Why is the paper I bought not straight? How do I cut the paper? Why is the cutting error so big? !
Share with everyone what you have learned, used, and realized in paper cutting throughout your life.
Divided into:
First, the universal paper cutting method. Divided into 1 diagonal and 2 side lines.
Second, the commonly used paper cutting method. Divided into two situations: 1 and 2.
3. Common problems and precautions for paper cutting.
The universal paper cutting method is actually the name given to the origami circle, and more specifically refers to how to cut squares. This tutorial is only for squares.
The general theoretical basis of the universal paper cutting method is the geometric properties of squares and the method of drawing with rulers and compasses (children who have attended junior high school should have heard of/understood/practiced it, right?).
Of course, you can also use the geometric properties of other geometric figures to achieve the purpose of cutting out various regular shapes.
1. Universal paper cutting method
1. Diagonal paper cutting method
It is a paper cutting method that uses the diagonal as the starting point.
Excellent: Absolute rule, in actual operation, it is the paper cutting method with the lowest technical requirements and the highest accuracy in achieving square points.
Disadvantage: It is relatively cumbersome and not very practical. The paper utilization is not high and is suitable for paper that is closer to round.
The steps are as follows:
①, take a line as a diagonal.
②, take a vertical line and make another diagonal line. (Try to take it in the middle to improve paper utilization.)
From ③ to ④, get a fixed length on the diagonal, draw a line and draw points, record them as the vertices of the square.
I only provide an idea for drawing with ruler and compass, see the picture for details. You can also use a scale to measure the trace points. In short, make the four line segments equal in length.
⑤, as shown in the picture above, connect the drawn points to form a square.
2. Edge cutting method
That is the paper cutting method starting from the edges of the square.
This paper cutting method has a high utilization rate, and the steps are simpler and more fixed. It is the basis of the "Practical Paper Cutting Method".
Excellent: High utilization rate and simple steps.
Disadvantage: Insufficient practical experience will lead to very large errors. If cutting from very irregular paper, using edges is not recommended. Suitable for square-shaped paper.
The steps are as follows:
①, take a straight line close to the edge of the paper as an edge of the square.
②, take two lines perpendicular to the side lines as the other two sides of the square.
ATTENTION!!!!
The diagram only depicts the ideal state. There are other operation methods starting from ②, and additional instructions will be added after the end of this floor.
③, draw the angle bisectors of two perpendicular angles.
ATTENTION!!!!
It is very likely that the intersection point is outside the paper. Please adjust the position of the vertical line in ② by yourself.
④, connecting line, as the last edge of the square.
There are actually many problems with this method in practice. Focus on step ②.
First point, the vertical line in ② is very unfriendly to large paper. Because of the malleability of paper, a straight line will deviate into a curve as it stretches. It requires extreme care and attention, taking your time and doing it step by step.
The second point is about the solution for the intersection point outside the paper. In ②, it is recommended to draw a line on the bottom side first, and then make a diagonal line of the square through the corner bisector. From the intersection of the diagonal line and the edge of the paper, draw two perpendicular lines from the two side lines to make the edge of the square paper.
Another unprinted diagonal line can be printed as an indicator to verify the accuracy of the square.
2. Edge cutting method. ****Additional steps****
If you encounter paper that is so irregular that it is impossible to judge whether it can be successfully cut through ordinary steps. . .
①, also take the edge.
②, vertical line, take only one as the side line.
③, take the diagonal of the square as the angle bisector.
Pay attention this time!!!
The intersection point of the diagonal line and the edge of the paper may be farther than the intersection point of the ② edge line and the edge of the paper. It depends on what to do next!
④, make two vertical lines as the sides of the square while ensuring that the vertical point is within the paper.
If the intersection point of ③ and the edge line is drawn as a perpendicular line to ① and ②, and the vertical center is in the paper, the perpendicular line can be drawn from line ③. This is the ideal situation.
If the intersection of ③ and the side line is a vertical line toward ① and ②, and at least one vertical center is outside the paper, then a vertical line ④1 should be drawn from the side line, and a vertical line ④2 should be drawn after the intersection with ③.
⑤, put a bracket. Selections.
Draw diagonal lines to verify the accuracy of the square. If it misses the mark, you can just throw it in the trash can and cut the paper again so that you don't find it after folding it in half.
2. Practical Paper Cutting Method
This paper cutting method is based on my experience. The master is just for reference, light spray.
As we all know, the paper we buy cannot be as messy as the noodles above. . This determines that we do not need such complicated steps to process a square piece of paper. .
Generally speaking, paper does not actually have curves. Even if it does, it is within an acceptable error (the original poster, Virgo, can accept it). The paper bought by merchants generally has the following conditions.
1. It’s very neat.
This situation is actually not too uncommon, so there is no need to be happy to buy lottery tickets. How should I put it, it’s almost like winning five dollars in the lottery.
2, parallelogram.
This is actually the most common situation. Many people find that the full-open paper is not at right angles! Don’t panic, look to see if the two adjacent corners are complementary. If so, then you may as well have a good time eating chicken tonight. Because this kind of paper is also very easy to handle.
3. Not neat, but also with right angles.
To be honest, I have never encountered such a situation. But what if it’s guaranteed?
4. Four-sided curve, no right angles.
It is recommended to buy lottery tickets. What can i say. . Maybe your life is a tragedy. .
1, Parallelogram case
I think if it’s a serious rectangular paper, I shouldn’t need to say more.
So jump to the parallelogram. How to deal with this situation.
In fact, it has the same idea as Universal Paper Cutting Method 2. As shown below.
The core is to take out ① and convert it into a serious rectangular paper cutting process, and determine the square through diagonals and vertical lines.
Why is a parallelogram the most convenient?
1. When determining the ① line, the error of the ① line can be reduced to 0 through the condition of "simultaneously perpendicular to the upper and lower lines".
(If you follow the right line to make a vertical line, and you find that it is not vertical when you go to the left. It must be that the ① line is not straight, try again.)
2. Lines ② and ③ detect each other, and you can find out in time where there is no hit.Straighten and adjust.
(The ③ line must pass through the two intersections of ② and the edge of the paper, and must be perpendicular to the edge of the paper. Similarly, you can also only draw one ②, and after drawing ③, draw another ② to detect the square Accuracy.)
I use this method all the time. If the error of the paper itself as a parallelogram is acceptable, this method can ensure high utilization and high accuracy.
2, right angle situation
Because a right angle can directly determine the two sides of a square, it is simpler.
①Vertical, determine the third side.
Then determine the square through the diagonal and ③.
You can also check each others accuracy.
3. Frequently Asked Questions and Suggestions
In fact, many friends have their own opinions and methods on paper cutting, but in actual situations they still cannot cut it well. . Its a matter of method and method.
1. How to cut paper?
It is recommended to cut horizontally with a paper knife.
First, the scissors must be clicked off. Pick up your notebook and write it down. Scissors are useless for cutting paper.
Secondly, the paper knife has two cutting methods.
The first is to use a cutting pad and stand up the knife to cut.
This is a paper film cutting method, which is good at slow work and meticulous work. This method is very demanding and laborious.
If the paper fiber is relatively tough, a dull knife may directly tear the paper.
Second, after folding the crease, cut it horizontally.
Recommended by millions of experts, the real way to use a normal office paper cutter. Simple and crude.
But be careful: before cutting, you should use your fingernail to mark the creases. When cutting, lay the paper flat and the knife flat. Press the knife slightly hard to stick to the paper.
Perfect.
2. Is the square crooked?
Consider it a matter of your wiring.
During the line-laying process, I definitely won’t believe that you can’t even align the vertical and angular bisectors correctly. . If thats the case, then you are too embarrassed and should quit the group. .
I definitely believe that the most common situation is when dealing with large paper, your creases are originally correct and straight, but they are bent.
Because paper is soft, it bends easily when making long creases.
I give the following suggestions:
Zero, meditate. Don't rush. Take your time and adjust slowly. This is the premise of all suggestions. (You also need to practice more to find the trick yourself)
One, find two reference points. Just like the center line of the parallelogram using the practical paper cutting method. The more references you have, the less likely you are to go astray.
Two, reserve the edge of the paper to enlarge. Improve accuracy by sacrificing paper utilization. For example: ① Make the paper on the edge of the line wider. The wider it is, the less likely it is to deform.
Third, don’t just use your fingertips to draw. If you are folding a very narrow strip, it is recommended to move it over little by little, and at the same time look back to see if it is crooked, and adjust it in time. If it is a straight line in the paper, it is recommended to slowly smooth it out with the palm of your hand and press out the trace; then use your fingertips or nails to press the crease.
Four, if it doesn’t work, use a ruler to compare the folds.
