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<link rel="preload" as="image" href="https://hexlet.io/rails/active_storage/representations/proxy/eyJfcmFpbHMiOnsiZGF0YSI6MTIzNTMsInB1ciI6ImJsb2JfaWQifX0=--f1948fb0c5a45a6d76671a1a32b8cf6f0b53ee57/eyJfcmFpbHMiOnsiZGF0YSI6eyJmb3JtYXQiOiJ3ZWJwIiwicmVzaXplX3RvX2xpbWl0IjpbNDAwLDQwMF0sInNhdmVyIjp7InF1YWxpdHkiOjg1fX0sInB1ciI6InZhcmlhdGlvbiJ9fQ==--5b6f46dacd1af664f27558553a58076185091823/Software%20code%20testing-cuate.png"/><link rel="preload" as="image" href="/vite/assets/development-BVihs_d5.png"/><div id="app" data-page="{"component":"web/courses/lessons/theory_unit","props":{"errors":{},"locale":"en","language":"en","httpsHost":"https://hexlet.io","host":"hexlet.io","colorScheme":"light","auth":{"user":{"id":null,"last_viewed_notification_id":null,"email":null,"state":null,"first_name":"","last_name":"","current_program":null,"current_team":null,"full_name":"","guest":true,"can_use_paid_features":false,"is_hexlet_employee":false,"sanitized_phone_number":"","can_subscribe":true,"can_renew_education":false}},"cloudflareTurnstileSiteKey":"0x4AAAAAAA15KmeFXzd2H0Xo","vkIdClientId":"51586979","yandexIdClientId":null,"formAuthToken":"fpdeaBWYr1CvTksNgU4eRfqXK9zeNmFBEUWNYWO6xGMtUTNeNPOUsMhEtOUz0CmE9j2lhxIoe02zwEdyLmYbuA","topics":[],"lesson":{"exercise":{"id":2073,"slug":"js_data_abstraction_abstractions_exercise","name":null,"state":"active","kind":"exercise","language":"javascript","locale":"en","has_web_view":false,"has_test_view":false,"reviewable":true,"readme":"The segment is another graphic primitive. You can express it in code via a pair of points, the start of the segment, and the end. A regular segment has no direction, so you are free to choose which point is considered the beginning and which is the end.\n\nIn this task, it is assumed that you already understand the abstraction creation principle and can build your own implementation: you can do this in different ways and there is no one-and-only correct.\n\n## segments.js\n\nImplement and export the following functions:\n\n* The `makeSegment()` takes two points and returns a segment\n* The `getMidpoint()` takes a segment and returns its midpoint\n* The `getStartPoint()` takes a segment and returns its start point\n* The `getEndPoint()` takes a segment and returns its end point\n\n### Example\n\n```javascript\nconst startPoint = makeDecartPoint(3, 2);\nconst endPoint = makeDecartPoint(0, 0);\nsegment = makeSegment(startPoint, endPoint);\n\ngetMidpoint(segment); // (1.5, 1)\ngetStartPoint(segment); // (3, 2)\ngetEndPoint(segment); // (0, 0)\n```\n","prepared_readme":"The segment is another graphic primitive. You can express it in code via a pair of points, the start of the segment, and the end. A regular segment has no direction, so you are free to choose which point is considered the beginning and which is the end.\n\nIn this task, it is assumed that you already understand the abstraction creation principle and can build your own implementation: you can do this in different ways and there is no one-and-only correct.\n\n## segments.js\n\nImplement and export the following functions:\n\n* The `makeSegment()` takes two points and returns a segment\n* The `getMidpoint()` takes a segment and returns its midpoint\n* The `getStartPoint()` takes a segment and returns its start point\n* The `getEndPoint()` takes a segment and returns its end point\n\n### Example\n\n```javascript\nconst startPoint = makeDecartPoint(3, 2);\nconst endPoint = makeDecartPoint(0, 0);\nsegment = makeSegment(startPoint, endPoint);\n\ngetMidpoint(segment); // (1.5, 1)\ngetStartPoint(segment); // (3, 2)\ngetEndPoint(segment); // (0, 0)\n```\n","has_solution":true,"entity_name":"Creating an abstraction"},"units":[{"id":6904,"name":"theory","url":"/courses/js-data-abstraction/lessons/abstractions/theory_unit"},{"id":6905,"name":"quiz","url":"/courses/js-data-abstraction/lessons/abstractions/quiz_unit"},{"id":6912,"name":"exercise","url":"/courses/js-data-abstraction/lessons/abstractions/exercise_unit"}],"links":[],"ordered_units":[{"id":6904,"name":"theory","url":"/courses/js-data-abstraction/lessons/abstractions/theory_unit"},{"id":6905,"name":"quiz","url":"/courses/js-data-abstraction/lessons/abstractions/quiz_unit"},{"id":6912,"name":"exercise","url":"/courses/js-data-abstraction/lessons/abstractions/exercise_unit"}],"id":3041,"slug":"abstractions","state":"approved","name":"Creating an abstraction","course_order":200,"goal":"Discover the rationale for hiding the data (structure) and examine the examples","self_study":null,"theory_video_provider":null,"theory_video_uid":null,"theory":"The Cartesian coordinate system is not the only way to define graphs. Another method you can use is the polar coordinate system.\n\n> ...the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. (c) Wikipedia\n\n\n\nImagine the following situation. You are developing a graphics editor (like Photoshop), and your library for working with graphical primitives is based on the Cartesian coordinate system. At some point, you realize that switching to a polar system will make your system easier and faster. What price to pay for such a change? You have to rewrite almost all the code.\n\n```javascript\nconst point = { x: 2, y: 3 };\nconst symmetricalPoint = { x: -point.x, y: point.y };\n```\n\nThis is because your library does not hide its internal structure. Any code that uses points or segments knows how they are programmed. This applies both to the code that creates new primitives and to the code that extracts the values from them. We can change the situation and hide the implementation using functions:\n\n```javascript\nconst point = makePoint(3, 4);\nconst symmetricalPoint = makePoint(-getX(point), getY(point));\n```\n\nIn the example we can see three functions: `makePoint()`, `getX()` and `getY()`. The `makePoint()` function is called a constructor because it creates a new primitive, while `getX()` and `getY()` — are called selectors or getters. Such a small change causes far-reaching consequences. The main thing is that the client (the one that uses the library) of our code does not work with the structure directly.\n\n```javascript\n// i.e., this isn't the right way\nconst point = [1, 4]; // we know that this is an array\nconsole.log(point[1]); // direct access to the array\n\n// So\nconst point = makePoint(3, 4); // we don't know how the point is set up\nconsole.log(getY(point)); // we only access its parts through selectors\n```\n\nLooking at the code, you can't even tell what the point is from the inside, or what language constructs are represented (you can use the debug print for this). This is how we do data abstraction. The essence of this abstraction is that we hide the inner implementation. You could say that creating abstraction with data results in hiding that data from external code.\n\nAnd here's one way to implement an abstraction when working with a point:\n\n```javascript\nconst makePoint = (x, y) => ({ x, y });\n\nconst getX = (point) => point.x;\nconst getY = (point) => point.y;\n```\n\nNow we can change the implementation without rewriting the whole code (however, we may still need to rewrite some parts). Although we use the `makePoint()`, function, which creates a point based on the Cartesian coordinate system (taking `x` and `y` coordinates as input), internally it may well be represented in the polar coordinate system. In other words, there is a translation from one system to another:\n\n```javascript\nconst makePoint = (x, y) => {\n // conversion\n return {\n angle: Math.atan2(y, x),\n radius: Math.sqrt(x ** 2 + y ** 2)\n };\n};\n```\n\nOnce you start working using data abstraction, there's no way back. Always stick to the features you created yourself or those provided by the library you are using."},"lessonMember":null,"courseMember":null,"course":{"start_lesson":{"exercise":null,"units":[{"id":6897,"name":"theory","url":"/courses/js-data-abstraction/lessons/intro/theory_unit"}],"links":[],"ordered_units":[{"id":6897,"name":"theory","url":"/courses/js-data-abstraction/lessons/intro/theory_unit"}],"id":3037,"slug":"intro","state":"approved","name":"About course","course_order":10,"goal":"Learn about the course, its structure, objectives, and goals","self_study":null,"theory_video_provider":null,"theory_video_uid":null,"theory":"Abstraction is the primary way to handle complexity in programming. It allows you to escape the implementation details and focus on the essentials.\n\nA good abstraction example is the array sort function. It doesn't matter how it's implemented; what matters is that it leads to the result we're interested in.\n\nAnother example is higher-order functions, such as `map`, `filter`, and `reduce`, which allow you to process collections without thinking about what goes on under the hood. Collections even don't have to be flat; you can build such functions for any complex structures, such as trees. And due to this abstraction, we can focus on the processing itself rather than the data traversal technicalities.\n\nOn the other hand, the data itself often has a complex structure. Representing a user in an unconventional system may require defining dozens or hundreds of different parameters and the associated data. In situations like this, it's a good idea to hide this structure behind a set of functions, which cover the internal complexity and simplify code support. This is called data-driven abstraction.\n\nIn this course, we'll learn some basic principles of program design, and how to model and represent objects from the real (and imaginary) world via a program. We'll design a library for working with graphical primitives, such as points, segments, and shapes. This library is lucid enough for everyone to understand (even visually), and it's pretty handy to express with code.\n\nMain course subjects:\n\n* Subject area \n* Ontology\n* Level design (abstraction barriers)\n* Invariants\n"},"id":299,"slug":"js-data-abstraction","challenges_count":1,"name":"JS: Building abstractions with data","allow_indexing":true,"state":"approved","course_state":"finished","pricing_type":"paid","description":"Programming is not just about computing: any nontrivial program models within itself the domain for which it was designed. For example, Hexlet works with the Course, Project, Student and other entities; they can interact and are somewhat related. This is what is called an abstraction. 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class="mantine-focus-auto mantine-active m_77c9d27d mantine-Button-root m_87cf2631 mantine-UnstyledButton-root" data-variant="gradient" data-size="xs" href="/u/new"><span class="m_80f1301b mantine-Button-inner"><span class="m_811560b9 mantine-Button-label">Sign up</span></span></a></div></div></div></div></div><div class="paywalled m_d08caa0 mantine-Typography-root"><p>The Cartesian coordinate system is not the only way to define graphs. Another method you can use is the polar coordinate system.</p>
<blockquote>
<p>...the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the pole, and the ray from the pole in the reference direction is the polar axis. (c) Wikipedia</p>
</blockquote>
<p><img style="--image-object-fit:contain;width:auto" class="m_9e117634 mantine-Image-root" src="/rails/active_storage/blobs/proxy/eyJfcmFpbHMiOnsiZGF0YSI6NzQwNSwicHVyIjoiYmxvYl9pZCJ9fQ==--779b846059ef530fe95ed744826f55d79b13570e/polar-coordinate-system.png" alt="Polar Coordinate System" loading="lazy"/></p>
<p>Imagine the following situation. You are developing a graphics editor (like Photoshop), and your library for working with graphical primitives is based on the Cartesian coordinate system. At some point, you realize that switching to a polar system will make your system easier and faster. What price to pay for such a change? You have to rewrite almost all the code.</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">const point = { x: 2, y: 3 };
const symmetricalPoint = { x: -point.x, y: point.y };</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>This is because your library does not hide its internal structure. Any code that uses points or segments knows how they are programmed. This applies both to the code that creates new primitives and to the code that extracts the values from them. We can change the situation and hide the implementation using functions:</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">const point = makePoint(3, 4);
const symmetricalPoint = makePoint(-getX(point), getY(point));</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>In the example we can see three functions: <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">makePoint()</code>, <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">getX()</code> and <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">getY()</code>. The <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">makePoint()</code> function is called a constructor because it creates a new primitive, while <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">getX()</code> and <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">getY()</code> — are called selectors or getters. Such a small change causes far-reaching consequences. The main thing is that the client (the one that uses the library) of our code does not work with the structure directly.</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">// i.e., this isn't the right way
const point = [1, 4]; // we know that this is an array
console.log(point[1]); // direct access to the array
// So
const point = makePoint(3, 4); // we don't know how the point is set up
console.log(getY(point)); // we only access its parts through selectors</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>Looking at the code, you can't even tell what the point is from the inside, or what language constructs are represented (you can use the debug print for this). This is how we do data abstraction. The essence of this abstraction is that we hide the inner implementation. You could say that creating abstraction with data results in hiding that data from external code.</p>
<p>And here's one way to implement an abstraction when working with a point:</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">const makePoint = (x, y) => ({ x, y });
const getX = (point) => point.x;
const getY = (point) => point.y;</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
<p>Now we can change the implementation without rewriting the whole code (however, we may still need to rewrite some parts). Although we use the <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">makePoint()</code>, function, which creates a point based on the Cartesian coordinate system (taking <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">x</code> and <code style="margin-bottom:var(--mantine-spacing-lg)" class="m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight m_e597c321 mantine-CodeHighlight-codeHighlight m_dfe9c588 mantine-InlineCodeHighlight-inlineCodeHighlight">y</code> coordinates as input), internally it may well be represented in the polar coordinate system. In other words, there is a translation from one system to another:</p>
<div style="margin-bottom:var(--mantine-spacing-lg)" class="m_e597c321 mantine-CodeHighlight-codeHighlight" dir="ltr"><div class="m_be7e9c9c mantine-CodeHighlight-controls"><button style="--ai-bg:transparent;--ai-hover:transparent;--ai-color:inherit;--ai-bd:none" class="mantine-focus-auto mantine-active m_d498bab7 mantine-CodeHighlight-control m_8d3f4000 mantine-ActionIcon-root m_87cf2631 mantine-UnstyledButton-root" data-variant="none" type="button" aria-label="Copy code"><span class="m_8d3afb97 mantine-ActionIcon-icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24" stroke-width="2" stroke="currentColor" fill="none" stroke-linecap="round" stroke-linejoin="round"><path stroke="none" d="M0 0h24v24H0z" fill="none"></path><path d="M8 8m0 2a2 2 0 0 1 2 -2h8a2 2 0 0 1 2 2v8a2 2 0 0 1 -2 2h-8a2 2 0 0 1 -2 -2z"></path><path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2"></path></svg></span></button></div><div style="--scrollarea-scrollbar-size:calc(0.25rem * var(--mantine-scale));--sa-corner-width:0px;--sa-corner-height:0px" class="m_f744fd40 mantine-CodeHighlight-scrollarea m_d57069b5 mantine-ScrollArea-root" dir="ltr"><div style="overflow-x:hidden;overflow-y:hidden;overscroll-behavior-inline:none" class="m_c0783ff9 mantine-ScrollArea-viewport" data-scrollbars="xy"><div class="m_b1336c6 mantine-ScrollArea-content"><pre class="m_2c47c4fd mantine-CodeHighlight-pre" style="padding:0"><code class="m_5caae6d3 mantine-CodeHighlight-code">const makePoint = (x, y) => {
// conversion
return {
angle: Math.atan2(y, x),
radius: Math.sqrt(x ** 2 + y ** 2)
};
};</code></pre></div></div></div><button class="mantine-focus-auto m_c9378bc2 mantine-CodeHighlight-showCodeButton m_87cf2631 mantine-UnstyledButton-root" data-hidden="true" type="button">Expand code</button></div>
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