Proko - Assignment - Tumble Cubes

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Assignment - Tumble Cubes

Marshall Vandruff

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About instructor

Marshall Vandruff

I Teach Creatives

assignments 263 submissions

I tried to combine both assignments by starting with the flaps, then finding their carried horizons and building out the rest of the cube.

LESSON NOTES

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The secret to drawing like masters who invent forms without copying is constructing with forms without slowing down. This lesson assumes you can draw a box in perspective but want to step up your accuracy.

Fixing Arbitrary Convergence

When you draw freehand lines aiming in a general direction, they often go wrong. This creates arbitrary convergence. This distorts the illusion of your drawing. Making straight lines with a ruler does not mean placing them well.

All receding lines must converge toward one point per system. Randomly choosing the positions of vanishing points is a mistake. You need a horizon to define what is level.

Tumbling Forms

Anything level has vanishing points on the setting's horizon. When cubes spin on their Y-axis, they stay level. This is called yaw. The vanishing points crawl back and forth on the horizon. Vertical lines stay vertical.

Things change when a cube tumbles.

Roll: Tumbling on the Z-axis. Vertical lines no longer stay vertical.
Pitch: Tumbling on the X-axis. The Z-lines no longer aim at the horizon.

How do you draw anything that is not level? You use two methods.

The Vanishing Trace

The first method is the vanishing trace, also called the vertical trace.

When you swivel a form on yaw, the vanishing points crawl left and right along the horizon. If you flip the scene 90 degrees, the horizon becomes vertical. This vertical line tracks non-level lines. A line right-angled to the horizon can trace tumbling lines in pitch or roll.

The Carried Horizon

What if you pitch, yaw, and roll a form all at once? You need to understand the carried horizon.

An object carries its horizon line with it. If you spin your drawing paper, the lines of the object stay intact. The Y-line is the stem of the form and the axis of aspect. The Y-line always stays fixed and perpendicular to its horizon line. This applies whether the horizon is level or carried.

Receding lines always aim to a point on a horizon. This is true even if the horizon is out of your vision or not horizontal. Tumbling cubes have carried horizons hidden from those who do not know this secret.

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ASSIGNMENTS

Assignment 1 - Box Flaps

Draw a solid box in a three-quarter view at ground level. Make sure it has good convergence and clean drawn-through lines.

Give the box a top flap in an open position. Place the vanishing points for these non-level planes up and down along the vanishing trace. Try a few flaps going up and away, and flaps going down and away. This teaches you to draw declined and inclined planes, stairs, or roofs.

Assignment 2 - Hidden Horizons

Choose 20 cubes you have drawn previously. Redraw them with your new understanding.

Find the hidden right-angled carried horizon and vanishing points for each tumbling block. You may need a T-square and triangle to be sure of that 90-degree angle.

Sketch them, check them, and correct them. Repeat this 20 times. Do this until you can clearly see the horizon as 90 degrees to the Y-line. You will imprint this relationship so deeply that you will never need to draw it out again. You will see horizons where others cannot.

Deadline - submit by July 05, 2026 for a chance to be in the critique video!

Maria Bygrove

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Assignment 2 - hidden horizons ... I'm confused. I understand the part about "cutting a box out of the page" and rotating it and how the horizon rotates with it. I understand that the lines have to not only converge, but they have to all converge to one single point. But I don't understand what is the Y-line that has to stay perpendicular to the carried horizon. I'm assuming it's a line on which the Y vanishing point is located - is that correct? But I don't understand how do we find it. When drawing a box, I used to start with the Y-shape of the nearest corner, and go from there. But if I do that, draw a box that looks ok-ish to my eye, and then drop a line from the Y vanishing point to the XZ carried horizon in a way so it's perpendicular... well, it's just a perpendicular line, that doesn't often even go through the box, so it's not exactly "the stem of the form". So this seems to indicate that, instead of starting with the Y-shape of the nearest corner, one should start with just a V-shape, then finish the bottom (or top) plane of the cube, establish the X and Z vanishing points, then the XZ carried horizon, then find the center of that bottom plane, and from that establish the Y-line... Is that how one should draw the box to get it sound? I read through the earlier discussions and it seems like more people are confused about it but I didn't find a clear answer. Hope it might be addressed in the critique but if anyone has a an answer, I'd be very grateful. Haven't done my 20 boxes because I fear that I'm doing this all wrong.

Pamela D

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Hi Maria, the way I understand the ‘y.’ Line is it’s the height line and it’s also the Yaw when the box spins. I think if you imagine the box spinning on its centre axis it helps to confirm it’s the Y line. The box pitching and rolling spins on the z and x lines. Also it’s easier to see the y axis on 2 point perspective as the y line is straight.

Maria Bygrove

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Assignment 1 - box flaps I think I understand this.

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These are my box flaps assignment submissions. I used a straight edge for my lines on these. My freehand ellipses are nothing to be proud of so I used an ellipse template for several of these. If my memory serves me correctly, all of these but page 23 were follow alongs. Cheers!

Max Long

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This is my assignment 2 Hidden Horizons submission. I traced and transferred some of the cubes from the “Control Depth on Paper with a Simple Box” assignment, and then corrected them with the red, green and blue pencils signifying the axis. If there is a #, that’s the reference number from the Control Depth on Paper…. assignment. Some of the horizons are level and some are not level. Some of the first ones, all the Y axis lines are parallel at a 90° angle to the horizon line. Some of these, I referenced a Zolly image, and I attached a screenshot of the Zolly image. I know that you said to do these freehand and then make the corrections, but I must confess that I cheated and used a straight edge for the assignment. The off the page vanishing points were a challenge to do. Cheers!

Angelica

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At first I mixed up which flaps should go to which vp and felt a bit confused. But after a while I started to get the hang of it. For the hidden horizon assignment I draw the box and then checked myself and found the vps with a red pencil then I corrected myself and checked again with a new color and so on.

Marshall Vandruff

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You got it Angelica!

Ishaan Kumar

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ASSIGNMENT: HIDDEN HORIZONS This was also an eye-opener in terms of being a great way to check if lines are converging correctly or not. I know for a fact that a lot of mine are not but the knowledge of carried horizons will definitely help me be less shabby. Apologies in advance for the untidy pages.

Marshall Vandruff

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Untidy but well used. May your brain benefit.

Ishaan Kumar

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ASSIGNMENT: BOX FLAPS There's a whole range of attempts here, from complete ones with darkened flaps to half-attempts that have been abandoned. I tried as best as I could to maintain proportions with the flaps. What was interesting was how much help this one vanishing trace line was to figure out the convergence of flap lines.

Jyayasi (*Jay-o-she*)

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For the carried horizon project, first I drew tumbled cubes with the newly heightened consciousness and then I decided to correct my old boxes. I have a doubt in the vanishing trace project. In the last attached image, considering the point O to be closest to me, the red flaps seem to be the correct ones logically but they suddenly go to the vanishing trace B whereas that plane when level goes to vanishing point A. Also, they look wrong as compared to the green ones which go to the same vanishing trace A as the plane when level. So, my question is, should we bother about which point is closer to us or we let the receding convergence of the same plane go to the same vanishing trace for any position, level or not level? Or am I doing something wrong. Because when I watched Marshall do it everything looked right but when I am doing it I am getting confused mid-way of the project.

Marshall Vandruff

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In your final drawing, none of those flaps would go to the trace on B (except, of course, the fulcrum , or width line of the flaps) because they point to the left, whether up to the left, or down to the left.

Carlos Javier Roo Soto

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Here's my final submission with the Box Flaps. I don't understand what happened in the last one I did today (Third image, bottom to your left), I tried to not use a ruler but when I did the slanted rooftops they weren't converging properly and on top of that when I tried to clean it up my lines kept waiving. Maybe is because I spent all day with the sketch I did for the 4th of July (Not my OC, fanart of the VTuber SmugAlana) and my carpal tunnel isn't been generous to me. Another thing I noticed is that I tend to overdo the flaps, maybe 2 or 3 is enough, and clutter them together too much and creates this visual mess. And I apologize again to Marshall, you told me to play around, but the only thing I played around with was the two characters you see, not enough play and exploration. I'm gonna rest-up my hand tomorrow and maybe Tuesday too, go do the Gestural Perspective from Stan's Basics course and try to play around more.

Kassjan (Kass) Smyczek

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Did a lot of flapping. Hope I also get to do assignment two in time. We‘ll see…

Dooby

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Part 2 I did the initial sketch freehand in pencil, then clean them up with a ruler and pen Some of the 2 point boxes with perfectly vertical y-lines look a bit skewed when I rotate the page. is that normal or did my hand somehow slip with the ruler?

Marshall Vandruff

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Sometimes 2-point boxes look skewed because they want a third point. You have every right to deny them this, but it makes you seem stern. Allow them a little as you feel generous or as they irritate you so much that you give in to them.

Leif

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got behind because of school and health but getting back into it. I feel like i am understanding the vanishing trace and the moving horizon line though I don't get how to maintain proportions through it all

Marshall Vandruff

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No prob. That's next.

Li Ming Lin

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Most of the box flaps seemed alright, except a few flaps turned out weird; and I'm not sure why??? In particular, the ones at the top-right corner next to the giant question mark. I wasn't sure where to put the VP on the "vertical horizon line", so I just randomly chose a place. For the 20 cubes, I first drew in the cubes with thicker lines without a ruler, and redrew them again using a thinner pencil and a ruler. They sometimes matched. However, I found the Carried Horizons… limiting…? Because for me to get the lines to match best I can, I had to think about the vanishing points BEFORE imagining the box that I wanted. Was that supposed to happen? Please let me know if I've done something wrong. Thank you

Marshall Vandruff

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The problem near your big question mark is that you are making lines converge as they come toward us, rather than as they go away from us.

Stevie Roder

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I drew my cubes freehand, Most of them I'm hoping are in three quarter view at least I treid to make them that way. While guessing where the Horizen and vanishing points go was a fun challenge. I also combined both challenges into one. Tumbling my cubes while drawing their flaps, as well as figuring out where the Horizen Lines go into one. I belive I had a bit better understand here this time now on where to place my Horizen Lines at i'm hoping. Tried to make it more fun with my tumbling cubes into different directions with each of them as well. Did these over last weekend just tried to find time to post these lovely cubes of mine was a challenge in itself. Overall had lots of fun on this assignment as usuall. I think I may now have a bit understanding know how to Tumble my cubes thanks for that Marshell.

Stevie Roder

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I'm hoping I'm starting to get the slow grasp of this. not sure if i'm doing this right or not. I believe I'm tumbling my cubes correctly here but would love some fun critisium.

Randy Pontillo

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10d

The vanishing trace felt more consequential than something to actively use, I only added the vanishing traces after the flaps were already drawn. I connected the flaps' ends' to the corners of the fulcrum on the cube. Then again, it DOES look off to me so i probably just did it wrong? Working from vanishing trace to fulcrum makes logical sense, but it doesn't sound very practical when drawing something.

Randy Pontillo

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10d

whoops! I wrote carried vp instead of vanishing trace on the paper

shaswat

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10d

Assignment 2: I don't think I have fully understood the concept of carried horizons. The critiques should help. Though, I did get quite a few of them accurate off the cuff, so grinding through the 100 cubes definitely helped :D

Sandy

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10d

I struggled a lot with the flaps, and still kind of felt like i was guessing but i will practice it more because i think i understand. the hidden horizon was nice to slow down and see the corrections in boxes i had already made