Parabolic Paper Stitching: Geometric Curves from Straight Lines

1. Introduction: Are you an artist, sewer or crafter, who enjoys using symmetry and pattern in your work? If so, you might be interested in learning how to create curved geometric patterns from a simple straight line grid. Hi everyone. I'm Clarissa and I'm a geometric artist and teacher from Suffolk in the UK. Welcome to this mini workshop where I'll be teaching you how to hand stitch parabolic curves onto watercolor paper. The stunning designs that you create will be suitable for framing and displaying in your home. For giving us to loved ones, or for using in card making for Christmas cards, or cards for all occasions. Join me as I take you through everything you need to know from the materials you'll need to complete the project. How to draw the pattern using the principal templates. How to prepare your paper or card for stitching. And how to sew both a simple and a more complicated multi layered pattern. Finally, I'll also be showing you some more design ideas to spark your imagination. So let's get started. 2. The Class Project: The project in this class is to design and hand stitch a parabolic curve pattern onto watercolor paper or card. We'll begin by looking at the materials needed to complete the project. I'll then carefully demonstrate the process of drawing the pattern on paper first so that you're confident with how it works. Next, I'll show you how to align the template centrally and how to punch the holes ready for stitching. Finally, I'll demonstrate the simple parabolic pinwheel design before showing you how to add further layers to build the complexity of your design. I'll also be showing you some alternative designs to spark your imagination. You'll need your printable templates at the ready. Do download the class notes below, which come with a handy materials list, as well as some additional design ideas to try. When you've finished your project. Remember to upload some photographs to the project section. I do so love seeing your work and it's also great for other students to have a bank of images to be inspired by. Let's get started on this project with a closer look at the materials that you'll need. 3. Materials for the Project: Before you start to stitch, you're going to need to pre punch the holes in the paper. For this stage, you're going to need a ruler, a pencil, and an eraser. You'll need to print off your chosen size of printable template. You can choose from small, medium, or large. You'll need something to pierce the paper with. I use this little paper piercer, You could use a pin. You could use the point of a drawing compass. Something that's going to pierce the paper, but not make too large a hole in it. You'll also need a soft surface to place under your paper while you're punching the holes. This old felt laptop cover of mine is really useful for that. Or a cork table mat, or if you haven't got either of those things, then a piece of cardboard from some packaging would be fine. You might find a small magnifying glass useful, depends on your eyesight. It can be useful just for precision purposes. And finally, you'll need the paper that you'd like to stitch your pattern on. I wouldn't go too large because you're going to be manipulating the paper quite a lot. You'll be turning it up and down as you stitch. So anything too large just gets in the way you could think about a little postcard size piece. This is a 20 centimeter by 20 centimeter square piece. This is an four letter sized piece. Watercolor paper is best round about 300 GSM. The paper needs to be quite stiff in order to support the weight of the stitching. For the stitching stage, you're going to need the thread you want to stitch your pattern in. I like this fine metallic machine embroidery thread. It adds a lovely decorative glint to a piece of work. But any sort of thin thread, I wouldn't go too chunky or thick. For example, two or three strands of embroidery floss would probably be perfect. You'll need a needle. A general purpose sewing needle is fine, nothing too thick. You don't want to make the hole in your piece of paper too large a pincushions useful. If like me, you're constantly losing your needles, you'll need a pair of scissors, any old scissors will do. And finally, some masking tape to secure the thread on the back of the sheet of paper. This I find is the easiest, most convenient way of doing so. 4. Curves From Straight Lines: Before we start, I think it's a really good idea to have an idea of how the pattern works. You can use one of the principle templates for this practice, drawing a few of the parabolas before you start to stitch. Essentially, the parabolas are formed between two lines that make up a V shape. You could have, for example, a parabol going between these two lines, or these two lines, essentially any pair of lines that met at a point. There are also wider V shapes within the pattern. For example, this is a wider V shape, two lines that met at a point. You can draw a parabola between any pair of lines that meet at a point. I encourage you to explore various different ways of doing so. What I'm going to do is highlight for you one of the V shapes. I'm going to be homing in on this red V shape here. And the parabola we draw will span this V shape. Now it's a really good idea when stitching to start one step in, and I'll explain why in a sec. Rather than starting by joining the outermost point on one arm of the V to the innermost point on the other arm of the V. I'm going to come one step in. I'm going to start here. That means I'm going to step one step out on this arm of the V. On one arm of the V, I'll call number one. We start on the outside, away from that center point, but on the other arm of V, which I'll call number two. We start on the inside, one step away from the center point of the V, where the two lines meet. Your first stitch will come up here, emerge onto the surface of the paper, and you'll stitch across to this point here. You'll then come out and come up right next door to save thread. It's a good idea to just take a short a step as possible on the underside of the paper. You'll come up this point next door. And this 11 step out on this line, we'll join up with one step in on this point. And this point will be where your next stitch occurs. You will enter the paper up here. You will then emerge one step in along this line and stitch to one step out on line number two. You'll then emerge on line number 21, Step out and stitch in to one step in on line number one, you work your way down line number one, line number two, joining up pairs of points or holes in that way until you get to the penultimate pair of points on each line. Stop there, Move onto your next parabola and only complete, if you like, the two red stitches, once all your parabols are drawn. Because if you put this stitch on straight away, this stitch along the line of the V, you've then got a piece of thread running on top of all the little holes that you want to be stitching in and out of. Next it'll just get in the way. You'll have to keep nudging it out of the way with your needle in order to enter the hole or emerge from the hole. These two stitches, or any of the stitches along these axes should be the final stitches you complete. I'll demonstrate that in the stitching section of the lesson. Okay, I would have a go at drawing some more parabola, V shapes, perhaps experimenting with overlapping. You could, for example, work on this one that I've done in green. On top of the one done in red, I would start on the outer 0.1 in on this green arm and join it to the inner point on this green arm and work in that way, one in one out. Working my way along, I can overlay way one parabol on top of another, parabola in another V. You can come up with all interesting combinations, patterns. In this way, you can see when you have two parabols overlapping each other, you get a whole new curvy shape emerge. I'd encourage you to get a feel first for how parabolas work. Perhaps join up a parabola along a wider V shape as well, just to see that you get a shallower curve from doing that. Then when you feel confident for how parabols work, you'll feel confident enough for the stitching stage. 5. Punching the Holes: Okay, so we're now going to punch the holes for our chosen pattern onto our sheet of paper. You'll need a ruler, a pencil eraser. You'll need your paper pricker of some sort. You'll need a pair of scissors to cut out your template. And it's also useful to have some low Tac tape just to secure the template down on the paper when you're punching the holes. What you'll notice on the template is that there is a pair of axes, one running horizontally and one running vertically, a pale gray line. These are here. So that we can accurately orient our template at the center of our piece of paper. The first thing we're going to do then, is to make in pencil parts of a horizontal and vertical axis in order to have something to align our template with. The first thing I'm going to do then is to draw a horizontal axis halfway up my page. To do that, I'm going to first measure the height of my page. It's just under 20 centimeters. It's actually I think 19.8 half of 19.8 is 9.9 I'm going to move my ruler into the left hand side of the piece of paper line, my zero of the ruler up with the base of the sheet of paper. And measure up, in my case, 9.9 centimeters. And then I'm going to do the same on the other side of the paper. I'm just making a small pencil mark each time. Then line your ruler up with your two little pencil marks. I'm not going to draw the line all the way across the sheet of paper. I only need it where it will emerge from both sides of the template. I'm going to just put a pencil line in the outer inch or so of my sheet of paper. Now I've drawn my pencil lines quite heavy. You will want to keep yours nice and light. I've only drawn mine quite heavy so that they're visible under the camera. I'm now going to do the same vertically. I now need to measure halfway in my sheet of paper is also 19.8 centimeters wide. Half of that is 9.9 in the top half my sheet of paper. I'm lining my zero up against the outside edge and I'm making a little mark, 9.9 centimeters in, which is my halfway point. Them in the bottom half of the sheet of paper line my ruler up along those two points. I'm only making my pair of lines on my vertical axis at the top and bottom of my sheet. Where they'll emerge outside the edges of the template. I'm going to cut my template out now. Just around the dotted line, you can choose to orient your hexagon with the points, the vertices facing along the vertical line or along the horizontal line. That's completely up to you. I like it in this orientation best. I'm going to align my hexagon template this way up. I'm just going to align one of the axis first. So I'll look at my vertical and make sure that little gray line is in line with the pieces of vertical axis I'd put on. And then looking at my horizontal line, I can see I now need to bring it down. Just make a few minor adjustments until it looks like all my pieces of axis are lined up together. Then I'm going to use a little piece of low Tac tape masking tapes perfect for this or washi tape. I might just detach mine on the back of my hand a couple of times because I don't want to tear the surface of my paper when I remove it. I'm going to pop one at the top and one at the bottom. Okay. The templates in place now, you have to double check which holes you're going to need to punch to make your chosen design. Because you don't necessarily need all the holes on the template for the pattern I'm going to demonstrate. I do need all the holes on the template, so I'm going to punch all the holes that you can see. I'm going to work systematically just so I can keep track of what I'm doing. I think I'll do the three axes first and then work my way round the outer edge of the hexagon. I'm going to press down on my sheet of paper with one hand just to keep it flat against the surface. I'm working on my corkboard. Remember, you should be pressing on your cardboard or a felt laptop cover, that sort of thing. Then you just press nice and firmly and cleanly through as best you can, the center of each dot. Then you want to check that you've punched all the lines that you need. You can run your finger along just to make sure there are holes everywhere. Or hold your piece of paper up in front of a window and check that there are a little pinpricks of light wherever you need them to be. The last thing we're going to do before the stitching stage is remove our template carefully and erase those alignment that we put on earlier. 6. Stitching the Pattern Part 1: Okay, this is the exciting stage. Then we get to trace out our pattern with our thread. Now I'm going to do the rotating pinwheel design, which means that I'll be putting one parabola in each of six V shapes as I move around the pattern. If you remember, I need to start on one of the V's. If I'm a, let's look at this V here. This V shape here is pointing to the right. I need to start on the outside of one of the arms of the V and then I'm going to stitch to the inside of the other, the side nearest the V. And then I'm going to come out next door and stitch back from the inner side of one of the arms of the V to the outer side of the other arm of the V, but moving one out each time on this arm and one in each time on this arm. So the first thing I'm going to do is to cut a length of thread. And I'm going to cut myself a length of thread round about an arm spans with. I wouldn't go any longer than that. And that's quite long really. But I need a fair old amount because I'm working on the largest template, so I'll be using up my thread pretty quickly. If you're working on one of the smaller templates, you won't need such a long piece of thread Each time I'm going to thread a needle, I like this metallic thread. It's nice and easy to thread your needles with. Then I'm going to draw most of the piece through which has the effect, or at least half the piece through that has the effect of considerably shortening the amount of thread I'm working with, which makes it easier to use. Then I can just lengthen it as I go. I'm going to identify my V shape. I'm going to come one in on one of the edges and I'm going to come up through the back through that point. I'm going to draw my thread through until I've got about 2 " two to 3 " remaining. I'm going to use a piece of tape to secure that piece down. I'm just making sure that it's not lying across any of the holes that I need to sew through. I've pulled it to the outside. I'm just going to place a piece of tape down. Press firmly all the way along the thread to make sure it's been gripped by the tape. And then press firmly all the edges of the tape so that they don't catch on the thread as I'm stitching. When I'm happy that that's nice and flat and secure, I can start stitching. I just need to keep tabs on where I'm going. I've started one in from the outside edge of this arm of the V. That means I'm going to go one in to the inside edge of this arm of the V. This hole here, Outer hole on one arm goes to the equivalent inner hole on the other arm. Then it's a good idea to keep the thread taut as you go, or just check on it regularly and give it a little tug just to keep it taut because you don't want to have to fix that after the event. What I'm going to do now is I'm going to come up through this next door hole on this arm of the V. And then I'm just using my finger on the back of the sheet of paper to clamp that down, keep it taut. And I'm going to pass through one hole in on this arm of the V, pulling it nice. And t I'm going to come up one step forward on this arm. Now one step further in this point gets joined to this 11 step out on this arm. We're always moving one step in on one arm and one step out on the other. I'm at the stage now where I'm going to pull a little bit more thread through my needle just to lengthen the piece I'm working with. I've just gone into this hole. That means I'm going to come out here having a gentle tug just to get all those threads. Nice. And. Clamp it down with my thumb. While I'm inserting my needle into the hole, I can see that lovely curve of the parabola beginning to emerge. For now, I've just got one more straight line to put in, going from the penultimate point on this arm to the one that's one step in from the point of the V on the other arm. For now, I'm going to leave those two final lines that go along the outside edges of the V. I'm going to leave them until I've stitched all my parabolas. And then the last thing I'm going to do is to put those edges in. I finished one parabola. I now need to think about where my next is going to be, because I still have a significant amount of thread left. I'm going to carry on and start a new parabola. The next I want is going to be pointing, if you like, another step around the shape. Because I'm going to always do a V pointing if you like, to the right. So you could turn your piece of paper over and get yourself oriented. Again, I've just seen that I missed a hole. Okay, that's better. So I'm going to emerge out of this hole here on this arm of the V. That's one step in from the end and I'm going to stitch to this hole on this arm of the V. That's one step in from the point V. Again, a little bit of a tug just to keep this parabola nice. And I'm going to go from this point to this one. Then I'm going to come up at this point here, one step out on my way away from the point of the V and come one step in on this, one step in to one step out, one step out to one step in, Because I'm keeping one shy of the very end and I've got a little bit of thread left. So I think what I'll do is start the next parabola, and then I'll have to cast off that one, sort of halfway through the parabola. So we'll have a look at how to do that. Now, working on a whole new V, I'm going to start one point in on this arm and join it to one point in for one point out on this arm. I'm going to stop here. All I'm going to do is turn my sheet of paper over, remove my needle. I've still got about 6 " or thread left there. And I'm going to get my piece of tape ready, get a decent piece. You could, of course, cut these pieces of tape with your scissors, but I'm not too worried about what the back looks like Then giving it a gentle tug, Just making sure I've pulled it nice and taut. I'm going to pull it away from the holes, secure with my tape. Running my finger along the tape, along the thread underneath the tape to make sure it's all stuck down securely. And then along all the edges just to make sure those are stuck down and won't catch on my thread. Then I'm going to cut my thread just before it emerges from the paper. About here, I'd like to leave a little bit of a length on about 2 " on, just in case at any stage I need to remove the tape and tug on the thread to tighten it a little. Having a little piece there to work with is handy. So I don't ever cut it off too close to the hole. Okay, So now I've got to pick up midway through my parabola. And the easiest way to do that is to think, well, where have I emerged? If I was continuing with this piece of thread, where would it have gone in? Well, I would have emerged here and then gone in at the next door point. That's where I'm going to start, as if I'd never broken my thread in the first place. I ended here. I'm going to go in at the next door point here. I would have gone if I'd just been continuing going to draw my thread through until I've got about a couple of inches. I'm going to secure that before I go any further, then I can just carry on. I need to reorient myself. I went through there, I've come out here, which means that I'm now going to stitch to the other arm of the V. One step along and then I'm off. Okay, so this is the final stitch of this parabola, because I'm leaving the very outermost holes free. For now, I'm going to move round to the next one, starting one hole in the final parabola. Now on my little pinwheel pattern, and then I'll have the axes and outer edges to stitch. I've ended here, I'm going to pop up in the V next door. Okay? So this is the final stitch of the parabolas before I put those final lines in. 7. Stitching the Pattern Part 2: To do the final edges, the three axes and the outer edge of the hexagon, you can just do it in one giant stitch like we've been doing. I might come out here, enter in there, come out here, and work my way round like that. You could actually just stitch through individual holes. So you could do either a back stitch that you've stitched through all the individual holes to make your line, or you could do a running stitch and then run back on yourself to fill in the gaps. But I'm just going to do one large stitch that goes from point, vertex to vertex. To do that, I'm going to come up now on one of these outer holes, you can go in either direction. I'm going to come down to here and stitch that outer edge, and it has the effect of covering up the holes a little with the piece of thread and finishes it all off. Now I can either come out here and double back on myself, or I could come out at the center and put the stitch in. I might come out at the center, actually, I haven't got very much thread left. I'm going to come out at the center now and put this stitch in along this half of the axis. What I've done now, I've finished off one parabol, it's got its two outer edges in now, so this one is complete now. I haven't got very much left. I might have enough. One more axis. What I'm going to do is I'm going to bring my needle up here and stitch back so that I've covered this outside edge here. I'm going to go all the way across here. Just got enough thread. Think yes, now that outside edge in, I'm going to secure my thread. Okay, I could really start because I'm just doing these outside edges and these axes, what I might do is come up at this vertex here and maybe stitch into the center or stitch this outside edge, then come out at the center and so on. And just fill in the last remaining edges as I go. This is probably one of the easiest patterns to do because I'm not overlaying a parabol on top of a parabola that's already there. That's when it can get a little more confusing. What I think I'll do is, although this one's complete, I think I'm going to demonstrate overlaying a parabol in a different orientation on one of the V' here so that you can see if you want to tackle a more complicated pattern where we've got lots of different parabolas rotated around the same triangle. How to think about it and how to keep yourself from getting too lost. The main thing is to keep tabs on, on the V that you're working in. Remember, you'll always be working in a V shape, whether it's a more acute angled V shape or a wider V shape, using one of the central axis or the outside axis, it will always be a V. You'll always have two arms of it. Just keep in mind which two arms you're working on. Ignore all the other visual noise and you should be fine. Remember, you're working down one arm towards the center of the V, and on the other arm, you're always working in the other direction out. 8. Stitching the Pattern Part 3: To demonstrate that. I think I'll use a different color. I'll use my copper thread, and I'll put on this one. Oh, I think I might do it going in the other direction. If we have a look at this here, it's pointing up out in that direction. I'm going to do one that's going to point in the opposite direction here. This one from top left into the center. The one I want will curve from top right into the center. I'm going to be working along this arm and this arm of V, which means I need to start one space in on this arm of the V. That point here will join to one step in from the point, or out from the point on the other arm of the V. I'll work from here to here. Then I'll step one along back, one a back, one along back and so on. I think if you map it out in your mind first, that will help you ignore all the other stuff that's already there. Let's have a go to in that I'm going to be working here, along here and do here. I think it's always better to start at the outer edge of the hexagon just because you can keep your tape along the sides. I'm going to come in one step in. I was at the end of this arm. Means I need to start near the point on the other one in from the point is where I'm going. Then I want to pop up one along to cross over to one in. When you're passing your needle through holes that have already got stitches going through them, just be careful not to split the thread, the thread that's already there with the needle as you pass it through. If you feel you have passed your needle through the thread, just withdraw the needle and have another go. You don't want to draw your thread up another piece of thread because it'll fray it. I've emerged out here, now I'm going to cross over the triangle to a space one in from where I emerged last time. And then I want to pop up one next door looking a bit baggy. So give everything. Ah, now what I've done here is I've emerged on the outside of this piece of thread that forms the edge of my hexagon. And that means when I pull my thread tight, I'm tugging that over. I don't want to do that. I want to come up on the inside of it. So, I'm just going to pop my needle through that. Actually, I I'm not pulling on that outer edge. That's why the outer edge is always the best thing, is always what you should do last of all, and then you don't risk catching it as you work. And I'm crossing my triangle over here. If you want to do overlapping parabolas like I'm doing now, I would do them before you've put your final etches in. Otherwise, you'll have this little bit of a hassle trying to avoid that edge. You can see that if I continued and did one in every triangle, I'd get this nice flower shape. In fact, maybe I will. Yes, I don't want to leave it half finished. I'm going to continue and finish the pattern with one half in gold and 12 in copper. One pretty little flower design. 9. More Design Ideas: I'll just finish by showing you some examples of different ways of stitching, as well as different types of paper to stitch on and different colors of thread being used. This is the pattern I've done with you today. It's the flower shape produced from two overlapping parabola in each triangle of the hexagon. It's really rather lovely, and I'm really pleased with it in two colors as well, the gold and the copper. This one would be perfect to mount on a card, to make your own Christmas cards. This is just the central three axes of the hexagon. The three diameters, if you like. I didn't punch holes around the outer edge of the hexagon, I left those and just punched the three diameters. And then I did one parabola in each V formed by next door diameters. It's this gorgeous, curvy six pointed star. This one here, I chose to work on black paper, and I've used my copper and gold thread again. And you can see in copper I have that six pointed curvy star, which was done using the central axis, but before I overlaid that copper star underneath it in gold, there is the flower shape, which is done with two overlapping parabolas in each of the triangles around the hexagon. You could either do this all in one color or you can pick out different elements of the pattern in different colors. I'm really happy with that one. I think it looks fab on the black. Then this one here is an example I wanted to show you where I stitched a wider V. And you can see the curvature of the parabol is much more shallow than it is when you stitch the narrower V shapes in this one here. Then I punched holes all the way around the outside of the hexagon. I also did three of the central axes. I went from the northmost point down to the center, then out down to the left and down to the right. And I didn't punch this axis, this axis, or this axis. I did type parabolas in this, this, and this. Then over the top in white thread, I stitched these wider s formed by the central axis, and you get this rather elegant, curved triangular shape sitting on top. 10. Conclusion: Thank you for joining me for this mini workshop. I do hope you're happy with your little paper stitched parabolas. I'd really love to see what you've made. So do share your work on Instagram. You can use the hashtag parabolic paper stitching, and you can tag me. I'm Clarissa Grandy Art. If you've got any questions about techniques or materials or anything else, then please pop a question in the comments section below and I'll be sure to get back to you. I regularly offer live online zoom classes on all things geometric art, and I'm building a growing collection of on demand video classes on skillshare too. So if you're interested in learning more, then do check out the links below to see what's currently on offer. So all that's left to say is take care and happy stitching.