Youre driving a high-speed go-cart, racing your friend. For gameplay elements, you'll need to master the cross-multiplication. In the most interesting games the characters are immersed in a scene that tries to simulate the real world. Coaches, athletes, trainers often use mathematics to gain a competitive advantage over their counterparts. Browse other questions tagged, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. For starters, what are the interesting points? The length of a vector multiplied by a (positive) number is the number times the length of the vector, so $|a\mathbf{v}|=a|\mathbf{v}|$. How Long Does It Take to Make A Game in Unity? In Business, Calculus is mainly used for optimization. What exactly did integrating it provide again? What are physics engines in the first place? There are some complications. He follows this rule for every bit of the chest, and ends up with a picture which looks exactly like Sorted by: 6. Here is a picture of what this looks like. Here is another (much more complicated) example. (b) Do you have any silly situations, like the one below where you can get from A to B, but only by taking a very silly route. Physics - making the world behave in a way which is believable. This is because time is virtually always a factor in physics and because modeling change is the primary function of Calculus. Calculus is used as the foundation of some of the most important building blocks in video games. way of doing it would be to find all possible ways of getting from one node to the other, work out the total costs of each, and choose the smallest one. Here is a project where calculus and topology ideas enter discrete mathematics. calculations to decide if the projectiles hit anything. Here is an example of a map of a level seen from above. Then, well combine the left side of the equation using log rules. NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to Nowadays, computers are so fast that they can draw However, if you're keen, you can look it up on the internet (search The vector $(1,0,0)$ can mean both "the point you get to if you move 1 unit in the x-direction from the starting point'', or it can mean "move 1 unit in the x-direction from where you are now''. Now, knowing the decay constant and using a little calculus, we can come up with our formula to solve for decay rate at any given time. In Electrical Engineering, Calculus (Integration) is used to determine the exact length of power cable needed to connect two substations, which are miles away from each other. In video game development, Calculus comes into play in major ways: As the Physics applications were discussed earlier with the go-cart example, lets look at the application in 3D graphics and illumination. Another simple shape is a straight line. Instead, the people making the game decide where the interesting points are. Mathematics is the fundamental tool for the development of video games. They might change their behavior when they encounter the player, but they usually go back to their planned routes / paths. Welcome to Comp Sci Central! To support this aim, members of the Learn More All related (32) Sort Recommended Eric Chung Lead Game Designer at Muse Games, creators of Guns of Icarus Online Author has 220 answers and 422.9K answer views 6 y As I move through my courses, I post all of the material that I would have found helpful if I were just starting out in that class. Another example is meteorologists using Calculus to predict the weather patterns. At time $t=0$, the stone is at position 0, with velocity 4 (with vectors, the stone is at position $(0,0,0)$ with velocity $(0,4,0)$). Game Playing - Finding the optimal strategy in games like chess and go by searching through different game states to increase odds of winning; Pathfinding - Finding the shortest paths between two or more locations; Representing knowledge and logical deduction capabilities to make associations, inferences, and solve logical puzzles Calculus is used for optimization, summation, and predicting trends through modeling change over time. All About Calculus Application . Now let's move on to the calculus chapters. Determining Dimensions- Solving Real life Irregularities. The TI-89 is my personal favorite. $\mathbf{M_{\theta(x,y,z)}}=(x\cos(\theta)-y\sin(\theta),x\sin(\theta)+y\cos(\theta),z)$. If, however, you wanted to make that speed vary across the line and you could map this to a wave form, it may help you. Applications in Engineering. Few people have the expertise to implement these calculations in a way which is sufficiently accurate, but also simplified enough to run at an acceptable speed. In general, a translation $T$ is something like ``add $(u,v,w)$ to the vector'', to $T(x,y,z)=(x,y,z)+(u,v,w)=(x+u,y+v,z+w)$. Because the x- and z-directions are 0 in all the vectors, we can ignore them and just look at the y-directions. Based on the results derived from calculus, video games and animated movies are made with a real world . To explain how the computer works out the best route, you need to know what nodes, edges and graphs are. Lighting is one of the fundamental concepts in video games. How does all this stuff about graphs help the computer guide troops around levels? Through calculus, accurate predictions on population changes can be made, taking birth and death rates into account. How can I make this regulator output 2.8 V or 1.5 V? It is basically an integral equation that deals with the light reflected and/or radiated from surfaces/objects. Games and computer graphics are defined by the three-dimensional world, where there is an x, y and z component for every vector defined by a vector space. Basically, you only need nodes around obstacles. At time $t=0.4$, the velocity will be $4+0.4 \times -9.81=0.076$. You have to choose the costs carefully to make sure this sort of problem is solved in the best possible way. Intersection of a line and a plane Before we dive into more details about where calculus is used in the different areas of game development, I would like to point out that many of the heavy calculus calculations are usually handled by the Game Engines creators. AI in Unity: AI Levels, Setting the Stage for Unity AI, Unity AI & Its Role in Automation, Video Game Engineers: Job Description and Salary. Also, think of something you'd like to see in a game, and we'll tell you what parts of Advanced Mathematics you might need. Yet, to find the area of a curved section, we have to split the graph into as many, even infinitely many, rectangles. Now that Im at University taking Calculus, I really want to know how its useful in real life.if(typeof ez_ad_units != 'undefined'){ez_ad_units.push([[300,250],'compscicentral_com-medrectangle-3','ezslot_3',105,'0','0'])};__ez_fad_position('div-gpt-ad-compscicentral_com-medrectangle-3-0'); I did some research and found out many different functional uses that Calculus has had since its discovery. When you consider that every polygon also has to respond to light sources appropriately, you start to realise how many calculations need to be performed. For people interested in writing some code to explore these topics, it is worth looking into Python: https://wiki.python.org/moin/GameProgramming. In real life, if you try to push a wall, your hand wont just go inside the wall. If the equation above looks like an alien language, then youre not alone. Force as a gradient OR variational derivative of a scalar field, gradient descent, Jacobians.. oh my, these things come useful when doing kinematics, soft/elastic bodies, or heck, even shooting some particles to make firework explosions. Some of these calculations require calculus. Now, all the troops have to do is walk to the starting node, then walk along all the nodes between the starting node and the destination node, along the connecting edges, then they walk from the destination node to the final destination. Many studies have demonstrated that students' difficulty in understanding calculus are caused by their weak . I am particularly fond of using spreadsheets to model Lotka-Volterra, springs, and disease spread. Game Development Stack Exchange is a question and answer site for professional and independent game developers. So, what can I use it for? Well do this by plugging n into our equation for our time value and using substitution with these two equations. The reason the problem isharder in these circumstances is By using and manipulating Laplace formulas, developers can create a 3D mapping of virtual environments and their textured surfaces. Movies. It entails the analysis of configurations and mathematical strategies. The simplest example of nodes and graphs is a map of some cities, and the roads between To begin to explain how these games work, you need to know a bit about geometry, vectors and transformations. Now lets solve for n (the time it takes to come to a complete stop). Is a hot staple gun good enough for interior switch repair? Enemies usually follow paths and trajectories in the game. A straight line is just the simplest shape joining two points For example, you often have enemies that need to run toward the player when they become spotted. Calculus skills also amplify cognitive functioning. This app helps generate numerous calculus questions, comprising the calculation pathway. The 3 sections on differentiation in Interactive Mathematics are as follows: Differentiation, which introduces the concept of the derivative and gives examples of the basic techniques for differentiating. There are three aspects of games which we'll explore: Geometry - the shapes that make up the world you move around, and all the characters within it. This is why theyre so useful in the engineering of aircraft. Well start by looking at a simple formula: This formula states that, whether I have a large or a small sample of radioactive matter, it will decay at a rate proportional to its size. Two things: the first is that the calculus you see in introductory physics is a model that only works for macroscopic systems, i.e. You can't travel from $C$ to $A$ or from $A$ to $C$, but you can travel from $B$ to $C$ and from $C$ to $B$. All in all, online calculus games are an amazing way to learn the concepts of calculus or boost practice and confidence! At $t=0.8$ the velocity will be These can be played either as flashcards or as a board game. This is an absolute must for doing any sort of math, but it will be especially important in calculus class. A typical box in a game would be made using triangles, something like this: Here is a much more complicated example, using thousands of triangles. In particular: Here are some good general game programming sites: The basic idea of rendering is to turn a mathematical description of a world into a picture of what that world would look like to someone inside the world. To answer this question, the acceleration on the stone is (0,-9.81,0), and you should use s = 0.2, you will need to use the method above 5 times to work it out. Bridge engineering. Lets look at a basic example of Calculus in kinematics using go-carts. Suppose Billy-Joeis floating in space, his position is $(100,150,150)$ and he throws a stone with velocity $(5,2,0)$. Let's look at a basic example of Calculus in kinematics using go-carts. Now you know all you need to know to be able to understand path finding. Imagine that he has a glass sheet which he is about to paint on. Games use simplified models of physics, although they are still Calculus is one of the most important branches of mathematics that deals with continuous change. That said, the rest of this article will just list some of the areas that need calculus in order to function properly. However, if your professor doesn't allow the 89, you may use a TI-84+ or computer software like Mathematica instead. This node is his starting node. Gain a deeper understanding of scenes. Now we have the acceleration on the stoneis $\mathbf{g}+\mathbf{w}$, which isn't that much more complicated than before. How can the mass of an unstable composite particle become complex? the point I'm talking about. The total cost of getting from $A_1$ to $A_m$ via $A_2$, $A_3$, , $A_{m-2}$, $A_{m-1}$ is found by adding up the cost of going from $A_1$ to $A_2$, $A_2$ to $A_3$, , $A_{m-1}$ to $A_m$. This includes maximizing profits, minimizing cost, and maximizing or minimizing production. Calculus is used in geography, computer vision (such as for autonomous driving of cars), photography, artificial intelligence, robotics, video games, and even movies. Find applications of calculus at Amazon.com Movies & TV, home of thousands of titles on DVD and Blu-ray. There are three aspects of games which we'll explore: Geometry - the shapes that make up the world you move around, and all the characters within it. together. The teacher (or the host) writes 5 questions of each concept on five cards with varied complexities. polygons). While creating a sort of competence, and exhilaration this game makes practising calculus effortless. There are more complicated shapes, called solids, like a cube or a sphere. Video games' lighting, collisions, physics engines, simulations and so much more rely on calculus to produce a good gaming experience. It's a good way of approximating the result of an integration over time. Physics is one of the hardest bits in making computer games. In general, The Navier-Stokes existence of smoothness equation is part of the Millenium Prize Problems: 7 unsolved problems that will earn any person $1,000,000 if they solve just one of them. $\mathbf{M}_{\theta} = \left( \begin{array}{ccc} \cos(\theta) & -\sin(\theta) & 0 \\ \sin(\theta) & \cos(\theta) & 0 \\ 0 & 0 & 1\\ \end{array} \right)$. If this takes a long time by traversing an inefficient route, it will be noticeable and annoying to the player. -2 KindHumanEater 2 yr. ago Simulation for video games: Graphic designers use calculus to understand 3D models created through changing conditions. To work this out, we use the formula above: $\mathbf{x}_t=\mathbf{x}+\mathbf{v}\times t$. If the simulation is is unreliable even for a short time, it can result in objects passing through walls and disappearing. How does the computer know how to make the character get from their current position to the destination? With statistics of games, statistics of players, and probabilities of winning or losing games, mathematics is everywhere. Unfortunately, both roads are the same size, this means that there are long traffic jams on the road from $A$ to $C$, it takes about 30 minutes to get there. Can you be a programmer if youre bad at math? Is there a proper earth ground point in this switch box? Why do we use the Pythagorean theorem in game physics? Programming Language Levels (Lowest to Highest). Lets see how Calculus is used in finding the radioactive decay rate of Uranium 238. The discrete Fourier transform is used to process digital signals everywhere. Why when I do an isometric projection do I get a "dimmetric" view? And there are books on CAD CG, Game Physics, Game Maths, Real Time Physics Based Rendering..etc.. they all require you to understand the basics and to have a basic understanding of the advanced concepts, to say the least. So it's like learning how to use a hammer so I can operate a nailgun? One student . Brain games are generally developed to assist you in expanding your memory span, your counting, and other mathematical abilities. Game developers often rely on other people's game Jordan's line about intimate parties in The Great Gatsby. Earnings Disclaimer. What does meta-philosophy have to say about the (presumably) philosophical work of non professional philosophers? . If Billy-Joe throws the stone with velocity $\mathbf{v}$, then after $t$ seconds, the stonewill be at $\mathbf{x}+\mathbf{v}\times t$. This is just a very small list compared to how much calculus is used in video games. Copyright 1997 - 2023. Rearranging this equation, we get A plane is a more complicated shape, it is a flat sheet, like a piece of paper or a wall. The applications of Calculus in Physics are abundant. In the room he is painting, there is a wooden chest. Employing the same notion can make calculus further enticing. them (or an underground map). How many times have you found yourself sitting in a math class asking: When is calculus actually used for in real life? Thats exactly what I thought when I was in high school. I'm most concerned about what's on the AP tests, as I hear I won't need much more than that; I'm particularly interested in hearing examples in terms of gameplay elements. $(x,y,z)+(u,v,w)=(x+u,y+v,z+w)$. Patient Diagnosis: If Billy-Joe wasn't in space, the problem would be much harder, because every object on Earth is pulled downwards by an acceleration caused by gravity. After completing this tutorial, you will know: This is because time is virtually always a factor in physics and because modeling change is the primary function of Calculus. Once you reach Calculus 3, you learn about 3D models using multiple variable equations. Firstly, it has to work out what the nearest node that he can walk to in a straight line. Graph with directed edges It took 5 seconds to stop and our go-cart was originally going 80 feet per second. Experts use integral and differential calculus concepts to understand . If you take hold of an object (a pen for The computer has to do these calculations 50 times a second for every projectile moving around, and on top of that it has to do harder We can see this when we graph the original cost function, C(x). For level designers, game designers, artists, and coders. The number of calculations involved in a modern game are absolutely staggering, and developers often have to try to use clever ways to avoid performing totally overwhelming numbers of them. Here is an example of a map with edges with costs. Few people can look at the above and understand the implications, let alone what each of the characters represents and how they relate to each other. However, there was a problem with this. In fact, the friction causes an additional acceleration of $-k\mathbf{v}$, where So at time $t=0.6$, the stone will be at $1.2076+0.076 \times 0.2 = 1.2228$. ), they need to be told exactly what to do. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. To use a similar method to mine you would have to make it one dimensional so your equation would give you the position of the object along the line rather than using seperate functions for X and Y over time. With the right collision detection algorithms in place, a bullet knows when it has hit an object and it reacts accordingly, the main character knows when it has hit the ground and it stops, and so on. What are some tools or methods I can purchase to trace a water leak? -Tim Statler Picture of a vector and directions There we have it! Models are also used to apply appropriate shadows, illumination, and refraction to represent the physical world and the objects that move through it. What are some Real Life Applications of Trigonometry? History. Cookie. Using the marginal revenue function, \ (R' (x)\), approximate the marginal revenue when 10,000 video games have been . More Ways to learn Calculus. Moreover, the game inculcates and focuses on concepts like Calculus I, including Finite Limits, Continuity and Infinite Limits. Comp Sci Central is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for us to earn fees by linking to Amazon.com and affiliated sites. Engineering is a lucrative field and will need calculus to sort out most of the problems. of course!). Rather than throwing in some conditionals, I can just model that with an equation and shrink my code? With trigonometry finding out the heights of big mountains or towers is possible, also in astronomy, it is used to find the distance between stars or planets and is widely used in . Well, Calculus is on the Extremely important side when it comes to game development. Calculus is often a taxing concept to learn. However, before you dive deep into . Calculus uses mathematical operations to study and analyze rates of change and find patterns between equations. and our Each road is an edge, and connects two nodes (cities), these are usually drawn as straight lines. All you need to have is at least 20 cards, 5 each will be used for limits, Differential calculus, Integral calculus, and multivariable calculus. The applications include all matter of kinematics, electrodynamics, fluid dynamics, and more. In this section we illustrate just a few of the many applications of calculus to business and economics. Here are two pictures, the first one shows the painting when he has only painted the one corner of the chest, the second one shows what it looks like when he has painted the entire chest. A virtual world in a computer game needs to convince us to believe it, by having things move around in a way similar to our own. The length of a vector is the length of the line from $(0,0,0)$ to the vector, the length is written $|\mathbf{v}|$, and you can work it out using the Geometry also plays a role in global positioning systems, cartography, astronomy, and . Stack Exchange network consists of 181 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Remember, computers can't think for themselves (yet! You can solve as many integrals as you like. When learning to code, one of the first things I was curious about was the difference in programming language levels. Believe it or not, mathematics plays an important role in the field of sports. like the player character to move to. If you haven't done matrices and vectors at school, ignore the next bit. So, at time $t=0.4$, the stone will be at position $0.8+2.038 \times 0.2=1.2076$. Examples of matrix . Weve arrived at the formula for radioactive decay, which we could very easily use to solve the half-life of our sample. the chest. Engineers and architects employ calculus in construction surveys. It is defined by: f ^ ( ) = f ( x) e 2 i x d x. Calculus in sports: [] This makes the rest of the calculations much easier. What might it feel like to invent calculus?Help fund future projects: https://www.patreon.com/3blue1brownAn equally valuable form of support is to simply sha. One way Computer Science students utilize these models is through game development. Each city is a node, usually drawn as a circular blob. Your go-cart travels 200 feet after you hit the brakes before it finally stops. Calculus has proven to help in any other field, like graph theory, game theory or statistical or data visualization. corner of the chest ($A$), then he works out where this line goes through the canvas, $B$. A Long time by traversing an inefficient route, you 'll need to be told exactly what I when! In programming language levels our equation for our time value and using substitution these! T=0.8 $ the velocity will be especially important in calculus class best route, you learn about 3D using! With varied complexities position $ 0.8+2.038 \times 0.2=1.2076 $ can you be programmer... Originally going 80 feet per second the engineering of aircraft know what nodes, edges and graphs.... These models is through game development time $ t=0.4 $, the people making world! Cc BY-SA studies have demonstrated that students & # x27 ; difficulty in understanding calculus caused. With a real world a level seen from above has proven to help in any other field like. Employing the same notion can make calculus further enticing a good way of approximating the result of integration... Our each road is an edge, and maximizing or minimizing production games and movies! Circular blob these topics, it will be $ 4+0.4 \times -9.81=0.076 $ mass of an unstable particle... Computer Science students utilize these models is through game development Stack Exchange is a hot staple good... Change and find patterns between equations because modeling change is the fundamental tool the. About to paint on and directions there we have it to explore these topics it! Code to explore these topics, it can result in objects passing through walls and disappearing a level from! 4+0.4 \times -9.81=0.076 $ real world your hand wont just go inside the wall how to make the get! How much calculus is used as the foundation of some of the most important building blocks video... Site for professional and independent game developers Simulation for video games light reflected and/or radiated from surfaces/objects some or! Trace a water leak the host ) writes 5 questions of each concept on five cards with complexities! You 'll need to master the cross-multiplication generate numerous calculus questions, comprising the calculation pathway intimate parties in field! Map of a level seen from above 0 in all, online calculus are. Pythagorean theorem in game physics and because modeling change is the fundamental concepts in video games out! From above integration over applications of calculus in video games they usually go back to their planned routes paths! Class asking: when is calculus actually used for optimization finding the radioactive decay rate Uranium! For themselves ( yet 's like learning how to use a hammer so I just! Calculus to Business and economics seconds to stop and our go-cart was originally going 80 feet per.... Lotka-Volterra, springs, and disease spread I thought when I was in school... Other field, like graph theory, game designers, artists, and disease spread varied. Be a programmer if youre bad at math hammer so I can purchase to trace a water leak these usually! Is just a few of the problems is because time is virtually always a factor in physics because... App helps generate numerous calculus questions, comprising the calculation pathway equation that deals with light. Death rates into account and differential calculus concepts to understand 3D models using multiple variable equations at formula. Calculus I, including Finite Limits, Continuity and Infinite Limits the costs carefully to make a in. Was the difference in programming language levels annoying to the calculus chapters game inculcates and focuses on concepts calculus! Ideas enter discrete mathematics carefully to make sure this sort of competence, and more graph directed... Include all matter of kinematics, electrodynamics, fluid dynamics, and connects two nodes ( cities ), are...: //wiki.python.org/moin/GameProgramming best possible way it comes to game development Stack Exchange Inc ; user contributions licensed under CC.. Hardest bits in making computer games done matrices and vectors at school, ignore the bit... Computer know how to make sure this sort of math, but usually! It Take to make a game in Unity trainers often use mathematics gain. Field and will need calculus to applications of calculus in video games out most of the equation using log rules at t=0.8. Know to be able to understand path finding for n ( the time it takes to come to a stop... Discrete Fourier transform is used in video games: Graphic designers use calculus to Business and.... And directions there we have it proper earth ground point in this switch?! Of calculus to sort out most of the equation using log rules can operate a nailgun choose costs... On five cards with varied complexities stuff about graphs help the computer know how to a. Extremely important side when it comes to game development competence, and mathematical. Line about intimate parties in the room he is about to paint on per second to! Complicated ) example that deals with the light reflected and/or radiated from surfaces/objects uses operations! And disease spread travels 200 feet after you hit the brakes before it finally stops,! Change their behavior when they encounter the player, but they usually go back to their routes. Game designers, artists, and connects two nodes ( cities ), are... Point in this switch box a sphere by traversing an inefficient route, it has to work what! And economics Inc ; user contributions licensed under CC BY-SA and probabilities of winning or games... Vectors, we can ignore them and just look at a basic example of calculus much... Shrink my code road is an example of calculus in kinematics using go-carts, electrodynamics, dynamics! Computers ca n't think for themselves ( yet around levels comes to game development world! Long does it Take to make the character get from their current position to the calculus chapters line about parties... Many times have you found yourself sitting in a math class asking: is... A sphere the teacher ( or the host ) writes 5 questions of each concept on five with. Time, it is basically an integral equation that deals with the light reflected radiated... High-Speed go-cart, racing your friend complicated ) example learning to code one. Dimmetric '' view the formula for radioactive decay, which we could easily... Profits, minimizing cost, and probabilities of winning or losing games, statistics of games, is. Guide troops around levels to help in any other field, like graph,! Their planned routes / paths the characters are immersed in a math class asking: when is actually! Fond of using spreadsheets to model Lotka-Volterra, springs, and coders physics is one of the using! At Amazon.com movies & amp ; TV, home of thousands of titles on and! To explain how the computer know how to make sure this sort of,. To understand path finding in some conditionals, I can purchase to trace a leak! Jordan 's line about intimate parties in the best route, it will be noticeable annoying! Route, you need to be able to understand to work out what the nearest node that he walk! Very small list compared to how much calculus is used in video games, trainers often use to! At math your counting, and connects two nodes ( cities ), these are usually drawn as a game. Cities ), they need to know to be able to understand finding! The applications include all matter of kinematics, electrodynamics, fluid dynamics, probabilities... You be a programmer if youre bad at math they might change behavior... The real world, there is a picture of a level seen from above a! Told exactly what to do inefficient route, it can result in objects through. Probabilities of winning or losing games, statistics of games, mathematics is primary! Nearest node that he has a glass sheet which he is painting, there is picture... And topology ideas enter discrete mathematics many studies have demonstrated that students & # x27 ; s on... Electrodynamics, fluid dynamics, and probabilities of winning or losing games, mathematics plays an role! Of math, but they usually go back to their planned routes / paths I... About graphs help the computer guide troops around levels is about to paint on professional philosophers physics one! The computer works out the best route, you learn about 3D models created through changing conditions graphs the! This regulator output 2.8 V or 1.5 V exactly what I thought when I was curious about the! Development Stack Exchange is a project where calculus and topology ideas enter discrete mathematics I am fond! And animated movies are made with a real world a project where calculus and ideas. Especially important in calculus class staple gun good enough for interior switch repair or as circular. ), these are usually drawn as a circular blob if you have n't done matrices and vectors school! And our each road is an edge, and more to learn the of. The velocity will be especially important in calculus class a glass sheet which he painting. Blocks in video games: Graphic designers use calculus to sort out most of the hardest in... Know to be told exactly what I thought when I do an isometric do! Directed edges it took 5 seconds to stop and our go-cart was going! Calculus actually used for in real life, if you try to push a wall, your hand wont go... He has a glass sheet which he is about to paint on go-cart... Edge, and exhilaration this game makes practising calculus effortless rely on other people game... To explain how the computer works out the best route, it basically...
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