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Drawing with perspective, part 2: Cavalier Projection
Well, of all the days one would want to do a post about perspective drawing, Christmas Eve probably isn't the best choice. ;o) But well, part 2 is all done and I figure I can always link back to it after the holidays.
Previously on Drawing with Perspective: a quick intro into parallel projection. Last time I constructed the simplest of shapes - a cube - using a simple form of parallel projection called cavalier projection or its sub-form, cabinet projection. (You don't need to know those denotations, honestly I never heard them before. I just use them here to keep things sorted.)
Okay, so today I'm gonna do a couple more complex shapes. Let's start with something that might pass for a table. It's not gonna win any design awards but should serve its purpose.
Example 1: table
We start off drawings of the front, side, and top (image below, left side) which contain all the info we need for a 3-D drawing. As in all cavalier projection, one plane remains unchanged. In this case I start off the front plane.
First I copy the front view exactly as is. The, as I did with the cube, I draw the receding lines at a 45° angle (it doesn't have to be 45° but it's easiest, thus common) and mark the end points using the information about the depth of the table and the legs (in this case 'b' and 'c'). To enhance the illusion of perspective all receding lines can get forshortened (commonly by a factor of 1/2 or 2/3; I decided on 1/2 in all my examples here).
(see pic 1)
note: all colored lines are just subsidiary lines.
Next I draw in the lines of the back side of the table, starting off the end point and going parallel to the lines of the front plane. I also add a bunch more subsidiary lines to determine the exact shape of the table legs. (see pic 2)
As you can see in (pic 3) the subsidiary lines cross each other, giving me the information I need to add the vertial lines of all four table legs. (pic 4)
It's kind of hard to describe with words but I hope the images make sense.
example 2: slightly trickier table
This table is a bit more difficult, since the table legs aren't on the outside; they aren't touching the base plane as the front of the table is. That's why I added the subsidiary lines (in blue) which are needed to construct the exact location of the table legs. It should become clear in the drawing.
Basically, perspective construction is all about subsidiary lines!
example 3: really ugly house
I made the construction drawing in two different versions. Version 1 starts off the front plane like I did with the tables above. Version 2 shows the same house, starting off the bottom plane. (Note that in that form of cavalier projection, no lines get foreshortened.)
The basic principles of construction are the same as in the table examples above.
As you can see, the second version looks quite distorted. Usually I'd change the angle or try a different base plane to get a better result (but in this case I was too lazy to re-do all the drawings... besides, it nicely illustrates the shortcomings of this type of perspective drawing.)
Here's another quick example of constructing the same shape while using a different plane as base each time:
example 3a: roof
example 4: cylinder
Alright, now comes the fun part: So far we've just worked with straight lines, so let's construct something more interesting:
Of course we could weasel out of it by simply declaring the round side as base plane that shall remain undistorted...
but that'd be boring, and ellipses are fun. :)
So, here's how one constructs an ellipse in parallel projection. (It's also the basic technique how you construct an ellipse in isometric projection, or in any kind of perspective. Useful stuff.)
Basically you create an octagon, wich is a close enough approximation of a circle that the missing bits can be fleshed out freehand. How to get these eight points:
Looking at the image below, you see I drew a circle inside a square right below the ellipse I want to create. My eight to-be-projected points are the four corner points in the top, bottom, left, and right, as well as the four points in which the circle intersects with the diagonals.
Now I just need to project those points onto the distorted plane above, by adding the same subsidiary lines. Now all that's left to do is to connect the points into a circle. (That takes a bit of practice.)
Once that is done, you draw two vertical lines starting at the outmost parts of the ellipse, and copy your elipse down at the bottom using the height of the cylinder, b.
Done!
I'm gonna stop here, since I want to do isometric projection next which is not entirely dissimilar.
But here's an excercise I've cooked up. The object to construct: this ink bottle.
The problem: draw this in cavalier projection starting off the bottom plane, or in cabinet projection starting off the front. Or both, for the overachievers.
(download worksheet here)
The solution is here but I figured maybe some of you want to try it on your own first, so I'm linking to it.
On to part 3: Isometric Projection
Previously on Drawing with Perspective: a quick intro into parallel projection. Last time I constructed the simplest of shapes - a cube - using a simple form of parallel projection called cavalier projection or its sub-form, cabinet projection. (You don't need to know those denotations, honestly I never heard them before. I just use them here to keep things sorted.)
Okay, so today I'm gonna do a couple more complex shapes. Let's start with something that might pass for a table. It's not gonna win any design awards but should serve its purpose.
Example 1: table
We start off drawings of the front, side, and top (image below, left side) which contain all the info we need for a 3-D drawing. As in all cavalier projection, one plane remains unchanged. In this case I start off the front plane.
First I copy the front view exactly as is. The, as I did with the cube, I draw the receding lines at a 45° angle (it doesn't have to be 45° but it's easiest, thus common) and mark the end points using the information about the depth of the table and the legs (in this case 'b' and 'c'). To enhance the illusion of perspective all receding lines can get forshortened (commonly by a factor of 1/2 or 2/3; I decided on 1/2 in all my examples here).
(see pic 1)
note: all colored lines are just subsidiary lines.
Next I draw in the lines of the back side of the table, starting off the end point and going parallel to the lines of the front plane. I also add a bunch more subsidiary lines to determine the exact shape of the table legs. (see pic 2)
As you can see in (pic 3) the subsidiary lines cross each other, giving me the information I need to add the vertial lines of all four table legs. (pic 4)
It's kind of hard to describe with words but I hope the images make sense.
example 2: slightly trickier table
This table is a bit more difficult, since the table legs aren't on the outside; they aren't touching the base plane as the front of the table is. That's why I added the subsidiary lines (in blue) which are needed to construct the exact location of the table legs. It should become clear in the drawing.
Basically, perspective construction is all about subsidiary lines!
example 3: really ugly house
I made the construction drawing in two different versions. Version 1 starts off the front plane like I did with the tables above. Version 2 shows the same house, starting off the bottom plane. (Note that in that form of cavalier projection, no lines get foreshortened.)
The basic principles of construction are the same as in the table examples above.
As you can see, the second version looks quite distorted. Usually I'd change the angle or try a different base plane to get a better result (but in this case I was too lazy to re-do all the drawings... besides, it nicely illustrates the shortcomings of this type of perspective drawing.)
Here's another quick example of constructing the same shape while using a different plane as base each time:
example 3a: roof
example 4: cylinder
Alright, now comes the fun part: So far we've just worked with straight lines, so let's construct something more interesting:
Of course we could weasel out of it by simply declaring the round side as base plane that shall remain undistorted...
but that'd be boring, and ellipses are fun. :)
So, here's how one constructs an ellipse in parallel projection. (It's also the basic technique how you construct an ellipse in isometric projection, or in any kind of perspective. Useful stuff.)
Basically you create an octagon, wich is a close enough approximation of a circle that the missing bits can be fleshed out freehand. How to get these eight points:
Looking at the image below, you see I drew a circle inside a square right below the ellipse I want to create. My eight to-be-projected points are the four corner points in the top, bottom, left, and right, as well as the four points in which the circle intersects with the diagonals.
Now I just need to project those points onto the distorted plane above, by adding the same subsidiary lines. Now all that's left to do is to connect the points into a circle. (That takes a bit of practice.)
Once that is done, you draw two vertical lines starting at the outmost parts of the ellipse, and copy your elipse down at the bottom using the height of the cylinder, b.
Done!
I'm gonna stop here, since I want to do isometric projection next which is not entirely dissimilar.
But here's an excercise I've cooked up. The object to construct: this ink bottle.
The problem: draw this in cavalier projection starting off the bottom plane, or in cabinet projection starting off the front. Or both, for the overachievers.
(download worksheet here)The solution is here but I figured maybe some of you want to try it on your own first, so I'm linking to it.
On to part 3: Isometric Projection
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Hee :)
Ich war zu faul für Lineal, aber ging trotzdem ganz gut, und es war gut zu wissen, wie ich das Lineal verwenden könnte, wenn ich nur wollte.
Ja, ich habe die meisten Sachen auch nur mit Lineal gezeichnet, damit die Details besser rauskommen. Gerade auf Millimeterpapier gehts auch gut ohne.
Ich hab mir gestern zu Weihnachten einen Skizzenblock und Buntstifte gekauft und will jetzt so viel zeichnen - theoretisch, aber praktisch hab ich einen "ich kann nicht zeichnen :(" Block im Schädel. Den werde ich überwinden!
Fanart ist super für das Überwinden so eines Blocks!
Und ich kann nur empfehlen, den Skizzenblock einfach überall mit hinzunehmen... einfach ganz zwanglos hier und da skizzieren, wenn einem was interessantes ins Auge fällt, oder wenn man irgendwo warten muss. Ich hatte das eine ganze Weile gemacht. Sollte es mir eigentlich wieder angewöhnen, da sind ein paar schöne Skizzen bei rausgekommen und das ganze fungiert auch als eine Art visuelles Tagebuch...
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