Chapter 16 Analytical Geometry and Cartesian Coordinate System
Gothe opened his eyes and subconsciously rubbed his temples.
The construction of spell models is very nerve-wracking.
His apprentice meditation skills have reached five petals. This level of mental strength is enough for him to complete the model construction of the trick, but it is a bit difficult.
If you can cultivate to the perfection of sixteen petals, with this level of spiritual power, you will be able to construct a spell model of a 0-level spell with much ease.
The difficulties in constructing a spell model are, firstly, the need for accuracy, which is within a thousand miles of accuracy, and secondly, the mage needs to have enough mental energy to consume it and try again and again.
With Gaode's current mental strength, he tried to build an acid splash spell model. Every time he failed, he would feel dizzy and tired.
After three failures at most, the brain will start to ache, mental energy will be exhausted, and you need to rest and wait for 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 construct a spell model for a 0-level spell, the efficiency would be ten times that of Gaode. Even if it failed, it would not be a problem for someone to fail dozens of times a day.
"Constructing a spell model is indeed not easy. No wonder it took more than a year for my predecessor to master the two tricks of repair and mage's hand." Gothe murmured 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 Dharma Master.
Master, Master, how can you become a master if you don’t become a grandson first?
Failure is the mother of success.
Gothe closed his eyes and reviewed the failed construction just now, and quickly found the problem - while focusing on controlling the movement of the third star, the position of the second star shifted a little.
One move affected the whole body.
Since the second star track connecting the second star and the third star has been extended, if the position of the second star shifts even slightly, the entire spell model will naturally collapse.
This is another difficulty in building a spell model:
There can't be a little mistake, otherwise everything will have to be done from scratch, and you can't just correct whatever is wrong
"This error tolerance The rate is too low." Gothe murmured to himself, subconsciously thinking: "Can we optimize the construction process of the spell model?" If his thoughts at this moment were known to other mages, they would definitely laugh at him for not knowing the heights of the world.
Leave aside the fact that 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 first determine the positions of all the planetesimals and then connect them to the star orbits?
Such an idea suddenly popped into Gaode's mind.
After this idea appeared, he was enlightened and 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. Everything will start from scratch, and the position of the star only needs to be adjusted in time.
Compared with the traditional method of constructing spell models, is this efficiency more than just a little improved?
That is simply the difference between an abacus and a computer.
Gaode has always been very capable of taking action. If you have an idea, you will execute it.
The first thing to be solved is how to determine the position of each star.
The construction process of the spell model recorded in all spell recipes is to connect the star tracks and determine the position of each star through relative displacement. It does not describe how to determine the position of the star without connecting the star tracks.
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, can we not determine the position of each planetesimal?
First of all, we 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.
There are no other objects in the magic star sea except for the stars and the spell model. However, the stars are constantly moving and 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. How can it be used as a reference?
If one of the star elements 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
An ordered three-element array is then used to determine the position of each node of the spell model.
A ternary array consists of three numbers, which 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 along the direction parallel to the y-axis.
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 pen 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).
The coordinates of the second star are (4/3, 1, 1/4).
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 - it is just a simple vector addition operation.
Through calculation, it can be obtained that the coordinates of the third planetoid 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 triple 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 in his mind.
"Try it."
Since the preliminary work has been done, Gaode did what he said and started trying it immediately.
(End of this chapter)