The curve of the katana was not an issue in executing a thrust. Some prefer thrusting horizontally. If you are going to thrust it vertically it would be easier to stop your opponent easily because the blade was curved upward, if it was on the stomach the tip of the blade will hit through the spine or hit other organs as well and when it will make the person leap up a little and make him hard to move because the blade will go deeper. So what you are saying about katana is bull *****.
In fact, I already explained to you that the katana cannot perform an "on-compass" thrust. You just agreed with me here. Methods for thrusting with a katana are slower, less powerful, have significantly less reach, and expose the wielder significantly more than an "on-compass" thrust for various reasons.
I noted before that katana can be wielded with one hand the use of (chinese straight swords as their weaponry validates this) and the use of two handed thrust may lack range but it has complete control of the blade making wielding faster and making the handler hard to get parried out of balance.
In fact, one-hand wielding of a Katana became noticed around the time of Musashi, who was not a fighter within the traditional bounds of Japanese culture. He had witnessed the fighting style of the Europeans and had adopted from them. Even in that case, he still preferred the two-handed grip, although he was influential in the development of the one-handed katana style. This is far after the 13th-15th century time period that you requested.
Katana was made curve because the use of long straight swords was not enough to use against their enemies. It will not be change if it was perfect.
In fact, the katana was developed with a curve for a variety of reasons, one of them being that the curve more easily induces a draw-cut, although a skilled user will perform as adept a draw-cut with a straight sword as they will with a curved sword. The katana did not change largely due to the fact that the Japanese valued tradition incredibly. Breaking with tradition was very much against their values, and although the katana could have seen refinement, they did not do such.
Take the saber, why the europeans created this weapons as a replacement for the longsword
You show your ignorance again. The saber was a European weapon that was primarily developed for mounted combat, the reason being that the curved blade was extremely effective in a mounted situation where it would be used to draw cut rapidly across an opponent, and did not need to be thrust. In no sense was a saber a superior sword - it just filled a niche.
The turkis use curved blade or the sabers to conquer parts of eastern europe which uses longswords at the time. The Islamic warriors used curved blades like falchion to conquer some parts of Spain with use of these blades. Gunpowder are the only thing that saved them in the war. It is clear how easy to use curved blades. Take the Damascus blades. The reason I brought up these is to state that curve blades is a great weapon for fighting especially and thrusting was never difficult. Actually the curved side of the blade can be used for hooking blocks and sweeping.
Once again, you demonstrate ignorance by assuming all of this. In fact, although Muslim occupation did occur in the areas of Palestine, as well as large parts of Spain - these occupations were ended during the Crusades and for quite some time thereafter. Eventually, the Europeans abandoned the Middle East because it no longer enticed them. However, the retained the whole of Spain for the entire time thereafter. And gunpowder was not an influential part in this, in fact noting that the Turkish were more adept in the use of firearms than the Europeans were for quite some time.
If you got thrust by rapier you can still move if a katana you are limping.
If you got thrust by a rapier, you are in significant pain. Furthermore, there is a huge amount of historical record to suggest that a rapier blow was eventually fatal. The reason for this was infection, as the rapier created a particularly nasty wound, and most successful rapier duelists would eventually die to an infection caused by a wound. In many cases, both fighters would end up killing each other through infection, although the fight itself had ended in a draw for one reason or another.
Once again, a thrust with a katana is far more difficult, and in no sense more powerful. The actual thrusting action itself, due to technique, caused a weaker blow. For your note, both the rapier and katana were good at making their opponent's limp, as thrust blows are very painful.
Rapier and katana are good weapons but if both are to fight, I'll put my money to the katana because firstly, it was an older blade and was tested in battlefield for centuries. Second, It has the value od experience and the more older the weapon is the more its techniques were develope. Lastly, it was still being use by mafia or the yakuza around the world. Here in the Philippines when you go south you'll find katana being use by some christian vigilants.
The katana is a shorter blade and is slower than a rapier. They are both very good weapons for their individual purposes, but in all honesty, it is like trying to compare apples and oranges. I would place my money with the rapier, because it has the advantages of reach, speed, and a great thrusting action. On the other hand, a solid blow with a katana against an unarmored fighter is almost certainly the loss of a limb or death.
In all truth, I'd take the rapier. The amount of wounds you take to your hands as well as non-vitals, will probably result in your death to infection - and there is huge historic record to back this up. Furthermore, I could hit you anywhere from your stomach to your face, and deal a killing blow in that area in hitting any of a number of vitals, such as the stomach, the lungs, the heart, the throat, the eyes, or even an artery leading away from the heart.
On the katana's part, I could perhaps make a swift killing blow, but it isn't necessarily that likely. Although the katana can do more physical damage, it doesn't have the advantages of reach or speed that were inherent to the rapier.