Chapter 16 Analytical Geometry and Descartes Coordinate System
Gothe opened his eyes and subconsciously rubbed his temples.
The construction of spell models is very tiring.
His apprentice meditation technique has reached five petals. This level of mental power is enough for him to complete the model construction of the trick, but it is a bit difficult.
If one can cultivate to the perfection of sixteen petals, with this level of spiritual power, it will be much easier to construct a spell model for a 0-level spell.
The difficulty in constructing a spell model is that, first, it requires accuracy, with accuracy ranging from a millimeter to a thousand miles, and second, the mage needs to have enough mental energy to consume it and try again and again.
With Gaode's current mental strength, he tries to build a spell model of acid splash. Every time he fails, he will feel dizzy and tired.
If you fail three times at most, your brain will start to hurt, your mental energy will be excessively consumed, you will need to rest and wait for your mental energy to recover, and you will no longer be able to construct spell models.
This is the disadvantage of not having strong mental power. If a first-level mage were to build a spell model for a 0-level spell, not to mention that the efficiency would be ten times that of Gaode, even if it was a failure, people would fail several times a day. No problem ten times.
"It is not easy to build a spell model. No wonder it took more than a year for my predecessor to master the two tricks of repair and mage's hand." Gothe muttered to himself.
Even mastering a level 0 spell is so hard. You can imagine how much effort it takes to become a powerful mage.
But he didn't complain.
It is said that the Master is the Master.
Master, Master, how can you become a master if you don’t become a grandson first?
Failure is the mother of success.
Gaode closed his eyes and reviewed the failed construction just now, and quickly found the problem - while focusing on controlling the movement of the third planet, the position of the second planet shifted a little.
One shot moves the whole body.
When the second star track connecting the second star child and the third star child has been extended, if the position of the second star child shifts slightly, the entire spell model will naturally collapsed.
This is another difficulty in building a spell model:
There can be no mistakes, otherwise everything will have to be started from scratch, and you cannot correct any mistakes
"This fault tolerance rate is too low." Gothe murmured to himself, subconsciously thinking: "Can you optimize the construction process of the spell model?"
If his thoughts at this moment were known to other mages, they would definitely Laughing at him for not knowing the heights of heaven and earth.
Not to mention this method of constructing spell models that has been passed down for countless years, how can there be room for optimization? Even if there is, how can it be thought of by a mage apprentice?
Gaode does not have these miscellaneous scruples.
In the world of mathematics, if a method doesn't work or is difficult to follow, it is very common to change your mind.
Can we determine the positions of all the planets first and then connect them to their orbits?
Such an idea suddenly popped into Gaode's mind.
After this idea appeared, he was suddenly enlightened. The more he thought about it, the more feasible it became. He even felt that this was the correct way to build a spell model.
——In this way, even if any star moves from its original position during the construction of the spell model, it will not cause the entire spell model to collapse. You will have to start over from scratch and only need to adjust the position of the star in time. That’s it.
Compared with the traditional method of constructing spell models, does this increase the efficiency just a little bit?
That's simply the difference between an abacus and a computer.
Gaode has always been very active. If you have an idea, just execute it.
The first thing to solve is how to determine the position of each star.
The spell model construction process recorded in all spell recipes is to connect the star tracks while determining the position of each star through relative displacement. It does not describe how to determine the star without connecting the star track. location.
But for Gaode, this is not a problem at all, the existing information is enough - isn't it just simple analytical geometry. By directly establishing a Cartesian coordinate system and then disassembling the vector coordinates of each planetesimal, wouldn't it be possible to determine the position of each planetesimal?
First, you need an origin.
The origin is the origin of all vectors.
Only when the origin is determined, can the length distance be determined, and then the vector coordinates of each node be determined.
Except for the stars and the spell model, there are no other objects in the magic star sea. However, the stars are constantly moving, so they are obviously not fixed reference objects and cannot be used as the origin.
Although the spell model does not move, it is a model composed of multiple planets, so how can it be used as a reference?
If one of the stars in the spell model is used as the origin, there will be situations where the nodes of the two spell models overlap or the star paths cross and interfere.
But this is easy to do, just regard the location of the first star as the origin.
With the origin as the center, establish the most classic xyz coordinate system
Use an ordered triple array to determine the position of each node of the spell model.
A triple array consists of three numbers that are responsible for guiding how to get from the origin (the starting point of the vector) to its tip (the end point of the vector).
The first number represents how far along the x-axis, a positive number represents moving to the right, and a negative number represents moving to the left.
The second number represents how far to go in the direction parallel to the y-axis after this.
The third number represents how far along the z-axis direction.
Similarly, through the direction of the stars recorded in the spell formula, the coordinates of each star can be deduced.
Gothe stood up, took out a charcoal pencil from the shelf nearby, and started recording directly on the blank space of the spell formula.
The first star is the origin, and the coordinates are (0, 0, 0)
“Go forward one, go right one and three-quarters, go up one-quarter and one-quarter”
The left and right are The x-axis, the front and back are the y-axis, and the up and down are the z-axis.
The coordinates of the second star are (4/3, 1, 1/4).
"Go forward by one-half, go right by two-thirds, and go down by one-half"
The third star moves from the second star as the starting point. It cannot be directly compared to the origin for recording, but it is not a big problem. ——Isn’t it just a simple vector addition operation?
Through calculations, it can be obtained that the coordinates of the third star are (2, 3/2, -1/4).
Just continue to calculate in this order.
Soon, Gothe disassembled the acid splash spell model into an xyz coordinate axis and nine vector coordinates including the origin.
Then, Gothe looked at the nine ternary arrays on the paper with burning eyes and began to try to memorize them.
Obviously, nine three-element arrays are much simpler than the complicated description of the spell formula, not to mention Gothe's innate sensitivity to numbers.
In just a few minutes, he memorized these nine coordinates.
“Try it.”
Now that the preliminary work has been done, Gaode just did it and started trying it immediately.
(End of this chapter)