Above the mage!

Chapter 16 Analytic Geometry and Cartesian Coordinate System

Gao De opened his eyes and rubbed his temple subconsciously.

The construction of the spell model is very troublesome.

His apprentice meditation technique has reached the fifth petal level. This level of mental strength is enough for him to complete the model construction of the trick, but it is a bit strenuous.

If one could cultivate to the perfection of sixteen petals, with this level of strong mental power, constructing the spell model of 0-ring spells would be much easier.

The difficulty in constructing a spell model is that, firstly, it requires precision, to the extent that a slight mistake can lead to a huge error; secondly, it requires the mage to have enough mental energy to expend and to try again and again.

With Gao De's current mental strength, he tried to construct a spell model for acid splashing. Every time he failed, he would feel dizzy and tired.

If it fails three times at most, the brain will start to hurt and the mental energy will be over-consumed. It will need to rest and wait for the mental energy to recover, and it will be impossible to construct the spell model anymore.

This is the disadvantage of not having strong enough mental power. If a first-level wizard is asked to construct a spell model for a 0-level spell, not to mention that his efficiency is dozens of times higher than that of Gaode, even if he fails, it is not a problem for him to fail dozens of times a day.

"Constructing a spell model is indeed not easy. No wonder it took my predecessor more than a year to master the two tricks, Restoration and Mage's Hand." Gao De muttered to himself.

Even mastering a 0th-level spell is so difficult, so you can imagine how much effort it takes to become a powerful wizard.

But he didn't complain.

It is said that a mage is a wizard.

Master Wizard, Master Wizard, how can you be a grandfather if you don’t be a grandson first?

Failure is the mother of success.

Gaode closed his eyes and reviewed the failed build just now, and quickly found the problem - when he was focusing on controlling the movement of the third star, the position of the second star was slightly offset.
Pulled around and moved 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 is slightly offset, the entire spell model will naturally collapse.

This is another difficulty in building a spell model:
There can't be even the slightest mistake, otherwise you have to start all over again, instead of just correcting where you made a mistake.
"This error tolerance is too low." Gao De muttered to himself, and subconsciously thought: "Can the construction process of the spell model be optimized?"

If other wizards knew what he was thinking at this moment, they would certainly laugh at him for being ignorant of the immensity of heaven and earth.

Not to mention that this method of constructing spell models that has been passed down for who knows how many years, how could there be room for optimization? Even if there is, how could a wizard apprentice think of it?

Gaode would not have such miscellaneous concerns.

In the world of mathematics, if a method doesn't work or is difficult, it is common to change your thinking.

Is it possible to determine the positions of all the stars first and then connect the star tracks?

This idea suddenly popped into Gaode's mind.

After this idea came to him, it was as if he had suddenly been enlightened. The more he thought about it, the more feasible it seemed to him. He even felt that this was the correct way to construct a spell model.

——In this way, even if any star deviates from its original position during the construction of the spell model, it will not cause the collapse of the entire spell model. Everything will start from scratch, and you only need to adjust the position of the star in time.

Compared with the traditional method of constructing spell models, this improves efficiency by more than just a little bit?

That's simply the difference between an abacus and a computer.

Gaode has always been very proactive and will execute ideas as soon as they come up with them.

The first problem to be solved 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 explain how to determine the position of the star without connecting the star tracks.

But for Amap, this is not a problem at all. The existing information is enough to use - isn't it just simple analytic geometry? Simply establish a Cartesian coordinate system, and then decompose the vector coordinates of each star, so that the position of each star can be determined, right?

First, you need an origin.

The origin is where all vectors originate.

Only when the origin is determined can we determine the length and distance, and then determine the vector coordinates of each node.

There are no other objects in the magic star sea except stars and spell models. However, the stars are constantly moving, so they are obviously not fixed reference objects and cannot be used as origins.

Although the spell model will not move, it is a model composed of multiple stars. 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 overlap of two spell model nodes or cross-interference of star tracks.

But this is easy to solve. Just regard the location of the first star as the origin.

With the origin as the center, establish a classic xyz coordinate system

Then use an ordered ternary array to determine the position of each node of the spell model.

A ternary array consists of three numbers that guide 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 we are going, with positive numbers moving to the right and negative numbers moving to the left.

The second number represents how far to go in a direction parallel to the y-axis after this.

The third number represents how far along the z-axis we are.

Similarly, the coordinates of each star can be deduced from the direction of the stars recorded in the spell formula.

Gao De stood up, took out a charcoal pencil from the shelf beside him, and started writing directly on the blank space of the spell formula.

The first star is the origin, and its coordinates are (0, 0, 0).

"One step forward, one and a third step right, one and a quarter step up"

Left and right is the x-axis, front and back is the y-axis, and up and down is the z-axis.

第二枚星子的坐标记为（4/3，1，1/4）。

"One half forward, two thirds to the right, and one half down"

The third star moves with the second star as the starting point, and cannot be directly compared with the origin for record, but it is not a big problem - it is just a simple vector addition operation.

Through calculation, we can get the coordinates of the third planet as (2, 3/2, -1/4).

Just continue to calculate in this way.

Soon, Gaode disassembled the acid splash spell model into an xyz coordinate axis and nine vector coordinates including the origin.

Then, Gao De looked at the nine ternary groups on the paper with burning eyes and began to try to memorize them.

Obviously, the nine-triple array is much simpler than the complicated description of the spell formula, not to mention that Gode is naturally very sensitive to numbers.

In just a few minutes, he memorized the nine coordinates.

"Try it."

Since the preliminary work had been done, Gaode got to work and started trying immediately.

(End of this chapter)