accurately reflect the angle between any two points on the actual box. During today's project, remember to use the two points from your first line segment for as many of your angle sights as possible. This is a great habit to get into, whether you're triangulating new points or checking existing points for accuracy. As you're drawing your box during today's practice, feel free to erase any initial lines that your drawing may have accumulated while going through the process of angle sighting. Once you develop a comfort and competence with angle sighting in triangulation, locating any point in your drawing becomes a straightforward process. The key to successful angle sighting is checking and rechecking every new angle you draw to ensure its accuracy. While you're learning, you cannot check for accuracy too much. While no measuring process can achieve perfect accuracy. A well-sighted drawing that is thoroughly checked and rechecked for accuracy, will get remarkably close. During your practice today, once you've located all corners of the box, you can continue to check it for accuracy by comparing each point to multiple other points in your drawing. With some practice, you'll be able to successfully construct a box that exists believably in space. It's worth noting here that a successfully angle sighted drawing will automatically be in correct perspective. Here's your project for today. You're going to find a box. Any box will do. Shoe boxes work great, kleenex boxes. It doesn't have to be a perfect cube. You just want to find a small to medium size box. Using angle sighting and triangulation, you're going to draw this box three different times from three different points of view. Between each drawing, you want to flip the box or put it in a different position to generate some new angles. Now if you want an extra challenge, you can try drawing two boxes at once. Now if you try this, remember, you can see if points are accurate in one box by angle sighting and checking them from the points of the other box, and vice versa. Now it's important to remember that during today's project, you're not drawing any details of this box. If there are any lines, if there are any words or graphics, if there any openings like a kleenex box, you don't need to draw any of that. We are simply trying to locate the accurate points and draw lines in between those points to arrive at the edges of the box. Now if you get hung up today, feel free to watch the demo as many times as you need, and to make things easy for you, here is a simple checklist of the steps to go through while you're triangulating a box. Step 1, place the front corner of the box leaving room above and below. This ensures that you'll have plenty of room to construct the rest of your box. Step 2, angle sight and draw the front vertical edge of the box. Remember to draw this line longer than you think you'll need. Step 3, angle sight and draw the left front edge of the top plane. You'll also want to draw this line longer than you think it will need to be. Step 4, place the bottom corner of the front edge. By doing this, you will be locking the scale of the entire drawing. Step 5, triangulate the location of the top left corner. By doing so, you will have completed your first accurately measured triangle. Step 6, repeat the process of triangulation until you have located all visible corners of the box. At this point, feel free to darken up all of your correct lines that you want to be seen by a viewer and clean up the drawing by erasing any process lines. My advice to you before you start your practice today is be patient and take your time. Remember angle sighting takes a good amount of practice to learn, and while you're learning, try not to get discouraged, celebrate your victories. If it takes you five or six attempts to arrive at an accurate line, that's great. At least you got there. The more you practice angle sighting and triangulation, the better you will get. So remember, while you're learning, be constructive if your angles aren't getting to the page accurately, investigate why and see if you can come up with solutions to make sure that your accurately getting angles from your subject to your page. Well, have fun with your practice today and I will see you during the next session, we are going to learn how to take all of the measuring processes you've learned and incorporate them into your normal drawing process. 7. Putting it all together: Today I'm going to show you how to pull all of the measuring techniques together so that you can measure and draw an actual object. So before we get into our demonstration today, there are just a few things I want to talk to you about. The first, is that you're going to see me leave all of my process lines on the page today. Normally if I were drawing, I would erase them or draw them so lightly they wouldn't be seen. But I really want you to get a sense of how these construction lines and measuring lines are useful to the final drawing, so they're all going to be left visible on the page. The next thing is that even though you're not going to explicitly see this in the demonstration today, all of the proportions that I'm going to show you through diagrams were taken using just my pencil. So either I was angle citing to get the angles between points or I was using my pencil and thumb to extract proportions from the subject. As always, while taking these measurements, I double and triple checked every aspect of my measuring before I put it down on the page. Finally, it's really important that you understand that there are an infinite number of possible ways that you could measure any subject. What you're going to see me doing in the demonstration today is just one possible variation. I don't want you to feel that there is one right way to measure any subject. There are numerous good measuring strategies and tools that will allow you to accurately transfer the proportions of your subject onto the page. So with that, let's get right into today's demonstration. This is our subject today, a tea kettle. Before we begin our measuring, let's just get a sense of the subject. Take note of its different parts. It has a handle, a spout, a top, and the kettle itself seems to be leaning to the left. Using my pencil, I'll start off by making a simple width to height comparison. What I found is that the tea kettle is slightly wider than it is tall. This is a good piece of information to have. But before we draw, let's get more specific. Using my pencil, I'll find the width of the lid of the kettle. Next, using my thumb to lock this proportion onto my pencil, I'll compare it to the height. Let's see how many of these units it takes to get from the base of the kettle all the way to the tip at the top of the lid. On our way up the kettle. Let's pause to note, that the ellipse of the lid falls just under two units. We can see here that the height of the kettle is more than two units, but less than three. To get more specific, I have a series of simple questions I ask myself. Does the top of the kettle occupy more than half or less than half of this third unit. Hopefully, you can see that the height of the kettle goes past the halfway mark on this third unit. Next, I'll ask myself if it's more than two-thirds of the way up. The answer appears to be yes. Let's visualize our third unit as being divided into quarters. Here, we can clearly see that when we compare the width of the lid of the kettle to the height of the entire kettle, we can see that the kettle is two and three quarters times higher than the lid is wide. Next, let's see how many units of the width of the lid it will take to get across the drum of the kettle. We can see here, that it is more than two, but not much. Once again, let's visualize that one of these units is divided into quarters. Hopefully, you can see that it takes two and one quarter units of the lid of the kettle to equal the width of the drum of the kettle at its widest point. So ignoring the smaller forums of the handle on the spout, we know that the biggest form, the drum of the kettle, has a width to height relationship of two and a quarter to two and three quarters. Let's begin our drawing by first making a box of this proportion. I'll start by drawing a vertical line for the height and a horizontal line for the width. Next, I'll mark my unit of one, leaving plenty of room above to make sure I can eventually arrive at a height of two and three quarters. You can see that to transfer this unit of one to other parts of my drawing, I've locked this unit onto the pencil using my pointer finger in the same way that I use my thumb on the pencil to extract proportions from the actual subject. To arrive at a box that has a width to height relationship of two and one quarter to two and three-quarters. I need to add one quarter to the width and three quarters to the height. Here, you'll see me divide one unit of the width in half and then dividing the further most half in half again, giving me the measurement of one-quarter of the unit of one. Now that I've carefully measured the exact length of one-quarter of one of our units, I can add it to the end of my horizontal line. Next, you'll see me go through the same process on the vertical line, this time adding three quarters to the top. Finally, I can draw in the horizontal and vertical lines necessary to complete my box, which has a width to height relationship of two and one quarter to two and three quarters. Let's summarize what we've done so far. We used the width of the lid of the kettle as a single unit of proportion, and compared that unit to the width and height of the entire drum of the kettle at its widest and tallest points. We found that when using this proportion, the drum of the kettle has a width to height relationship of two and one quarter to two and three quarters. To get this box on the page, we drew one horizontal and one vertical line that gave us an initial width to height relationship of two to two. Next, through careful measuring, we divided our unit of one into quarters, which allowed us to add one-quarter onto the width and three-quarters onto the height. I'll actually draw in the two-by-two box. So we can clearly see how our initial unit of one derived from the width of the lid relates to the rest of the kettle. It's important to remember here that as long as you're drawing sticks to these proportions, you can make the drawing itself as big or as small as you want. To make this demonstration as clear as possible. I'm drawing my kettle. So it's not only in proportion with the kettle you're seeing on the screen, but also the exact same size as the reference photograph. While we were taking our initial measurements, I noticed that the exact moment that the side of the kettle turns and becomes the ellipse at the bottom of the kettle occurred almost exactly halfway up our unit of one starting from the bottom. I also know that because the ellipse is on a flat surface, the axis of the ellipse will be exactly horizontal. So by dividing our lowermost unit of one in half horizontally, I can find the exact moment on both sides of the kettle, where the side becomes the ellipse at the bottom. I can now lightly draw in the ellipse at the base of the kettle. While taking my initial measurements. I also noticed that the very tip of the top of the kettle was directly above the halfway point of the entire base of the kettle. To verify this, using my pencil, I dropped a vertical plumb line from the tip down toward the base, and sure enough, it fell exactly halfway in between the two sides of the ellipse of the kettle. To put this into the drawing, I need to divide the entire width of the kettle in half. I know that the entire width is two and one quarter units across and half of that would be one in one eighth. By dividing one of the quarter segments of our unit in half, I can arrive at one eighth. I can add that one eighth onto our initial unit of one, revealing the exact halfway point of the width of the kettle. I already know the height of the kettle. So all I need to do is project a vertical line up from this halfway point to reveal the exact location of the tip at the top of the kettle, which I can now lightly sketch in. So only using proportional measuring and plumb lines, we were able to extract some of the biggest and most important proportional relationships from the subject itself and get it onto the page. Although it's nearly impossible to do a drawing that is perfectly accurate, you can see that by using proportional measuring, I can get remarkably close. Proportional measuring works great for finding width-to-height relationships, but now I want to find the exact location of specific points of the kettle. For this, we'll switch over to angle citing. Using proportional measuring, we found the location of these three points. We're going to use these three points to triangulate the location of numerous other points. Using these two points at either side of the ellipse of the base of the kettle, I'm going to triangulate the location of the left side of the ellipse of the lid of the kettle. After holding my pencil up in front of the actual subject and capturing the angle between two of these points, I'll carefully transfer the angle over to my drawing, making sure that the angle of my pencil does not change while I'm moving it. Once I've got a sense of it, I'll draw in my first light attempt at the angle, double and triple checking that it's correct and making any adjustments necessary until I'm confident that the angle I've drawn is correct. I'll repeat this process on the other side. Once I'm confident that both angles are accurate, where they cross one another reveals the exact location of the left side of the ellipse of the lid of the kettle. We know that the axis of this ellipse is exactly horizontal. We also know its width because this is the unit that we used to discover the proportional relationships at the beginning of the drawing. Using my pencil and finger to capture this unit of one on the pencil, I can transfer it over to the lid in order to reveal the exact location of the right side of the ellipse of the lid of the kettle. You might also remember that the lowest point of the ellipse of the lid was just under our measurement of two units starting from the bottom of the kettle. With this knowledge, I'm now comfortable drawing in the ellipse of the lid of the kettle. It's important to remember that not every aspect of your subject needs to be measured in order to be drawn. It's entirely up to you to decide how much you want to measure. With the measurements I've taken, I feel comfortable drawing in the curved sides of the kettle. I'm paying particular attention to the locations where the sides of the kettle meet the ellipse at the bottom. I also feel comfortable sketching in the rest of the lid of the kettle. With the biggest shapes and volumes of the kettle measured and drawn in, I now feel comfortable addressing the handle and the spout. Using two known points, I can triangulate the location of the tip at the end of the handle. As always, I'm double and triple checking my angles for accuracy. You'll notice that once I locate a specific point on the subject, I'll lightly sketch in just enough of the context to be able to tell what the point actually is on the subject. This way, I don't have to remember what every point is in the drawing. I'm free to move around the whole subject, taking measurements, and then come back to the point that I've measured and know what it was. Next, I'll triangulate the location of the spout at its outermost point. Once again, I'll sketch in just enough of the context so that it will jog my memory when I come back to finish the spout. When accuracy is important to your drawing, you should move back and forth between measuring and drawing. When I draw, I'm always looking for the moment that I feel comfortable just drawing and letting go of the measuring process. I've reached that point with the kettle. Let's speed up the process so you can see how the drawing progresses. With the biggest and most prominent measurements and proportions already taken, I can draw with confidence knowing that my drawing is in proportion, but I'm always able to go back to the measuring process if I'm unsure about something. If you're unsure where something is or how big it is, and you're not comfortable guessing or just using your eyes alone, that's the signal to measure it. If you want to know how big or small something is compared to another aspect of the subject, that's when you should use proportional measuring. If you want to know the exact location of a particular point of your subject, angle citing is probably your best bet. We started off this drawing working with the biggest proportions and shapes. It's not until the end of the drawing that I start working with the smaller shapes and the details. I want you to notice that in today's demonstration, I've left all of my measuring and process lines on the page to be seen by the viewer. I'll encourage you to do the same when you're practicing today. Feel free to clean up and erase any mistakes or inaccurate lines, but leave your accurate angle sites and proportional boxes visible on the page so that you can clearly see how measuring provides a solid foundation for you to build the rest of your drawing on. Hopefully, you really have a sense of what it looks like to prioritize accuracy and measuring in a drawing. The important thing to remember is that, again, measuring is not a simple step-by-step process. There's no one-size-fits-all solution. Although measuring can be very technical, you also want to think of it as a creative act. It's your job as an artist to investigate your subject, to see what proportions make sense to you, and to use the different tools and strategies that you've learned in a way that best suits your needs. What you've gotten this week is a toolkit of basic measuring tools and strategies, but it's up to you to decide how and when to use them. Some artists rely almost exclusively on angle citing, other artists rely almost exclusively on proportional measuring, and some artists rarely measure anything at all, they just rely on their eyes and their own evaluations to determine proportions. Now, the artists that do rely on measuring tools and strategies, like you've learned this week, sometimes they start off doing a basic light drawing of their subject before they measure, other times they begin with measuring. Again, it is up to you as an artist to figure out what process suits you best. As you move forward with your drawing process, here are a few things to keep in mind. If you really want to prioritize accuracy in your drawings, then at least while you're learning to draw, you should rely heavily on measuring. If you do decide to measure, the next question is when and how to incorporate it into your process. Doing an extremely light and simple sketch of your subject first can really help with the size and placement of the subject on the page, or if you're more comfortable, you can begin the drawing with measuring like you saw me do today. Remember, it is up to you. During your project today, I'm going to ask you to experiment with this to see which way works best for you. Whether you start off your drawing by measuring or by doing a simple light sketch and then measuring, the next question is which strategy is going to work best. The general rule of thumb is that if you want to know the size of one part of your subject in relationship to another, use proportional measuring, but if you want to locate a specific point on your subject, then usually angle citing will work best. But remember, those are soft rules and it really is up to you. One more thing to keep in mind when you're learning how to incorporate these measuring tools and strategies into your drawing process, you want to think about these measuring tools and strategies as similar to training wheels. When you're learning how to do them, it's best to rely heavily on them, but the more you practice measuring, the more your eyes and mind will automatically make these evaluations, and you'll notice that your drawings will actually be more accurate before you even start measuring. The more you practice, the less you'll have to rely on physically using your pencil to measure things. Here's your final project. I want you to find three objects of moderate complexity. You want to choose objects that are at a similar level of complexity to the tea kettle that we drew today. You don't want anything too simple, but you don't want anything that's beyond your current skill level either. Choose something that's interesting to you and at a moderate level of complexity. I'd like you to measure and draw each one of these subjects using the measuring tools and strategies that you've learned this week. I would really encourage you to experiment with different ways of using these tools and strategies. You can start one drawing with a simple light sketch and then incorporate measuring, and on your next drawing, try starting off with measuring and then fitting your sketch into the measurements that you've gotten down on the page. Just like you saw me do in today's demonstration, I'm going to ask you to leave your process and measuring lines visible on the page. In future drawings, you'll want to minimize them, but while you're practicing, I really want you to see the impact they'll have on a final drawing. Finally, if you're going through the Art and Science of Drawing series in order, which I would highly recommend, this is an opportunity to pull together everything you've learned in the whole series. Well, I really want to congratulate you for making the investment in learning these kinds of measuring tools and strategies. They will absolutely improve the accuracy and believability of your drawings. With practice, you'll be amazed at how quickly these kinds of evaluations become second nature to you. As always, thank you so much and I hope to see you again.