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    Perspective 101

    Welcome to Perspective 101! Every illustrator needs to know what perspective is, and how to use it. There are many books out there on the subject – but until you’ve learned a bit about the basics, those books can seem intimidating. So, this thread is meant as an introduction to perspective. From here you can dive into those books with enthusiasm instead of fear; or you can just pick up the basics and run with that.

    Before I go on, a word of warning. Unlike most other skills in art, perspective is logical. Because of this, one mistake that people make with perspective is to give it a quick glance, understand it, and then because they understand it, they assume that they can use it at will without ever practicing it. (I was guilty of this at one point.) This is about the same as assuming that since you know what a piece of music sounds like, that you can play it on the piano.

    Perspective and piano both require practice. Fortunately for you, perspective is the easier of the two to learn. I have suggested assignments with each subject below.

    Index
    What is Perspective?
    One-Point Perspective
    Assignment: Rectangular Volumes in One-Point Perspective
    Two-Point Perspective
    Assignment: Rectangular Volumes in Two-Point Perspective
    Three-Point Perspective
    Assignment: Rectangular Volumes in Three-Point Perspective
    Three-Point Perspective, Continued
    Assignment: More Rectangular Volumes in Three-Point Perspective
    How Many Vanishing Points Do I Need?
    Assignment: Rectangles with Different Numbers of Vanishing Points
    Drawing From Observation Using Perspective
    Assignment: Apply Perspective to a Drawing from Observation
    Drawing Shadows in Perspective
    Assignment: Draw Boxes with Shadows
    Finding the Center
    Assignment: Mess Around with Centerpoints
    Circles in Perspective
    Assignment: Ellipses
    Drawing Shadows Part Two
    Assignment: Draw More Boxes With Shadows

    This is a work in progress. I will be adding more to it over time. If you see an error or have a request, please send me a PM and let me know!

    If you do the assignments, please post your results elsewhere. I would like to keep this thread strictly as a reference. However, if you have a particularly good example of something that you think would make this thread a better resource, let me know!

    For a much more thorough look at perspective, Elwell recommends a couple of books: Creative Perspective for Artists and Illustrators, by Ernest W. Watson, and Perspective! For Comic Book Artists, by David Chelsea. These books are inexpensive, and from the quick skimming I’ve given them so far, I am thoroughly impressed with the knowledge they contain. (I was going to add a third book to this list, but I seem to have misplaced it the darn thing. But it’s no big loss, because the former two books seem far superior.)

    For discussion on perspective, there’s a thread in progress in the Fine Arts, Studies, And Discovery section.

    Happy reading!

    Last edited by Seedling; October 22nd, 2007 at 02:58 AM.
    I think you are awesome, and I wish you the best in your endeavors, but I am tired of repeating myself, I am very busy with my new baby, and I am no longer a regular participant here, so please do not contact me to ask for advice on your career or education. All of the advice that I have to offer can already be found in the following links. Thank you.

    Perspective 101, Concept Art 101, Games Industry info,Oil Paint info, Acrylic Paint info, my sketchbook.
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    What is Perspective?

    As things move away from you in space, they appear smaller and smaller, until they vanish from sight. When you are drawing this 3D phenomena on the 2D plain that is a sheet of paper, then you are faced with a challenge: how do you know for sure that you are drawing your distant objects small enough? This is what “perspective drawing” is for.

    There is only one rule in perspective drawing that you have to know: parallel lines in space are parallel forever, but those same parallel lines, when drawn on that 2D paper, converge at a point. That point is called the “vanishing point”, because it is the point at which those lines appear to vanish.

    The most clichéd demonstration of this, of course, is the train tracks going off to the horizon.

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    One-Point Perspective

    That train-track images has a single vanishing point, so we call it “one-point perspective”. There are three types of lines in one-point perspective: lines that go horizontally across the page (such as the railroad ties in the previous drawing), lines that go vertically (imagine a line of telephone poles marching alongside those tracks), and lines parallel to the train tracks that all converge at the vanishing point.

    With those three sets of parallel lines: horizontal, vertical, and receding-into-the distance, you have to tools you need to make rectangular volumes.

    Assignment: Rectangular Volumes in One-Point Perspective

    Draw a horizontal line across your paper – and use a straight-edge. That’s the horizon. Put a point on that horizon line right in the middle. That’s your vanishing point. Then above, below, and crossing that line, draw assorted rectangles. (A) They should be orthogonal – that is, at tidy right angles to the line.

    Then, using your straight-edge (if you don’t have a ruler handy, try using a folded sheet of paper) connect the points of those rectangles to the vanishing point. (B) That turns your rectangles into rectangular volumes that extend all the way to the vanishing point. You can then shorten those super-long shapes by adding in more horizontal and vertical lines. (C)

    You’ll notice I’ve left lightly-drawn lines all over my drawing. You’ll want to do this as well, because that scaffolding will come in very handy when you get into more complicated shapes. I suggest drawing lightly with a hard pencil, so that when you really mess up you can erase, and when you’ve got a line in the right place, you can make it stand out by darkening it. Also, draw your shapes as if they are made out of glass. That is, you want to be drawing the far edges (the ones that are blocked from view) of the boxes as well as the near edges. This, again, will be necessary later when you’re drawing more complicated subjects.

    Try doing some variations on this exercise as well. Do things such as moving the vanishing point way off to the top, bottom, or side of the page, or punching holes in the boxes, or creating other shapes. The goal with these explorations will be for you to find out where this technique ceases to give good results, and get you thinking about what is necessary to accurately construct other sorts of shapes in space.

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    Two-Point Perspective

    It takes three sets of parallel lines to make a rectangular volume: horizontal, vertical, and receding-into-the distance. What if we replace those horizontal lines with another vanishing point?

    Assignment: Rectangular Volumes in Two-Point Perspective

    This time, instead of one vanishing point in the center of the page, you’ll want to put two - one on the left, and one on the right. Also this time, instead of drawing orthogonal rectangles here and there, just draw vertical line segments. Try one above the horizon, one below, and one crossing over, for starters. Make sure those line segments are between the two vanishing points for now. Then, draw lines from both vanishing points to the ends of each of those line segments. (A) The vertical line segment is now the corner of a building that extends all the way to the horizon. Add in more vertical lines - the far corners of your rectangle. (B) Connect the ends of those new line segments back to the vanishing points to fill in the rest of your box. Those lines will meet at and define the furthest corner of your rectangle.

    Everywhere that a corner occurs, there should be lines from that corner to both vanishing points. (And remember to leave all of those light scaffolding lines lying about. The more complicated this gets, the more you will need that information to identify mistakes and to continue your drawing successfully.)

    A quick word about tools and precision. When setting up a complex scene involving buildings or space-ships, it will start off exactly like this: a bunch of simple shapes in space. If your drawing contains small errors at this stage, then by the time you are down to the details, those details will be magnified. A good picture can be ruined by small mistakes made at the outset. You may find, for instance, that in a picture of the courtyard of a building, everything on the near side of the image works, but everything on the far side of the courtyard is crooked beyond hope.

    The key to keeping a perspective drawing from going badly like that is to keep those vertical and horizontal lines at perfect right angles and perfectly straight. So, either you have to eyeball where you are putting your ruler very closely (and expect that some of your drawings will go terribly wrong), or you must use a t-square and drafting table.

    A t-square is a ruler with a segment that is designed to hang over the edge of a drafting table to hold the ruler perfectly horizontal. It’s typically used with a triangle and drafting table. It isn’t necessary to have a drafting table to use a t-square, but some sort of rectangular surface is necessary. The paper is taped down to the surface while drawing to hold it in place.

    Here’s an image of how a t-square, triangle, and drafting table are used: http://etc.usf.edu/clipart/21900/219...uare_21986.htm

    You should use a t-square if you can get your hands on one, to get yourself in good habits. If you don’t have a t-square available, then at the very least use a straight-edge and a careful eye. Don’t be sloppy.

    Try out the exercise above, making various sorts of rectangles in space. Perhaps try to figure out how to make other sorts of shapes. Try starting a drawing, and then turning the paper up-side-down, or sideways, and continuing it that way. See what happens if you draw your rectangles outside of the vanishing points. See what happens if you draw your rectangles far above or below the horizon, or if the two vanishing points are closer together. Mess around to get a feel for where this system of two vanishing points works, and where it breaks.

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    Three-Point Perspective

    A rectangular volume is made up of three sets of parallel lines. You have now seen that two of those three sets can be pointed at vanishing points. Now let’s try all three.

    One-point and two-point perspective are actually simplifications of what our eye actually sees. To see why, in one-point perspective, think of the lines on the box that you draw parallel to the horizon. Imagine that instead of being entirely parallel, those lines are actually just slightly tilted towards one-another, so that somewhere, hundreds of feet off the edge of your paper, those lines actually do meet at a vanishing point. The same with the vertical lines in both one- and two-point perspective. Somewhere far above or below the horizon (and off the edge of your sheet of paper) those “parallel” lines meet in another vanishing point.

    Those parallel and perpendicular lines in one- and two-point perspective represent a shortcut. Three-point perspective is actually quite simple: every corner of a rectangular volume must be connected to three vanishing points.

    You might be wondering about the horizon. Forget about it. The horizon is something we as humans are used to seeing because we stand on the surface of the earth, and most of our life we are surrounded by big rectangular box-structures that sit neatly on the ground-plane. As long as the boxes that surround us remain neatly orthogonal, and we remain on the ground (as opposed to high above in a helicopter), then one- and two-point perspective suffice for drawing what is around us.

    But if you were standing at the foot of a sky scraper and looking up at it, or flying above and looking down, you would need a third point of perspective. That third point would not fall on the horizon, but would instead be up in the sky, or down underground. So for the sake of clarity, we can throw away the horizon for now.

    Assignment: Rectangular Volumes in Three-Point Perspective

    Draw three points on your paper in a roughly equilateral triangle. They’ll need to be close to the edges to give you enough room. These are your three vanishing points. Label them “1”, “2”, and “3”. Put a third point somewhere in the center. That point is the nearest point of a rectangular volume in space.

    Draw a line from all three vanishing points one to that first corner of your cube. (A) Then pick a second point somewhere between that point and vanishing point 1. That will be the next corner of your box. Draw lines from that point to vanishing points 2 and 3. (B)

    This gives you two triangles. Extend two more lines out from vanishing point 1, intersecting each of those triangles. That will give you a shape that looks like a book. (C) That shape is the near sides of your box.

    To find the rest of your box, just remember the rule: all corners of the box must connect to all three vanishing points. (I say “find”, because after the initial steps, you no longer get to decide where the remainder of the box goes.) There it all is! Now you just have to sort through the mess of lines for the outlines of your cube. Darken those up so that it stands out clearly.

    Try using those same three points to draw multiple boxes in space. Look for the following things to happen:

    A. Overlapping boxes. As long as you don’t get lost among all of those scaffolding lines, you can layer as many cubes over one-another as you like. The tricky part becomes deciding which one is in front of the other. That’s up to you, actually. You can also choose to turn the boxes into conjoined twins. (And as you do, start thinking about how you could make use of this to construct scenes of buildings.)

    B. If you were to connect those three vanishing points, you would get a triangle. Notice what happens when a cube extends over the edge of that triangle: it behaves like a box in one- or two-point perspective that crosses the horizon. Instead of seeing three faces of the cube, you can now only see two.

    This is more easily understood if you think about what is going on back on the surface of the earth. Think of a rectangular building from a street-level perspective. You can’t see the floor of the building because the walls are in the way; you also can’t see the ceiling because the walls are in the way. From some locations you would only be able to see a single wall!

    C. Lastly, and most importantly, think about what is going on when all of these boxes share the same vanishing points. This means the boxes are all orthogonal to one-another.

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    Three-Point Perspective, Continued

    If you want to draw boxes in three-point perspective that aren’t parallel to one-another, then each box will need to have its own three vanishing points.

    Watch out! Things will start to get confusing here with all the lines flying about. Make sure you aren’t using the wrong perspective point.

    Line management starts to become more necessary when you’ve got such a tangle of scaffolding. You might want to start selectively erasing some of the lines to keep yourself sane. Don’t obliterate all of it, however. You will need at lest two lines from each vanishing point so that you can tell at a glance which vanishing point goes with which box.

    Assignment: More Rectangular Volumes in Three-Point Perspective

    Try it!

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    How Many Vanishing Points Do I Need?

    In any given scene, the position of the rectangular objects will dictate whether you will need to use one-, two- or three-point perspective, and whether any of those objects share vanishing points with each other.

    It is entirely possible for different objects in a scene to require different numbers of perspective points. For example, a scene with buildings that sit at a thirty-degree angle to one-another. Those two buildings might each be best drawn with two-point perspective, but one or both of their vanishing points would be at different places along the horizon. If a flying car were zipping around the corner between them at a dramatically tilted angle, then that flying car would require three entirely different points of perspective, none of which would be on the horizon.

    Assignment: Rectangles with Different Numbers of Vanishing Points

    Try drawing rectangular volumes with one, two, and three points of perspective all in the same image.

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    Drawing From Observation Using Perspective

    Rectangular blocks are fun for a while, but ultimately they need to be combined with drawing from life or imagination if they are going to do you any good.

    This is a sample of how perspective can be applied to a drawing made from direct observation. On the left I scribbled down my impression of a cardboard box. For every line I drew, I was asking myself two things: where is the vanishing point that this group of parallel lines points to? And compared to a horizontal or vertical line, what angle is this edge on the 2D plain of my paper?

    On the right side, I scribbled out the same loose drawing a second time, and then used a straight edge over top of that sketch to correct and adjust the drawing in perspective.

    A, B, and C are the locations of the box’s vanishing points. A is the only one that happens to be on the page. B is close enough that the lines visibly converge towards it. C is far enough away that this drawing could just as well be considered two-point perspective.

    So what can be done about a vanishing point that is off the edge of the page? One method is to attach another piece of paper. In this case, I’ve just eyeballed my lines carefully. As long as the lines appear to be converging at the same rate, that might be all the precision I need for a drawing of a simple cardboard box.

    The drawing itself will tell me if I have improvised poorly, because the more incorrect my improvisations are, the more errors will spring up. The biggest telling point will usually be the far, hidden points of any rectangular volume. If only two of the three lines meet properly there, then a mistake has been made. (Which is why it is important to draw the hidden sides of objects.)

    There are, of course, more precise ways of dealing with this sort of problem, because architectural draftsmen can’t rely on any sort of guesswork in their drawings. But that stuff can come later.

    Assignment: Apply Perspective to a Drawing from Observation

    Find a tissue box, cereal box, brick, or other simple rectangular volume, and draw it from multiple angles by first sketching, and then correcting with a ruler. Identify the locations of all three vanishing points.

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    Drawing Shadows in Perspective

    If you take the time to draw an object properly in perspective, you can spoil it by guessing where its shadow will fall. Hard light falling on hard-edged objects create hard-edged, precise shadows. All the same rules that apply to boxes apply to rays of light, too.

    The sun, a light bulb, and the flame of a candle all have one thing in common: under certain conditions each behaves like a vanishing point. Rays of light extend in straight lines in all directions from such a light-source.

    The first drawing below is a diagram of how to think of light when drawing in perspective. A rectangle sits on the ground, and above is a light-source. A ray of light drawn from the light source to the corner of the rectangle and then to the ground shows where the shadow of that object would end.

    From the light I have also extended a line straight down to the ground. Where that line meets the ground is just as important as the light-source. Look at the next drawing to see why. Lines drawn from that point through the lower corners of the boxes then intersecting with the rays drawn from the light to show where the shadow ends.

    Basically, when a light is in a scene, you have to draw several right-angled triangles to calculate where the shadow will fall.

    The third drawing shows the sun. The only difference between the sun and a nearer point of light is that the point below the sun goes on the horizon.

    If the sun is behind you then it will behave differently, but this method works if the sun is in the picture or just beyond the edges of the picture.

    The edges of shadows cast by a box will be parallel to the edges of the box. This means that if you do this correctly, the edges of your box’s shadows will point to the same vanishing points as your box.

    Assignment: Draw Boxes with Shadows

    Try drawing boxes with one- and two-point perspective lit by points of light in different locations. Try drawing a box with a light directly above it. Try drawing a box that is lit with two light-sources.

    One thing to note: for now, use one shade of gray for everything that falls in shadow, and leave the rest white. This is because a common mistake that people make when shading cubes is to use gradients. In reality, reflected light may cause some gradients, but reflected light is small potatoes compared to direct light. Keep it simple for now by using only flat gray.

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    Finding the Center

    Here is an easy trick that you will use over and over. To find the center-point of a rectangle in perspective, draw lines connecting the opposite corners. Where those lines meet is the center.

    Connect the center to a vanishing-point to cut your rectangle in half.

    This trick can be used to subdivide rectangles over and over and over.

    Assignment: Mess Around with Centerpoints

    Use this trick to make checkerboards or other patterns on rectangles in perspective. Or, for more of a challenge, use this trick to make a rectangular donut, or other 3D shape.

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    Beautiful, Michelle. Great work on the thread and very thought out, I'm going to go over all this again. Five stars from me.

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    Wow, Seedling, this is fantastic.
    Very detailed and easy to understand, five stars.
    Thank you so much.

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    So wonderful and helpful! Thank you very much, Seedling. Sums up a good chunk of my illustration class

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    I have one doubt, how can I draw a perfect cube in perspective

    thanks for your efforts, its great

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    Seedling will you be also covering the human body in perspective, with foreshortening as well?

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    Thanks everyone!

    FYI, here is a list of topics I plan to get to. I need to finish doing more research before I'll be prepared to cover all of them. Please feel free to suggest more.

    perfect cubes
    repeating patterns
    circles
    constructing scenes from imagination
    field-of-vision
    fish-eye perspective
    humans in space

    I read the first half of Perspective! For Comic Book Artists last night, and I am absolutely delighted with it. The comic-book medium is absolutely perfect for teaching perspective, and the author provides detailed (and humorous) illustrations of absolutely everything. My little tutorial is a pale and boring shadow next to his book.

    Last edited by Seedling; October 14th, 2007 at 10:07 AM. Reason: adding to the list
    I think you are awesome, and I wish you the best in your endeavors, but I am tired of repeating myself, I am very busy with my new baby, and I am no longer a regular participant here, so please do not contact me to ask for advice on your career or education. All of the advice that I have to offer can already be found in the following links. Thank you.

    Perspective 101, Concept Art 101, Games Industry info,Oil Paint info, Acrylic Paint info, my sketchbook.
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    Quote Originally Posted by White Rose View Post
    Seedling will you be also covering the human body in perspective, with foreshortening as well?
    Good idea! (Just as soon as I figure out how!)

    I think you are awesome, and I wish you the best in your endeavors, but I am tired of repeating myself, I am very busy with my new baby, and I am no longer a regular participant here, so please do not contact me to ask for advice on your career or education. All of the advice that I have to offer can already be found in the following links. Thank you.

    Perspective 101, Concept Art 101, Games Industry info,Oil Paint info, Acrylic Paint info, my sketchbook.
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    all of that is covered in a Andrew Loomis's books. just google him, you should find them somewhere.

    or just find all of Kevin Chen's demos that should still be up on CA somewhere.

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    you've got some good stuff here. nice to see someone attacking the task of understanding perspective.

    perhaps it would be best to cover things that many people have the most trouble with:

    accurate ellipses from all angles
    constructing angled surfaces accurately (i.e. how do i construct a surface at a 45deg angle from the ground)
    measuring distances (along perspective planes)
    constructing non-rectilinear surfaces from crossections.

    i realize a lot of this has been covered in books and by people such as scott robertson, but it would be nice to have it all in one place.

    Last edited by Mark Bot; October 14th, 2007 at 11:18 PM.
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    Quote Originally Posted by Seedling View Post
    If you take the time to draw an object properly in perspective, you can spoil it by guessing where its shadow will fall. Hard light falling on hard-edged objects create hard-edged, precise shadows. All the same rules that apply to boxes apply to rays of light, too.
    Just a note: Not really. This is outside of the scope of the thread, but shadows of any object will have the same type of edge as any other object based on light conditions, including straight edged ones. The farther away an object is from the surface onto which it falls, the softer its edges will be. You can test this very simply by observing how shadows change with height under an overhead lamp. I think it's caused by dust in the air, but I really don't know. It's cool seeing trees and buildings with clearly defined shadows on the base and blurry on the shadows of top.

    I'm surprised if you didn't know this, it's an easily observed phenomena, although (for me) not an easily renderable one. Unless you're using "hard edged' to mean something different; in which case, this is really outside the scope of the thread.

    By the way, I'm really anxious for the perfect cube installment. I always figured you might be able to do it with Pythagorean theory, but I never had the intellectual toolkit to figure it out. But if you can do it without math that'd be awesome.

    Last edited by Zaxser; October 15th, 2007 at 06:16 AM. Reason: out
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    Quote Originally Posted by Zaxser View Post
    This is outside of the scope of the thread, but shadows of any object will have the same type of edge as any other object based on light conditions, including straight edged ones. The farther away an object is from the surface onto which it falls, the softer its edges will be. You can test this very simply by observing how shadows change with height under an overhead lamp.
    While this is correct, please note I said “hard light”. When a light is filtered through substances that scatter the light, such as particles in clear air over a great distance, it becomes softer. However, even when a light is quite soft, the shadows are still going to fall in a mathematically precise place based around the shadow that can be calculated in perspective. Guessing at the location of such a shadow may expedite things, but novices at perspective typically guess poorly and glaringly, so it’s a good idea to get in the habit of using perspective to calculate shadows before getting back out of the habit.

    Quote Originally Posted by GusTheRobot View Post
    i realize a lot of this has been covered in books and by people such as scott robertson, but it would be nice to have it all in one place.
    Thanks Gus. I’ll have to point people in the direction of published sources for certain information, because I struggle to understand the concepts involved. The folks who have taken the time to write actual published books on this stuff are the real experts, and there is no way I could summarize everything they have written here even if I wanted to.

    I think you are awesome, and I wish you the best in your endeavors, but I am tired of repeating myself, I am very busy with my new baby, and I am no longer a regular participant here, so please do not contact me to ask for advice on your career or education. All of the advice that I have to offer can already be found in the following links. Thank you.

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    Quote Originally Posted by Zaxser View Post
    Just a note: Not really. This is outside of the scope of the thread, but shadows of any object will have the same type of edge as any other object based on light conditions, including straight edged ones. The farther away an object is from the surface onto which it falls, the softer its edges will be. You can test this very simply by observing how shadows change with height under an overhead lamp. I think it's caused by dust in the air, but I really don't know.
    The softening of shadow edges (the penumbra) depends on both the distance of the object from the surface and the distance and quality of the light source. It is caused by light "spilling" around the edges of the form.


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    Specifically, the distance and size of the light source together determine its angular or apparent size, which is the really crucial factor, since the penumbra is the zone where the light source is partly obscured. The penumbra can be easily mapped using seedling's construction by taking lines from opposite sides of the light source. This diagram below may clarify why the width of the penumbra would increase with the angular size of the light source as well as with the distance from the object casting the shadow.

    Incidentally, seedlings construction can be adapted for situations where the sun is behind the observer (and hence not appearing in the picture plane). You apply the same sort of construction, but use the point on the ground opposite the sun (i.e. the shadow of your head) in place of the sun. Your shadows will converge toward the point on the horizon directly above this anti-solar point, and lines from the latter still give the length of the shadows.

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  36. #24
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    Thanks for sharing that, Briggsy.

    I think you are awesome, and I wish you the best in your endeavors, but I am tired of repeating myself, I am very busy with my new baby, and I am no longer a regular participant here, so please do not contact me to ask for advice on your career or education. All of the advice that I have to offer can already be found in the following links. Thank you.

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    Dude I was just looking for a simple, beginners perspective tutorial. This is great, thanks. If you have time/enthusiasm I would love to see this extended on.

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    Ding lol grats, Lohan, you just hit 1000 posts!

    I certainly will be adding to this. . . teehee!

    I think you are awesome, and I wish you the best in your endeavors, but I am tired of repeating myself, I am very busy with my new baby, and I am no longer a regular participant here, so please do not contact me to ask for advice on your career or education. All of the advice that I have to offer can already be found in the following links. Thank you.

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    great tutorial! covers most of what i learned in perspective at school, minus a few more complicated things like staircases and whatnot. There goes $1600 bucks, :-(, although it forced my lazy butt to do all the work, . I would also show how to make a grid in one and two pt perspective, comes in handy, you kind of show it in the centerpoints part but not extended on.

    center-points ftw.

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    Thanx people here... i really do learned something here.. now i understand more about perspective... Seedling, your tutorials are more than i learnt before.especially about why we do 3 vanishing points perspective.. cuz i was wondering alot.
    And thanx Briggsy for the shadow tutorial i really enjoyed it

    wish you the best and show us more

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    Hurray for my first reply on the forums.
    This was EXTREMELY helpful. I have finally started getting into perspectives. It is enjoyable and consumes time that I only can waste at the moment. (No worries, not saying it's a waste of time)
    But, again, thank you for this. :]

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    Great thread. Clear and precise illustrations.

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